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Manual for Corporate Recruitment

Contents I.

Preface1.

Why this book?2. What does it contain?

II.

Selection Procedures of MNC’s III. Importance of Aptitude in Recruitment ProcessIV.

Patterns of various MNC Aptitude PapersV. Quantitative Aptitude

1. Percentagesa. Percentage changeb.

Percentage differencec.

Multiple percentage changes2. Profit & Loss

a.

Discountsb. % Profit

c.

% Loss3. Averages and Ages4.

Ratios and Proportionsa.

Partnershipsb. Mixtures & Allegations

5.

Test on chapters 1 to 46. Solutions for the test7.

Time and Distancea. Trainsb.

Boats & Streamsc. Races

8.

Time and Worka.

Work & Wagesb. Pipes & Cisterns

9.

Mensurationa. Areasb.

Volumesc. Basics of Geometry

10.

Test on chapters 6 to 911.

Solutions for the test12. Interest

a.

Simple Interestb.

Compound Interest13.

Clocks14. Calendars15.

Probabilitya. Playing Cardsb.

Dicesc.

Coloured Balls16. Test on chapters 10 to 13

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17.

Solutions for the test18. Comprehensive Test on Quantitative Aptitude19.

Solutions for the testVI. Logical Aptitude

1. Blood Relations2.

Directions

3.

Coding & Decoding4.

Seriesa. Letter Seriesb.

Number Seriesc.

Odd Man Out Series5.

Test on chapters 1 to 46. Solutions for the test7. Analytical Reasoning

a.

Arrangementsb. Comparisonsc.

Selections

d.

Family Based Problemse.

Intersection Type8. Critical Reasoning9. Test on chapters 7 to 810.

Solutions for the test11. Cubes

a.

Counting the cubesb. Painting with equal cuttingsc.

Painting with inequal cuttingsd. Miscellaneous

12.

Logical Deductions

13.

Test on chapters 11 to 1214. Solutions for the test15.

Data Interpretation16. Data Sufficiency17.

Venn Diagrams18. Test on chapters 15 to 1719.

Solutions for the test20. Comprehensive Test on Logical Aptitude21.

Solutions for the testVII. Verbal Aptitude

1. Reading Comprehension

2.

Vocabulary Test3. Sentence Completion

a.

Prepositionsb. Adverbsc.

Conjunctionsd. Verb Forms

4. Sentence Correction

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2.

Every logic is strengthened by solved examples, exercises, tests and solutionsto ensure that the reader gets all the required inputs at the required level ofcomplexity.

3. The CD contains Diagnostic Tests, Vocabulary Building List and PracticePapers with real-time difficulty to provide the user with extra benefits.

In all, there is a guarantee that this book will be a very helpful and effective tool forthe job-seekers by providing them with all the inputs and guiding them towardstheir placement in the companies.

Recruitment Patterns of various MNC’s

Various MNC‟s have different patterns for recruitment but the skeletal structure ofthe patterns is commonly aid to be as follows:

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Round I: Written test on aptitude

Round II: Written test on technical knowledge

Round III: Group Discussion

Round IV: Technical Interview

Round V: HR Interview

So unless you prove yourself in aptitude test you will never get a chance to proveany other expertise you possess in other aspects.

This is the reason why aptitude is considered the most important factor by theaspirants of various MNC recruitments.

Importance of aptitude in recruitment process

Aptitude test is the first round of recruitment process for any company in any sectorlike Banking, Software, Insurance, Pharmaceutics etc. All the graduates with 60%or above are eligible for the recruitment process and everyone is tested on the same

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grounds of aptitude. This gives us the clear idea that the companies are givingaptitude more importance than the academic percentages.

What is aptitude?

Aptitude literally means a natural talent. It is something that comes with us by our

birth. But it is to be explored and developed within by us and that can be achievedby understanding and practicing the concepts of aptitude.

The candidates with good aptitude skills are considered better than others becausethey are fast at their mind and good at problem solving skills. Thus aptitude hasbecome the most important soft skill these days.

Why aptitude?

Even if the candidate is good at academics and communication skills, he will not geta chance to prove them unless he passes through the initial round of aptitudetesting. So we can conclude that without appropriate levels of aptitude an aspirantcan never achieve success in the recruitment process of any corporate sectorcompany.

This book helps all the aspirants in clearly understanding the concepts of aptitudethat are required for the recruitment processes of various companies. For furtherpractice on these concepts covered in the book you can refer to the books onaptitude by Pearson Education like Test of reasoning and general intelligence byShowick Thorpe and Quantitative Techniques by Khattar.

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QUANTITATIVE

APTITUDE

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Percentages

Understanding Percentages:

The word percent can be understood as follows:

Per cent => for every 100.

So, when percentage is calculated for any value, it means that that you calculate thevalue for every 100 of the reference value.

Why Percentage?

Percentage is a concept evolved so that there can be a uniform platform forcomparison of various things. (Since each value is taken to a common platform of100.)

Eg: To compare three different students depending on the marks they scored wecannot directly compare their marks until we know the maximum marks for whichthey took the test. But by calculating percentages they can directly be comparedwith one another.

Before going deeper into the concept of percentage, let u have a look at some basicsand tips for faster calculations:

Calculation of Percentage:

Percentage = (Value / Total value) X 100

Eg: 50 is what % of 200?

Soln: Percentage = (50/200) X 100 = 25%.

Calculation of Value:

Value = (Percentage/100) X total value

Eg: What is 20% of 200?

Soln: Value = (20/100) X 200

Note: Percentage is denoted by “%”, which means “/100”.

Eg: What is the decimal notation for 35%?

Soln: 35% = 35/100 = 0.35.

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For faster calculations we can convert the percentages or decimal equivalents intotheir respective fraction notations.

Percentages – Fractions Conversions:

The following is a table showing the conversions of percentages and decimals intofractions:

Percentage Decimal Fraction

10% 0.1 1/10

12.5% 0.125 1/8

16.66% 0.1666 1/620% 0.2 1/5

25% 0.25 1/4

30% 0.3 3/10

33.33% 0.3333 1/3

40% 0.4 2/5

50% 0.5 1/2

60% 0.6 3/5

62.5% 0.625 5/8

66.66% 0.6666 2/3

70% 0.7 7/10

75% 0.75 3/4

80% 0.8 4/5

83.33% 0.8333 5/6

90% 0.9 9/10

100% 1.0 1

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Similarly we can go for converting decimals more than 1 from the knowledge of theabove cited conversions as follows:

We know that 12.5% = 0.125 = 1/8

Then, 1.125 = [8(1)+1]/8 = 9/8 (i.e., the denominator will add to numerator once,denominator remaining the same.

Also, 2.125 = [8(2)+1]/8 = 17/8 (here the denominator is added to numerator twice)

3.125 = [8(3)+1]/8 = 25/8 and so on.

Thus we can derive the fractions for decimals more than 1 by using those les than1.

We will see how use of fractions will reduce the time for calculations:

Eg: What is 62.5% of 320?

Soln: Value = (5/8) X 320 (since 62.5% = 5/8)

= 200.

Percentage Change:

A change can be of two types – an increase or a decrease.

When a value is changed from initial value to a final value,

% change = (Difference between initial and final value/initial value) X 100

Eg: If 20 changes to 40, what is the % increase?

Soln: % increase = (40-20)/20 X 100 = 100%.

Note:

1. If a value is doubled the percentage increase is 100.

2.

If a value is tripled, the percentage change is 200 and so on.

Percentage Difference:

% Difference = (Difference between values/value compared with) X 100.

Eg: By what percent is 40 more than 30?

Soln: % difference = (40-30)/30 X 100 = 33.33%

(Here 40 is compared with 30. So 30 is taken as denominator)

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Eg: By what % is 60 more than 30?

Soln: % difference = (60-30)/30 X 100 = 100%.

(Here is 60 is compared with 30.)

Hint: To calculate percentage difference the value that occurs after the word “than”in the question can directly be used as the denominator in the formula.

Important Points to Note:

1. When any value increases by

a. 10%, it becomes 1.1 times of itself. (since 100+10 = 110% = 1.1)

b. 20%, it becomes 1.2 times of itself.

c.

36%, it becomes 1.36 times of itself.

d.

4%, it becomes 1.04 times of itself.

Thus we can see the effects on the values due to various percentage increases.

2.

When any value decreases by

a. 10%, it becomes 0.9 times of itself. (Since 100-10 = 90% = 0.9)

b. 20%, it becomes 0.8 times of itself

c. 36%, it becomes 0.64 times of itself

d. 4%, it becomes 0.96 times of itself.

Thus we can see the effects on a value due to various percentage decreases.

Note:

1. When a value is multiplied by a decimal more than 1 it will be increased and

when multiplied by less than 1 it will be decreased.

2. The percentage increase or decrease depends on the decimal multiplied.

Eg: 0.7 => 30% decrease, 0.67 => 33% decrease, 0. 956 => 4.4% decrease and soon.

Eg: When the actual value is x, find the value when it is 30% decreased.

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Soln: 30% decrease => 0.7 x.

Eg: A value after an increase of 20% became 600. What is the value?

Soln: 1.2x = 600 (since 20% increase)

x = 500.

Eg: If 600 is decrease by 20%, what is the new value?

Soln: new value = 0.8 X 600 = 480. (Since 20% decrease)

Thus depending on the decimal we can decide the % change and vice versa.

Eg: When a value is increased by 20%, by what percent should it be reduced to getthe actual value?

Soln: (It is equivalent to 1.2 reduced to 1 and we can use % decrease formula)

% decrease = (1.2 – 1)/1.2 X 100 = 16.66%.

3. When a value is subjected multiple changes, the overall effect of all thechanges can be obtained by multiplying all the individual factors of thechanges.

Eg: The population of a town increased by 10%, 20% and then decreased by 30%. The new population is what % of the original?

Soln: The overall effect = 1.1 X 1.2 X 0.7 (Since 10%, 20% increase and 30%decrease)

= 0.924 = 92.4%.

Eg: Two successive discounts of 10% and 20% are equal to a single discount of ___

Soln: Discount is same as decrease of price.

So, decrease = 0.9 X 0.8 = 0.72 => 28% decrease (Since only 72% isremaining).

Exercise:

1. If 20% of 40% of a = 25% of a% of b, then what is b?

a. 8/5 b. 16/25 c. 8/25 d. None

2. By what % is 200 more than 50?

a. 100 b. 200 c. 300 d. None

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3. A value changes from 30 to 80. What is the percentage change?

a. 125 b. 166.66 c. 156 d. None

4. The population of a city is increased by 30% and thus became 78000. What is theoriginal population?

a. 76000 b. 64200 c. 60000 d. None

5. In a theatre, the number of seats is increased by 20% and the price per ticket isincreased by 10% but the public response decreased by 30%. What is the net effecton the economy of the theatre?

a.10% rise b. 7% fall c. 7% rise d. None

6. A saves 20% of his income. His income is increased by 20% and so he increasedhis expenditure by 30%. What is the percentage change in his savings?

a. 20% fall b. 4% fall c. 20% rise d. 4% rise

7. The price of petrol is increased by 25%. By what percent the consumption bereduced to make the expenditure remain the same?

a. 25% b. 33.33% c. 20% d. None

8. The side of a square is increased by 20%. The percentage change in its area is ___

a. 20% b. 44% c. 36% d. None

9. If the length of a rectangle is increased by 33.33%, by what percentage should the

breadth be reduced to make the area same?

a. 20% b. 33.33% c. 25% d. None

10. In an election between two candidates, A and B, A secured 56% of the votes andwon by 48000 votes. Find the total number of votes polled if 20% of the votes weredeclared invalid.

a. 500000 b. 400000 c. 600000 d. None

11. A reduction of 10% in price of sugar enables a housewife to buy 5 kg more for

Rs. 300/-. Find the reduced price per kg of sugar.

a. 5/- b. 4.5/- c. 6/- d. None

12. From a 20lt solution of alt and water with 20% salt, 2lt of water is evaporated.Find the new % concentration of salt.

a. 20% b. 23% c. 25% d. None

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13. In a list of weights of candidates appearing for police selections, the weight of Ais marked as 58 kg instead of 46.4 kg. Find the percentage of correction required.

a. 30 b. 20 c. 24 d. None

14. A person spends 20% of his income on rent, 20% of the rest on food, 10% of theremaining on clothes and 10% on groceries. If he is left with Rs. 9520/- find hisincome.

a. 10000/- b. 15000/- c. 20000/- d. None

15. A shopkeeper offers three successive discounts of 10%, 20% and 30% to acustomer. If the actual price of the item is Rs. 10000, find the price the custome hasto pay to the shopkeeper.

a. 5040/- b. 4000/- c. 6000/- d. None

16. If 10lt solution of water and alcohol containing 10% alcohol is to be made 20%

alcohol solution, find the volume of alcohol to be added.

a. 1 lt b. 1.25 lt c. 1.5 lt d. 2 lt

17. A is twice B and B is 200% more than C. By what percent is A more than C?

a. 400 b. 600 c. 500 d. 200

18. In an examination, a student secures 40% and fails by 10 marks. If he scored50%, he would pass by 15 marks. Find the minimum marks required to pass theexam.

a. 250 b. 100 c. 110 d. 125

19. If A is 20% taller than B, by what percent is B shorter than A?

a. 20% b. 25% c. 16.66% d. None

20. The population of a town increases at a rate of 10% for every year. If the presentpopulation is 12100, find the population two years ago.

a. 11000 b. 9800 c. 10000 d. 10120

21. A solution of salt and water contains 15% salt. If 30 lt water is evaporated fromthe solution the concentration becomes 20% salt. Find the original volume of theliquid before water evaporated.

a. 100 lt b. 120 lt c. 200 lt d. None

22. If 240 lt of oil is poured into a tank, it is still 20% empty. How much more oil isto be poured to fill the tank?

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a. 300 lt b. 60 lt c. 120 lt d. None

23. A and B were hired for the same salary. A got two 40% hikes whereas B got a90% hike. What is the percentage difference in the hikes thay got?

a. 16% b. 6% c. 10% d. 8%

24. The population of a town doubled every 5 years from 1960 to 1975. What is thepercentage increase in population in this period?

a. 800 b. 400 c. 700 d. 600

25. In a test of 80 questions, Jyothsna answered 75% of the first 60 questionscorrectly. What % of the remaining questions she has to answer correctly so thatshe can secure an overall percentage of 80 in the test?

a. 80% b. 90% c. 85% D. 95%

Solutions:

1. 1/5 X 2/5 X a = ¼ X a X b => b = 8/25

2.

% difference = (200-50)/50 X 100 = 300 %

3.

% increase = (80-30)/30 X 100 = 166.66 %

4.

1.3 x = 78000 => x = 60000.

5.

Net effect = 1.2 X 1.1 X 0.7

= 0.924 => 7.6% decrease.

6. Let I be the income.

Expenditure = 0.8I Savings = 0.2I => 20%

New income = 1.2I (since 20% rise)

New expenditure = (0.8I) X 1.3 (Since 30% rise)

= 1.04I

So, new savings = 1.2I – 1.04I = 0.16I => 16%

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(So income decreased form 20% to 16%)

% decrease = (20-16)/20 X 100 = 20%.

7. It is equivalent to 1.25 decreased to 1.

% decrease = (1.25-1)/1.25 X 100 = 20%

8. % change in area = 1.2 X 1.2 (since area = side X side)

= 1.44 => 44%.

9. It is equivalent to 1.25 decreased to 1. So 20% decrease.

10.

Valid Votes:

A got 56% => B got 44%

Difference = 12% = 48000So, 100% = 400000. These are valid votes.

But valid votes are only 80% of total votes.

So, 80% of total votes = 400000 => total votes = 500000

11. Total money = Rs. 300.

Saving of the lady = 10% of 300 = 30/-

With 30/- she bought 5 kg sugar => each kg costs Rs. 6/-

12.

In 20lt, salt = 20% => 4 lt.

New volume = 18 lt (2 lt evaporated)

So, new % = 4/18 X 100 = 22.22%

13.

% correction = (58-46.4)/58 X 100 = 20%

14. Three successive decreases of 20%, 20% and 10% => 0.8 X 0.8 X 0.9 =0.576

Again 10% decrease => 0.576 – 0.1 = 0.476.

So, 0.476 x = 9520 => x = 20000.

15.

Total discount = 0.9 X 0.8 X 0.7 = 0.504 of actual price.

So, price = 0.504 X 10000 = 5040.

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16.

In 10 lt, alcohol is 10% = 1 lt.

Let x lt alcohol is added.

So, (1+x)/(10+x) = 20% = 1/5 => x = 1.25 lt.

17. A = 2B and B = 3C (ince 200% more)

A = 6C => 500 % more.

18. 50% of max marks – 40% of max marks = 25

max marks = 250

Pass marks = 40% of max + 10 => 100 + 10 = 110.

19.

A = 1.2 B => B = A/1.2 => 0.8333A => 16.66%.

(OR) Decrease from 1.2 to 1 => 16.66%.20.

1.1 X 1.1 X x = 12100 => x = 10000.

21. Salt = 15% of x = 0.15x (x = volume of solution)

Now, 0.15x/(x-30) = 20% = 1/5 (since 30 lt evaporated)

x = 120 lt

22. 20% empty => 80 % full = 240 lt => 20% = 60 lt

23.

A => 1.4 X 1.4 = 1.96

B => 1.9 => 6% difference.

24. From 1960 to 1975, in 15 years population doubled every 5 yrs => three times

So, 2 X 2 X 2 = 8 times => 700% more.

25.

[(75% X 60) + (x% X 20)] / 80 = 80% => x = 95. (since required is80%)

(OR) 60 out of 80 is 3/4. So, (3/4 X 75) + (1/4 X x) = 80 => x =95.

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Profit and LossWhat is Profit?

When a person does a business transaction and gets more than what he hadinvested, then he is said to have profit. The profit he gets will be equal to theadditional money he gets other than his investment.

So profit can be understood as the extra money one gets other than what hehad invested.Eg: A person bought an article for Rs. 100 and sold it for Rs. 120. Then he got Rs.

20 extra and so his profit is Rs. 20.What is Loss?

When a person gets an amount less than what he had invested, then he issaid to have a loss. The loss will be equal to the deficit he got than the investment.Eg: A person bought an article at Rs. 100 and sold it for Rs. 90. Then he got adeficit of Rs. 10 and so his loss is Rs. 10.Cost Price (CP):

The money that the trader puts in his business is called Cost Price. The priceat which the articles are bought is called Cost Price.

In other words, Cost Price is nothing but the investment in the business.Selling Price (SP):

The price at which the articles are sold is called the Selling Price. The moneythat the trader gets from the business is called Selling Price.

In other words, Selling Price is nothing but the returns from a business.Marked/Market/List Price (MP):

The price that a trader marks or lists his articles to is called the Marked Price. This is the only price known to the customer.

Discount: The waiver of cost from the Marked Price that the trader allows a customer is

called Discount.

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Note:1. Profit or loss percentage is to be applied always to the Cost Price only.

2.

Discount percentage is to be applied always to the Marked Price only.

Relationship Among CP, SP and MP:A trader adds his profit to the investment and sells it at that increased price.

Also he allows a discount on Marked Price and sells at the discounted price.So, we can say that,o SP = CP + Profit. (CP applied with profit is SP)

o SP = MP – Discount. (MP applied with discount is SP)

Understanding Profit and Loss:So, by now we came to know that if CP is increased and sold it would result in

profit and vice versa.Also whatever increase is applied to CP, that increase itself is the profit.For Rs. 10 profit, CP is to be increased by RS. 10 and the increased price

becomes SP.

For 10% profit, CP is to be increased by 10% and it is the SP.(From previous chapter we know that any value increased by 10% becomes

1.1 times.)So, for 10% profit, CP increased by 10% => 1.1CP = SP.

o

SP = 1.1CP => SP/CP = 1.1 => 10% profit

o SP = 1.07CP => SP/CP = 1.07 => 7% profit

o

SP = 1.545CP => SP/CP = 1.545 => 54.5% profit and so on.

Similarly,o

SP = 0.9CP => SP/CP = 0.9 => 10% loss (Since 10% decrease)

o SP = 0.76CP => SP/CP = 0.76 => 24% loss and so on.

So, to calculate profit % or loss %, it is enough for us to find the ratio of SP toCP.Note:

1. If SP/CP > 1, it indicates profit.

2.

If SP/CP < 1, it indicates loss.

Multiple Profits or losses:A trader may sometimes have multiple profits or losses simultaneously. This

is equivalent to having multiple changes and so all individual changes are to bemultiplied to get the overall effect.Examples:

1. A trader uses a 800gm weight instead of 1 kg. Find his profit %.

Soln: (He is buying 800 gm but selling 1000 gm.

So, CP is for 800 gm and SP is for 1000 gm.)

SP/CP = 1000/800 = 1.25 => 25% profit.

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2.

A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his

profit/loss %.

Soln: 1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8

20% increase in price => profit (increase) => 1.2

So, net effect = (0.8) X (1.2) = 0.96 => 4% loss.

3. A milk vendor mixes water to milk such that he gains 25%. Find the

percentage of water in the mixture.

Soln: To gain 25%, the volume has to be increased by 25%.

So, for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt

% of water = 0.25 / 1.25 X 100 = 20%.

4.

A trader bought an item for Rs. 200. If he wants a profit of 22%, at what price

must he sell it?

Soln: CP=200, Profit = 22%.

So, SP = 1.22CP = 1.22 X 200 = 244/-.

5.

A person buys an item at Rs. 120 and sells to another at a profit of 25%. If thesecond person sells the item to another at Rs. 180, what is the profit % of the

second person?

Soln: SP of 1st person = CP of 2nd person = 1.25 X 120 = 150.

SP of 2nd person = 180.

Profit % = SP/CP = 180/150 = 1.2 => 20%.

6.

A milk vendor mixes water to 20 lt of milk such that the ratio of milk and

water is 4:3. He sold the mixture at Rs. 12 per liter but bought the milk at Rs.

10 per liter. Find the profit % of the vendor.

Soln: milk : water = 4:3 => he bought 4 parts (milk) but sold 7 parts (mixture)

CP = 10 and SP = 12.

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So, profit % = (SP/CP) X (SP/CP) = (7/4) X (12/10) = 2.1 => 110% gain.

7.

A trader buys some apples at a price of 10 apples for Rs. 8 and sold them at a

price of 8 apples for Rs. 10. Find his profit or loss %.

Soln: He bought 10 apples for Rs. 8 and sold 8 apples for Rs. 10 => clearly got

profit

SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625

=> 56.25 % gain.

8. A trader allows a discount of 25% on his articles but wants to gain 50% gain.

How many times the CP should be marked on the items?

Soln: CP applied with profit = MP applied with discount = SP

1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP.

9. By selling an item at a price a trader gains 40%. What is the profit / loss % if

the item is sold at half the price?

Soln: SP =1.4CP => (SP/2) = 0.7CP => 30% loss.

10.

A trader gets a profit of 25% on an article. If he buys the article at 10%

lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual

CP of the article.

Soln: 25% gain => SP = 1.25CP…..1.

Now, CP is 10% less => 0.9CP and SP is Rs. 2 less => (SP-2).

Still, profit is 25% => (SP-2)=1.25(0.9CP) , where SP = 1.25CP (From 1)

CP = Rs. 16.

11.

A trader gets a discount of 20% from the dealer and marks it at 20%

more price then the actual MP to the customer. Find his overall gain %.

Soln: Let MP be the price on the item.

Then, CP=0.8MP (20% discount) and SP = 1.2MP.

So, gain => SP/CP = 1.2/0.8 = 1.5 => 50%.

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12.

A trader allows a discount of 20% to the customer after marking the

item up by 25%. Find his gain/loss% if he is given a commission of 20% of the

MP by the dealer.

Soln: Trader‟s SP = 0.8 X (1.25MP) = MP (since 20% discount on 25% raised

price)

Trader‟s CP = 0.8 MP (20% commission)

So, gain = SP/CP = MP/0.8MP = 1.25 => 25%.

Exercise:

1. The profit obtained by selling an article for Rs.56 is the same as the loss obtainedby selling it for Rs.42. What is the cost price of the article?

1) Rs.40 2) Rs.50 3) Rs.49 4) None of these

2. A dealer professes to sell his goods at cost price and uses an 880gm weightinstead of a kg. What is his percentage of gain?

1) 13.13% 2) 13.33% 3) 13.36% 4) 13.63%

3. P sold an article for Rs.1,080 thereby losing 10% Q sold another article forRs.1,800 at a loss of 10%. Who incurred a greater loss?

1) P 2) Q 3) Cannot say 4) Both have equal

4. Swapna bought 15 apples for Rs.10 and sold them at the rate of 12 apples forRs.12. What is the percentage of profit made by her?

1) 100% 2) 150% 3) 125% 4) None of these

5. By selling some cloth at the cost price a merchant still gained 191/21%. How

much less cloth does he measure for a meter?

1) 15cm 2) 16cm 3) 20cm 4) None of these

6. 30% loss on cost price in what percent loss on selling price?

1) 30% 2) 20% 3) 15% 4) None of these

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7. Arun purchased a house for Rs.75,000 and a site for Rs.15,000 respectively, if hesold the house for Rs.83,000 and the site for Rs.10,000, then find the resultantpercentage of gain?

1) 3% 2) 31/3% 3) 30% 4) 331/3%

8. The manufacturing cost of a watch is Rs.180 and the transportation lost isRs.500 for 100 watches. What will be the selling price if it is sold at 20% gains

1) Rs.222 2) Rs.216 3) Rs.221 4) Rs.220

9. A person, by selling an article at three-fourths of the list price incurs a loss of20%. Find the profit percentage if he sells at the list price?

1) 25% 2) 6.66% 3) 111/9% 4) None of these

10. A sells an article to B at a gain of 20%. B sells is to C at a gain of 25% and C in

turn sells is to D at a loss of 331/3%. If D paid Rs.1,000 for it, then what is thecost price of A.

1) Rs.1,000 2) Rs.2,000 3) Rs.3,000 4) Rs.4,000

11. Ajay had purchased a second hand scooter for 18,000 and spent Rs.1,800 forrepairs. After one year he wanted to sell the scooter. At what price should he sell itto gain 111/9%, if 91/11% is to be deducted at the end of every year on account ofdeprecation?

1) Rs.18,000 2) Rs.19,800 3) Rs.20,000 4) Rs.22,500

12. After getting three equal successive discount percentages over a marked price ofRs.1,000 a customer has to pay 729 for an article. What is the rate of each of thesuccessive discounts?

1) 10% 2) 20% 3) 30% 4) 40%

13. One-fifth of the cost price, one-seventh of the marked price and one-sixth of theselling price are all equal. What is the gain or loss to the trader?

1) 20%gain 2) 162/3% loss 3) 142/7%gain 4) 10%loss

14. Due to a slump in the market, A, while selling 12 apples to B, allows him tocount them as 9. But due to an overnight demand A is forced to buy them back atthe same rate as he sold and allows B to count 9 apples as 12. What is overallgain percentage of B

1) 777/9% 2) 75% 3) 50% 4) 662/3%

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23. A man sells an article at a profit of 20%. If he had bought it at 10% less and soldit for Rs.18 more, he would have gained 40%. Find the cost price of the article.

1) Rs.500 2) Rs.300 3) Rs.400 4) Rs.550

24. An article was sold at a profit of 20%. If both cost price and selling price are

Rs.100 less each, then magnitude of the percentage of profit would have been 4percentage points more than that in the first case. Then the cost price is

1) Rs.500 2) Rs.600 3) Rs.800 4) None of these

25. A man bought 2 articles at the same price and sells them together at 30% gain.Had he bought the first article at 20% less and the second article at 10% moreand then sold them together for Rs.48 less, he would have gained 20% on thewhole. What is the total cost of 2 articles?

1) Rs.200 2) Rs.300 3) Rs.400 4) Rs.500

26. A trader marks up the price of the product by 40%. If the discount is increasedfrom 15% to 25%, his profit comes down by Rs.42. What is the cost price?

1) Rs.150 2) Rs.200 3) Rs.250 4) Rs.300

27. The catalogue price of an article is Rs.15,000. If the discount is increased from15% to 20%, then profit falls from 27.5% to 20%. Find the cost price of thearticle?

1) Rs.12,000 2) Rs.10,000 3) Rs.12,250 4) Rs.12,750

28. The marked price of an article is Rs.300. If the selling price is 50% more thanthe amount of discount allowed, find the selling price

1) Rs.180 2) Rs.150 3) Rs.200 4) Rs.175

29. The cost of an apple is 331/3% less than the cost of 1 mango. If a man sells fourapples at the cost price of 5 mangoes, what is his percentage of profit?

1) 75% 2) 81% 3) 87.5% 4) 90%

30. A merchant professed to sell 20 articles at a loss which is equals to the costprice of 2 articles but sold 18 articles at the cost price of 20 articles. What is thegain percent?

1) 191/11% 2) 10% 3) 111/9% 4) 0%

31. The percentage by which the marked price exceeds the cost price of an articleand the percentage of discount allowed on the article are in the ratio of 3:2. If it issold at the cost price, what is the percentage of discount allowed?

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1) 20% 2) 25% 3) 331/3% 4) 50%

32. The purchase prices of three articles are in the ratio 3:4:5 the first one is sold ata profit of 10% and the second at a loss of 7.5%. If the overall percentage of profitor loss of the first two articles is the same as the percentage profit or loss of all the

articles taken together, what is the percentage of profit or loss in the case of thethird article?

1) 8.75 2) 1.25 3) 0 4) Can‟t be determined.

33. A dishonest oil merchant claims that he gets a profit of only 5% but he givesonly one litre of oil instead of 1kg. If 1.25 litre of oil weighs 1kg what is his overallpercentage of profit?

1) 31.25% 2) 25% 3) 26% 4) None of these

34. A fruit vendor sells mangoes and bananas and gets equal revenue from each. Hegets a profit of 20% on each mango and a profit of 25% on each banana. If theratio of the number of bananas sold to the number of mangoes sold is 4:1, what isthe ratio of the cost price of a banana to that of a mango?

1) 1:5 2) 6:25 3) 2:9 4) Can‟t be determined.

35. A trader buys 150 pens for Rs.1,000 and he marks each of them at Rs.10. Hegives a discount of 20% on each pen and he gives 1 pen free on bulk purchases of9 pens. What is his minimum possible overall percentage of profit?

1) 8% 2) 10% 3) 20% 4) 5%

36. A trader gives a discount on an article such that the profit as a percent ofmarked price is the same as the discount as a percent of cost price. What is theratio of the actual profit percentage to the actual discount percentage an thearticle?


37. The cost price of a computer is Rs.1,000 less then the selling price of a televisionand the selling price of the computer is 30% more than the cost price of the

television. If the selling price of the computer is 4% more than the selling price ofthe television, what is the percentage of profit on selling the television?

1) 20% 2) 25% 3) 162/3% 4) Can‟t be determined.

38. The marked prices of two articles are in the ratio of 1:2, their discountpercentages are also in the ratio of 1:2 and the profit they get is also in the ratio of1:2. What is the ratio of their cost price?

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39. A trader purchases two watches. He marks the first one up by Rs.200 over thecost price and gives a discount of 20% on it. The second one he marks up by 50%and gives a discount of Rs.160. If he gains 15% on both the watches put togetherand 8% on the first alone, what is the percentage of profit on the second watch?

1) 21% 2) 22% 3) 18.5% 4) Can‟t be determined.

40. Javed sells 2,000 mangoes in a week. He recovers his total cost by selling first1,200 Mangoes. He sells the next 300 Mangoes for a loss of 20% and he sells thelast 500 Mangoes for a loss of 40%. What is his overall percentage of profit?

1) 45% 2) 35% 3) 27% 4) 12.5%

Solutions:

1.

Profit at a price = loss at other price => CP must be numerically between

those prices

CP = (56+42)/2 = Rs. 49.

2. Gain % = 1000/880 => 1. 1363 => 13.63%

3.

For P, SP=1080 and loss=10% => CP = 1080/0.9 =1200 => loss = 1200-1080

= 120.

For Q, SP=1800 and loss=10% => CP = 1800/0.9 = 2000 => loss = 2000-1800

= 200.

4. She got profit => profit % = 15/10 X 12/12 = 1.5 => 50%.

5.

Profit % = 19 1/21 => 1.19047.

Let he measure x cm for 100 cm. Then, 100/x = 1.19047 =>

x=84 cm

So he measures 16 cm less for every meter.

6. Loss = 30% on CP i.e., 0.3CP => SP = 0.7CP

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Loss % on SP = loss/SP X 100 = 0.3CP/0.7CP X 100 =

42.85%.

7. Total CP = 90000 & total SP = 93000 => gain = SP/CP = 93000/90000

=1.0333 = 3.33%

8.

Total cost of a watch = 180 + (500/100) = 185.

Gain = 20% => SP = 1.2CP = 1.2 X 185 = 222

9.

0.75 MP = 0.8 CP (since 20% loss)

So, MP = 1.0666CP => 6.66% gain

10. 1.2 X 1.25 X 0.6666 X CP = 1000 => CP = 1000 (profits of

20%, 25% & loss of 33.33%)

11.

Total CP=18000+1800 = 19800.

Depreciation = 9.09% and gain = 11.11% => SP = (0.9091)X(1.1111)X19800

= 20000.

12. Let „f‟ be the factor of discount => 1000 X f X f X f = 729 => f =

0.9 => 10% decrease.

13.

CP/5 = SP/6 => SP/CP=1.2 => 20% gain.

14.

In two transactions B is gaining => SP > CP for B in two

transactions.

So, gain% = 12/9 X 12/9 = 1.7777 => 77.77%.

15. 2 articles free for every 10 articles bought. So 10 free articles => 50

articles bought.

Money of 60 articles (10 articles free) is obtained by selling only 10

articles.

So SP of 10 articles = CP of 60 articles => SP/CP = 6 => 500% gain.

16. Total CP = 45000. Depreciation = 20% =>new CP = 0.8 X 45000 =

36000.

SP = 40000 => SP/CP = 40/36 = 1.1111 => 11.11% gain

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17. CP => 6 apples for Rs. 10. SP => 4 apples for Rs. 10 => 6 apples for Rs. 15

So, for 6 apples, gain is Rs.5 => Rs. 60 gain requires 72 apples.

18.

CP of 5 kg ghee = 300. Loss = 10% => SP = 0.9 CP = 270. For Rs. 270, 4

kg are sold

SP for 1 kg = 270/4 =Rs. 67.5

19.

Let w be the weight of the second stone.

Now, 0.9 X (1000/800) X (1000/w) = 1.0285 (since profit is 2.85%)

w = 900 gm (nearly)

20.

SP = 39. Profit % = CP.

CP + (CP% of CP) = SP => CP = 30/-.

21. ratio = 3:4 => investments are 3/7 and 4/7.

Overall loss/gain % = (3/7)(-10) + (4/7)(20) = 50/7 = 7 1/7 %.

22. 3/5th are sold at gain of 25% and 2/5th are sold at loss of 25%.

First, (3/5 X 25 – 2/5 X 25) = 5% gain.

23.

20% gain => SP = 1.2 CP.

New CP = 0.9 CP and New SP = SP + 18 => 1.2CP+18.

40% gain => new SP = 1.4 X new CP => (1.2CP+18) = 1.4(0.9CP) => CP =

300.

24. 20% gain => SP = 1.2CP.

New CP = CP – 100 and new SP = SP -100 & 24% gain => new SP=1.4 X new CP

CP – 100 = 1.4 ( 1.2CP – 100) => CP = 600.

25.

Let each article costs x => Total CP = 2x and SP = 1.3 X 2x = 2.6x.

New total CP = 0.8x + 1.1x = 1.9x, New SP = SP – 48 = 2.6x – 48 and gain = 20%

So, 2.6x – 48 = 1.2 X 1.9x => 2x = 300.

26. MP = 1.4CP. Also 10% change is discount => Rs. 42 gain => 10% of

1.4CP = 42

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CP = 300.

27.

MP = 15000. 5% change in discount i.e., 5% of MP = 7.5 % of CP (profit

change)

So, CP = 5/7.5 X MP = 10000.

28.

MP = 300. SP = 1.5 X discount. Now, SP = MP – discount => SP = 180.

29. CP of apple = 0.6666 X CP of mango…….1

Man sold 4 apples for CP of 5 mangoes => his CP = 4 X CP of apple

And his SP = 5 X CP of mango.

So, SP/CP = (5XCP of mango)/(4XCP of apple) = 1.875 => 87.5%.

30.

SP of 18 articles = CP of 20 articles => SP/CP = 20/18 = 1.1111 =>11.11% gain

31.

If CP is raised by 3x %, the discount should be 2x %.

Also, after discount SP=CP => increase of 3x% X decrease of 2x%.

From inspection, 33.33% discount => 50% increase (since 3:2) and 1.5 X 0.6666

= 1.

32.

CP of first two articles are in ration of 3:4.

So for 2 articles, gain/loss % = (3/7)X10 – (4/7)X7.5 = 0.

So, overall profit/loss% = 0 => (3/12)X10 – (4/12)X7.5 + (5/12)x = 0 => x=0%.

33. Overall profit = 1.05 X (1.25/1) = 1.3125 => 31.25% gain

34.

For mango, SP = 1.2 CPm and for banana SP = 1.25 CPb.

Revenue from mango = revenue from banana => 1.2 CPm = 4 X 1.25

CPb (since they are sold in ratio of 1:4)

So, CPb/CPm = 6:25.

35. 150 pens for Rs.1000 => total CP = 1000.

1 pen free for every 9 pens => he can sell 135 pens (for least possible profit)

SP of each pen = 10 and discount = 20% => SP = 8.

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Total SP = 135 X 8 = 1080 => SP/CP = 1080/1000 = 1.08 => 8%.

36.

Profit% of MP = discount% of CP => profit%/discount% cant be

determined without the values of MP and CP.

37. CP computer = SP TV – 1000 and SP computer = 1.3 X CP TV.

SP Computer = 1.04 SP TV => 1.3 CP TV = 1.04 SP TV => SP/CP = 1.25 => 25%

gain.

38.

Without the knowledge of atleast on of the prices the ratio of CP‟s cant

be determined.

39. MP1 = CP1 + 200 and discount = 20%.Also MP2 = 1.5CP2 and discount

= Rs. 160.

Also SP1/CP1 = 8% gain. With this information it can‟t be said what is the

profit % on 2nd watch.

40. 300 sold at loss of 20% and 500 old at a loss of 40% => loss% =

(3/8)X20 + (5/8)X40

= 32.5 => loss factor = 0.675

Already he got a gain by SP of 1200 = CP of 2000.

So overall profit % = (2000/1200) X 0.675 = 1.125 => 12.5% gain.

Averages and Ages

What is average?

The concept of average is equal distribution of the overall value among all the things or personspresent there. So the formula for finding the average is as follows:

Average, A = Total of all things, T / Number of things, N

Therefore, Total, T = AN

If any person joins a group with more value than the average of the group then the overall averageincreases. This is because the value in excess than the average will also be distributed equally amongall the members.

Similarly when any value less than the average joins the group the overall group decreases as thedeficit is divided equally among all the people present there.

Example:

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Consider three people A, B and C with total of Rs. 30/-. Their average becomes Rs. 10/- for each. Ifanother person D joins them with Rs. 50/- then he has Rs. 40/- more than actual average of Rs.10/-.

So this Rs. 40/- will get distributed among those four and each gets Rs. 10/-. Thus the averagebecomes Rs. 20/- each.

Example:

The average age of a class of 30 students is 12. If the teacher is also included the average becomes13 years. Find the teacher‟s age.

Soln:

When the teacher is included there are totally 31 members in the class and the average is increasedby 1 year. This means that everyone got 1 extra year after distributing the extra years of the teacher.

So extra years of the teacher are as follow: 31x1=31 years.

Age of the teacher = actual avg + extra years = 12 + 31 = 43 years.

Exercise:

1. The average of 13 papers is 40. The average of the first 7 papers is 42 and of the last seven

papers is 35. Find the marks obtained in the 7th paper?

(A) 23

(B) 38

(C) 19

(D) None of these

2. The average age of the Indian cricket team playing the Nagpur test is 30. The average age of 5 of

the players is 27 and that of another set of 5 players, totally different from the first five, is 29. If it

is the captain who was not included in either of these two groups, then find the age of the

captain.

(A) 75

(B) 55

(C) 50

(D) Cannot be determined

3. A bus goes to Ranchi from Patna at the rate of 60 km per hour. Another bus leaves Ranchi for

Patna at the same times as the first bus at the rate of 70 km per hour. Find the average speed for

the journeys of the two buses combined if it is known that the distance from Ranchi to Patna is

420 kilometers.

(A) 64.615 kmph

(B)

64.5 kmph(C) 63.823 kmph

(D) 64.82 kmph

4. A train travels 8 km in the first quarter of an hour, 6 km in the second quarter and 40 km in the

third quarter. Find the average speed of the train per hour over the entire journey.

(A) 72 km/h

(B) 18 km/h

(C) 77.33 km/h

(D) 78.5 km/h

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5. The average weight of 6 men is 68.5 kg. If I is known that Ram and Tram weigh 60 kg each, find

the average weight of the others.

(A) 72.75 kg

(B) 75 kg

(C) 78 kg

(D) None of these

6.

The average score of a class of 40 students is 52. What will be the average score of the rest of thestudents if the average score of 10 of the students is 61.

(A) 50

(B) 47

(C) 48

(D) 49

7. The average age of 80 students of IIM, Bangalore of the 1995 batch is 22 years. What will be the

new average if we include the 20 faculty members whose average age is 37 years?

(A) 32 years

(B) 24 years

(C) 25 years

(D)

None of these8. Out of the three numbers, the first is twice the second and three times the third. The average of

the three numbers is 88. The smallest number is

(A) 72

(B) 36

(C) 42

(D) 48

9. The sum of three numbers is 98. If the ratio between the first and second is 2 : 3 and that

between the second and the third is 5 : 8, then the second number is

(A) 30

(B) 20

(C)

58(D) 48

10. The average height of 30 girls out of a class of 40 is 160 cm and that of the remaining girls is 156

cm. The average height of the whole class is

(A) 158 cm

(B) 158.5 cm

(C) 159 cm

(D) 157 cm

11. The average weight of 6 persons is increased by 2.5 kg when one of them whose weight is 50 kg is

replaced by a new man. The weight of the new man is

(A) i65 kg

(B)

75 kg(C) 76 kg

(D) 60 kg

12. The average age of A, B C and D five years ago was 45 years. By including X, the present average

age of all the five is 49 years. The present age of X is

(A) 64 years

(B) 48 years

(C) 45 years

(D) 40 years

11

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13. The average salary of 20 workers in an office is Rs. 1900 per month. If the manager‟s salary isadded, the average salary becomes Rs. 2000 per month. What is the manager‟s annual salary?

(A) Rs. 24, 000

(B) Rs. 25,200

(C) Rs. 45,600

(D) None of these

14.

The average weight of a class of 40 students is 40 kg. If the weight of the teacher be included, theaverage weight increases by 500 gm. The weight of the teacher is

(A) 40.5 kg

(B) 60 kg

(C) 62 kg

(D) 60.5 kg

15. In a Infosys test, a student scores 2 marks for every correct answer and loses 0.5 marks for every

wrong answer. A student attempts all the 100 questions and scores 120 marks. The number of

questions he answered correctly was

(A) 50

(B) 45

(C)

60(D) 68

16. The average of the first ten natural numbers is

(A) 5

(B) 5.5

(C) 6.5

(D) 6

17. The average of the first ten whole numbers is

(A) 4.5

(B) 5

(C) 5.5

(D)

418. The average of the first ten even numbers is

(A) 18

(B) 22

(C) 9

(D) 11

19. The average weight of a class of 30 students is 40 kg. If, however, the weight of the teacher is

included, the average become 41 kg. The weight of the teacher is

(A) 31 kg

(B) 62 kg

(C) 71 kg

(D)

70 kg20. 30 oranges and 75 apples were purchased for Rs. 510. If the price per apple was Rs. 2, then the

average price of oranges was

(A) Rs. 12

(B) Rs. 14

(C) Rs. 10

(D) Rs. 15

21. A batsman made an average of 40 runs in 4 innings, but in the fifth inning, he was out on zero.

What is the average after fifth innings?

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(A) 32

(B) 22

(C) 38

(D) 49

22. The average weight of a school of 40 teachers is 80 kg. If, however, the weight of the principle be

included, the average decreases by 1 kg. What is the weight of the principal?

(A)

109 kg(B) 29 kg

(C) 39 kg

(D) None of these

23. The average age of Ram and Shyam is 20 years. Their average age 5 years hence will be

(A) 25 years

(B) 22 years

(C) 21 years

(D) 20 years

24. The average of 20 results is 30 and that of 30 more results is 20. For all the results taken

together, the average is(A) 25

(B) 50

(C) 12

(D) 24

25. The average of 5 consecutive numbers is 18. The highest of these numbers will be

(A) 24

(B) 18

(C) 20

(D) 22

26. Three years ago, the average age of a family of 5 members was 17 years. A baby having been

born, the average of the family is the same today. What is the age of the baby?

(A) 1 years

(B) 2 years

(C) 6 months

(D) 9 months

27. Varun average daily expenditure is Rs. 10 during May, Rs. 14 during June and Rs. 15 during

July. His approximate daily expenditure for the 3 months is

(A) Rs. 13 approximately

(B) Rs. 12

(C)

Rs. 12 approximately(D) Rs. 10

28. A ship sails out to a mark at the rate of 15 km per hour and sails back at the rate of 20 km/h.

What is its average rate of sailing?

(A) 16.85 km

(B) 17.14 km

(C) 17.85 km

(D) 18 km

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29. The average temperature on Monday, Tuesday and Wednesday was 41 0C and on Tuesday,

Wednesday and Thursday it was 40 0C. If on Thursday it was exactly 39 0 C, then on Monday, the

temperature was

(A) 42 0C

(B) 46 0C

(C) 23 0C

(D)

260

C30. The average of 20 results is 30 out of which the first 10 results are having an average of 10. The

average of the rest 10 results is

(A) 50

(B) 40

(C) 20

(D) 25

31. ten years ago, Mohan was thrice as old as Ram was but 10 years hence, he will be only twice asold. Find Mohan‟s present age.

a) 60 yearsb) 80 years

c)

70 yearsd) 76 years

32. The ages of Ram and Shyam differ by 16 years. Six years ago, Mohan‟s age was thrice as that ofRam‟s, find their present ages. a) 14 years, 30 yearsb) 12 years, 28 yearsc) 16 years, 34 yearsd) 18 years, 38 years

33. 15 years hence, Rohit will be just four times as old as he was 15 years ago. How old is Rohit atpresent?

a) 20b) 25c) 30

d)

3534. A man‟s age is 125% of what it was 10 years ago, but 83 1/3 % of what it will be after ten 10

years. What is his present age?a) 45 yearsb) 50 yearsc) 55 yearsd) 60 years

35. If twice the son‟s age in years be added to the father‟s age, the sum is 70 and if twice the father‟sage is added to the son‟s age, the sum is 95. Father‟s age is

a) 40 yearsb) 35 yearsc) 42 yearsd) 45years

36. Three years ago, the average age of a family of 5 members was 17. A baby having been born theaverage age of the family is the same today? What is the age of the child?

a) 3 yearsb) 5 yearsc) 2yearsd) 1 year

37. The ratio of A‟s and B‟s ages is 4:5 If the difference between the present age of A and the age of B5 years hence is 3, then what is the total of present ages of A and B?

a) 68 yearsb) 72 years

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c) 76 yearsd) 64 years

38. The ages of A and B are in the ratio of 6:5 and sum of their ages is 44 years. The ratio of theirages after 8 years will be

a) 4 : 5b) 3 : 4c) 3 : 7d) 8 : 7

39. 5 years ago, the combined age of my mother and mine was 40 years. Now, the ratio of our age is4:1. How old is my mother?

(A) 10(B) 40(C) 60(D) 20(E) 50

40. Honey was twice as old as Vani 10 years ago. How old is Vani today if Honey will be 40 years old10 years hence?

a) 20b) 25c) 15d) 35e)

3041. One year ago, a mother was 4 times older to her son. After 6 years, her age become more thandouble her son‟s age by 5 years. The present ratio of their age will be?

a.13 : 12b.11 : 13c.3 : 1d.25 : 7e.4 : 3

42. Vandana‟s mother is twice as old as her brother. She is 5 years younger to her brother but 3 years older to her sister. If her sister is 12 years of age, how old is her mother?

a.30b.35c.45d.40e.50

43. Sonu is 4 years younger Manu while Dolly is four years younger to Sumit but 1/5 times as old asSonu. If Sumit is eight years old, how many times as old is Manu as Dolly?

a.3b.½c.2d.1e.¼

44. Our mother is 3 times as old as my brother and I am 1/3rd times older than my brother. If 4 years ago I was as old as my brother today, what is the age of my mother.

a.40b.36c.44d.42e.48

45. Ruchi‟s age was double that of Niti 2 years ago. If Ruchi was 2 years older to Niti then, try toguess how old she is today.

a.6b.4c.8d.2e.20

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46. If we add the age of three brothers Sunil, Sanjay and Sonu, then it becomes 60 years today. If 6 years ago the Sonu was of half the age of Sanjay and 1/3rd to the age of Sunil, then find out thepresent age of Sanjay.

a.14b.15c.16d.18e.24

47. Sonu‟s age is 2/3rd of Manu‟s. After 5 years Sonu will be 45 years old. Manu‟s present age isa.55b.56c.58d.60e.64

48. Ratio of Sonu‟s age to Manu‟s is equal to 4:3. If Sonu will be 26 years old after 6 years, thepresent age of Manu is

a.11b. 15c.14d.17e.13

49. Binny is born on 1st October. He is younger to Sunny by one week and two days. If on 1 st Octoberit was a Saturday, then Sunny‟s birthday will come on which day this year?

(A) Wednesday (B) Thursday (C) Monday(D) Saturday (E) Sunday

50. Binny is half as old as Sunny. Chinky is twice old as Sunny. How many times is Chinky as old asBinny?

(A) 6 (B) 4 (C) 8(D) 3 (E) 2

Ratios and Proportions

What is a ratio?

A ratio is a representation of distribution of a value present among the persons present and is shownas follows:

If a total is divided among A, B and C such that A got 4 parts, B got 5 parts and C got 6 parts then itis represented in ratio as A:B:C = 4:5:6.

So, 4:5:6 means that the total value is divided into 4+5+6 = 15 equal parts and then distributed asper the ratio.

Example 1:

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Divide Rs. 580 between A and B in the ratio of 14:15.

Soln:

A:B = 14:15 => 580 is divided into 29 equal parts => each part = Rs. 20.

So A‟s share = 14 parts = 14 x 20 = Rs. 280 B‟s share = 15 parts = Rs. 300.

Example 2:

If A:B = 2:3 and B:C = 4:5 then find A:B:C.

Soln:

To combine two ratios the proportions common for them shall be in equal parts. Here the commonproportion is B for the given ratios.

Making B equal in both ratios they become 8:12 and 12:15 => A:B:C = 8:12:15.

Example 3:

Three numbers are in the ratio of 3: 4 : 8 and the sum of these numbers is 975. Find the threenumbers.

Soln:

Let the numbers be 3x, 4x and 8x. Then their sum = 3x+4x+8x = 15x = 975 => x = 65.

So the numbers are 3x = 195, 4x = 260 and 8x = 520.

Example 4:

Two numbers are in the ratio of 4 : 5. If the difference between these numbers is 24, then find thenumbers.

Soln:

Let the numbers be 4x and 5x. Their difference = 5x – 4x = x = 24 (given).

So the numbers are 4x = 96 and 5x = 120.

Example 5:

Given two numbers are in the ratio of 3 : 4. If 8 is added to each of them, their ratio is changed to 5 :6. Find two numbers.

Soln:

Let the numbers be a and b.

A:B = 3:4 => A / B = 3 / 4.Also, (A+8) / (B+8) = 5 / 6.

Solving we get, A=12 and B = 16

Example 6:

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A garrison has provisions for 120 soldiers for 240 days. After 180 days 60 more soldiers will join thegroup. For how many more days will the provisions last?

Soln:

Actually after 180 days,

If 120 members are there provisions come for 60 more days (since total 240 days)But now 180 members are there.

So number of days = (120/180) X 60 = 40 days.

Example 7:

If 24 men working for 12 hrs a day can do a work in 16 days, in how many days can 8 men working6 hrs a day do it?

Soln:

24 men – 12 hrs – 16 days8 men – 6 hrs - ? days (n)

n =16 X (12 / 6) X (24 / 8) ( since no of hrs reduced no of days has to increase and no of menreduced also increases no of days i.e., inverse proportional)

=> n = 96 days.

EXERCISE

1. Divide Rs.1870 into three parts in such a way that half of the first part, one-third of the

second part and one-sixth of the third part are equal.

1. 241, 343, 245 2. 400, 800, 670 3. 470, 640, 1160 4.None

2. Divide Rs.500 among A, B, C and D so that A and B together get thrice as much as C and D

together, B gets four times of what C gets and C gets 1.5 times as much as D. Now the

amount C gets?

1. 300 2. 75 3. 125 4. None

3. If 4 examiners can examine a certain number of answer books in 8 days by working 5 hours a

day, for how many hours a day would 2 examiners have to work in order to examine twice the

number of answer books in 20 days.

1. 6 2. 1/2 3. 8 4. 9

4. In a mixture of 40 liters, the ratio of milk and water is 4:1. How much water much be added

to this mixture so that the ratio of milk and water becomes 2:3

1. 20 litres 2. 32 litres 3. 40 litres 4. 30 litres

5. If three numbers are in the ratio of 1:2:3 and half the sum is 18, then the ratio of squares of

the numbers is:

1. 6:12:13 2. 1:2:4 3. 36:144:324 4. None

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6. The ratio between two numbers is 3:4 and their LCM is 180. the first number is:

1. 60 2. 45 3. 15 4. 20

7. A and B are tow alloys of argentums and brass prepared by mixing metals in proportions 7:2

and 7:11 respectively. If equal quantities of the two alloys are melted to form a third alloy C,

the proportion of argentums and brass in C will be:

1. 5:9 2. 5:7 3. 7:5 4. 9:5

8. If 30 men working 7 hours a day can do a piece of work in 18 days, in how many days will 21

men working 8 hours a day do the same work?

1. 24 days 2. 22.5 days 3. 30 days 4. 45 days

9. The incomes of A and B are in the ratio 3:2 and their expenditure are in the ratio 5:3. If each

saves Rs.1000, then, A‟s income is

1. 3000/- 2. 4000/- 3. 6000/- 4. 9000/-

10. If the ratio of sines of angles of a triangle is 1:1:2, then the ratio of square of the greatest

side to sum of the squares of other two sides is1. 3:4 2. 2:1 3. 1:1 4. Can‟t say

11. Divide Rs.680 among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 th of what

C gets. Now the share of C is?

1. 480/- 2. 300/- 3. 420/- 4.

None

12. A, B, C enter into a partnership. A contributes one-third of the whole capital while B

contributes as much as A and C together contribute. If the profit at the end of the year is

Rs.84, 000, how much would each received?

1. 24,000, 20,000, 40,000 2. 28,000, 42,000, 14,0003. 28,000, 42,000, 10,000 4. 28,000, 14,000, 42,000

13. The students in three batches at AMS Careers are in the ratio 2:3:5. If 20 students are

increased in each batch, the ratio changes to 4:5:7. the total number of students in the three

batches before the increases were

1. 10 2. 90 3. 100 4. 150

14. The speeds of three cars are in the ratio 2:3:4. The ratio between the times taken by these

cars to travel the same distance is

1. 2:3:4 2. 4:3:2 3. 4:3:6 4.

6:4:3

15. Rs.2250 is divided among three friends Amar, Bijoy and Chandra in such a way that 1/6th of

Amar‟s share, 1/4th of Bijoy‟s share and 2/5th of Chandra‟s share are equal. Find Amar‟sshare.

1. 720/- 2.1080/- 3. 450/- 4.

1240/-

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16. After an increment of 7 in both the numerator and denominator, a fraction changes to ¾.

Find the original fraction.

1. 5/12 2. 7/9 3. 2/5 4. 3/8

17. The difference between two positive numbers is 10 and the ratio between them is 5:3. Find

the product of the two numbers.1. 375 2. 175 3. 275 4. 125

18. If 30 oxen can plough 1/7th of a field in 2 days, how many days will 18 oxen take to do the

remaining work?

1. 30 days 2. 20 days 3. 15 days 4. 18 days

19. A cat takes 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the

cat. What is the ratio of the speed of the cat to that of the dog?

1. 11:15 2. 15:11 3. 16:15 4.

15:16

20. The present ratio of ages of A and B is 4:5. 18 years ago, this ratio was 11:16. Find the sum

total of their present ages.

1. 90 years 2. 105 years 3. 110 years 4. 80 years

21. Three men rent a farm for Rs.7000 per annum. A puts 110 cows in the farm for 3 months, B

puts 110 cows for 6 months and C puts 440 cows for 3 months. What percentage of the total

expenditure should A pay?

1. 20% 2. 14.28% 3. 16.66% 4. 11.01%

22. 10 students can do a job in 8 days, but on the starting day, two of them informed that they

are not coming. By what fraction will the number of day required for doing the whole work getincreased?

1. 4/5 2. 3/8 3. 3/4 4. 1/4

23. A dishonest milkman mixed 1 liter of water for every 3 liters of milk and thus make up 36

liters of milk. If he now adds 15 liters of milk to the mixture, find the ratio of milk and water

in the new mixture.

1. 12:5 2. 14:3 3. 7:2 4. 9:4

24. Rs.3000 is distributed among A, B and C such that A gets 2/3 rd of what B and C together get

and C gets ½ of what A and B together get. Find C‟s share

1. 750/- 2. 1000/- 3. 800/- 4. 1200/-

25. If the ratio of the ages of Maya and Chhaya is 6:5 at present, and fifteen years from now, the

ratio will get changed to 9:8, then find Maya‟s present age. 1. 24 years 2. 30 years 3. 18 years 4. 33 years

26. If Rs.58 is divided among 150 children such that each girl and each boy gets 25 p and 50 p

respectively. Then how many girls are there?

1. 52 2. 54 3. 68 4. 62

5

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c.

33.33d. 66

5. In an election 10 % of the votes were invalid. 40% of the votes were for A andthe rest to B. B won with a majority of 243 votes, the total number of votespolled is

a.

1250b.

1350c. 1155d.

None

6.

In a class there were 80 boys and 70 girls. If 25% of boys and 30% of girlspassed in an exam find the fail % of the class.

a. 27b.

72.66c. 27.5d.

72.5

7.

A person‟s salary was increased by 25% in one year. In the next year itincreased by 50%. What is the % increase in the salary?

a. 87.5b.

75c. 37.5d.

None

8.

A man scores 42.5% and failed by 5 marks in an exam. If he scored 52.5% hewould pass by 15 marks. Find the minimum marks to pass.

a.

200

b.

100c. 90d.

80

9.

A trader bought some oranges. 4% of them were spoiled, 10% of remainingrotten and he sold 90 % of the good ones. If 540 oranges were left the numberof oranges he bought was

a. 6000b.

6250c.

6500d. 6750

10. The population of a city was 9000. If the male population increased by15% and the female population increased by 16% the total populationincreased by 1390. The number of men were

a.

4000b. 4250c. 4750d.

5000

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11.

By selling an article for Rs. 1000 the person loses 20%. At what price ithas to be sold to gain 30%?

a.

1500b. 1625c. 1675d.

1680

12.

SP of 4 articles is equal to CP of 3 articles. The % of gain or loss isa. 25b.

50c.

75d.

80

13. A man bought 60 apples for Rs. 100 and 40 other apples for Rs. 50.How many apples has he to sell for Rs. 120 to gain 25%?

a. 10b.

64

c.

88d.

90

14. X sold 3/5th of his goods at 50 % gain. If he sells the remaining at CPfind the overall profit %.

a. 10b.

25c. 30d.

40

15.

A radio was sold for 18% profit. If it were sold for Rs. 30 more a profit of

20% would have gained. Find the CP.a. 1000b.

1200c. 1500d.

1800

16.

A shopkeeper had calculated profit % on SP and announced it as 40%.His actual profit % is

a.

60b.

66.5c. 66.66

d.

66.33

17.

The price of an article increased by 20% and later decreased by 20%. Ifpresent value is Rs. 480 the original price is

a.

480b. 490c. 500d.

520

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18.

Due to increase in price of eggs by 20% two eggs less were available forRs. 20. The present price of eggs per dozen is

a.

24b. 20c. 25d.

18

19.

After two successive discounts on list price of Rs. 5000 an article wassold for Rs. 3600. If the first discount was 20% the second discount is

a.

5%b.

10%c.

15%d. 20%

20.

Kiran bought a radio on 15% discount. If he got a discount of 18% hewould save Rs. 63. The SP is

a.

1785

b.

1722c.

1745d. 1740

21.

A shopkeeper buys toffees at rate of 40 for Rs. 5 and sells at rate of 50for Rs. 10. The profit % is

a.

60b. 50c.

25d. 30

22.

A man sells his articles at 5% above CP. If he had bought them for 5%lesser price and sold them for Rs. 2 less, he wiuld have gained 10%. The CP ofthe articles is

a. 500b.

360c. 425d.

400

23.

The marked price of a table is Rs. 1200, 20% above CP. It is sold at adiscount of 10%. The profit % is

a. 10

b.

8c. 7.5d.

6

24.

The average monthly salary of 20 employes is Rs. 1500. If the manager‟ssalary is added the average becomes Rs. 1600. The manager‟s salary is

a. 3500b.

3600c. 3800

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d.

3900

25.

Of the three numbers the first is twice the second and half of the third. Their average is 56. Find the smallest number.

26. a. 2027.

22

28.

2429.

26

26.

A batsman scores 64 runs in his 16th innings and increases his averageby 3. His average after 16th innings is

a.

18b. 17c. 19d.

16

27.

12 yrs ago, the average age of a husband and his wife was 20yrs. The

average age is same today, they having two children. What is the present ageof the youngest child if children differ in age by 2yrs?

a. 6b. 5c.

8d. 7

28. The average age of jawans in army of 40 is reduced by 1yr when 10 menwith average 20 yrs are replaced by 10 new men. Find the average age of thenew men?

a.

14

b.

15c. 16d.

17

29.

The average weight of 8men in increased by 2 kg when one of them withweight of 50kg is replaced by a new man. The weight of the new man is

a.

60b. 65c.

63d.

66

30.

The average age of husband, wife and their child 3yrs ago was 27yrsand that of the wife and the child 5yrs ago was 20yrs. The present age of thehusband is

a. 40b.

30c. 33d. 43

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Time and Distance

Speed:

We have the relation between speed, time and distance as follows:

Speed = distance / time.

So the distance covered in unit time is called speed.

This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or Time = Distance / Speed.

Units of Speed:

The units of speed are kmph (km per hour) or m / s.

1 kmph = 5 / 18 m / s

1 m / s = 18 / 5 kmph

Average Speed:

When the travel comprises of various speeds then the concept of average speed is to be applied.

Average Speed = Total distance covered / Total time of travel

Note: In the total time above, the time of rest is not considered.

Example 1:

If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph findits average speed.

Soln:

Average Speed = Total distance / Total time.

Let each side of square be x km. Then the total distance = 4x km.

The total time is sum of individual times taken to cover each side.

To cover x km at 100 kmph, time = x / 100.

For the second side time = x / 200.

Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph.

Example 2:

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A man if travels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usualtime.

Soln:

Let s be the actual speed and t be the actual time of the man.

Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same.

So distance 1 = distance 2 => s X t = (5/6)s X (t+10) => t = 50 min.

Example 3:

If a person walks at 30 kmph he is 10 min late to his office. If he travels at 40 kmph then he reachesto his office 5 min early. Find the distance to his office.

Soln:

Let the distance to his office be d. The difference between the two timings is given as 15 min = 1 / 4hr.

Now if d km are covered at 30 kmph then time = d/30. Similarly second time = d/40.

So, d/30 – d/40 = 1 / 4 => d = 30 km.

Note:

When two objects move with speeds s1 and s2

a. In opposite directions their combined speed = s1 + s2b. In same direction their combined speed = s1 ~ s2.

Example 4:

Two people start moving from the same point at the same time at 30 kmph and 40 kmph in oppositedirections. Find the distance between them after 3 hrs.

Soln:

Speed = 30 + 40 = 70 kmph (since in opposite directions) Time = 3 hrs

So distance = speed X time = 70 X 3 = 210 km.

Example 5:

A starts from X to Y at 6 am at 40 kmph and at the same time B starts from Y to X at 50 kmph.When will they meet if X and Y are 360 km apart?

Soln:

Distance = 360 kmSpeed = 40 + 50 = 90 kmph.

Time = distance / speed = 360 / 90 = 4hrs from 6 am => 10 am.

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Example 6:

A starts from X to Y at 6 am at a speed of 50 kmph. After two hours B starts from Y to X at 60 kmph.When will they meet if X and Y are 430 km apart?

Soln:

By the time B started A traveled for 2 hrs => 2 X 50 = 100 km.

So at 8 am, distance = 430 – 100 = 330 kmSpeed = 50 + 60 = 110 kmph.

Time = distance / speed = 330 / 110 = 3 hrs from 8 am => 11 am.

Note:

When a train crosses a negligible length object (man / pole / tree) the distance that it has to travel isits own length.

When a train has to cross a lengthy object (train / bridge / platform) the distance it has to travel is

the sum of its length and the length of the object.

Example 7:

If a train traveling at 40 kmph crosses another train of length 100m traveling at 14 kmph in oppositedirection in 30 s find the length of the train.

Soln:

Let length of train be d.Distance to be covered = d + 100.Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s

Time = 30 s.Distance = speed X time => d+100 = 15 X 30 => d = 350 m.

Note:

If a man rows a boat along the stream flowing at speed S2 then it is termed downstream speed and isgiven by

S down = S1 + S2 , where S1 is speed of boat in still water.

If a man rows a boat opposite to the stream flowing at S2 then it is termed upstream and is given by

S up = S1 – S2.

Exercise:1. A car moves at a speed of 80km/hr. What is the speed of the car in meters per second?

1)9

212 2)

9

222

3)9

120 4)

2

921

2. If a man can cover 12 meters in one second, how many kilo meters can be cover in 3hours 45 minutes?

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1) 168 km 2) 162 km3) 150 km 4) 156 km

3. If a man running at 15 kmph. Crosses a bridge in 5 minutes, then the length of the bridgeis

1) 1230 m 2) 1240 m3) 1250 m 4) 1220 m

4.

Walking at

th

43 of his usual speed a man is late by 2 hours 30 minutes. The usual time

would have been

1)2

17 hrs 2)

2

13 hrs

3)4

13 hrs 4)

8

7 hrs

5. In a 1 km race, A beats B by 100 m and C by 150 m. In a 2700 m race, by how manymeters does B beat C?

1) 100 m 2) 120 m3) 150 m 4) 180 m

6.

Traveling at a speed of 8 kmph a student reaches school from his house 10 minutes early.If he travels at 6 kmph, he is late by 20 minutes. Find the distance between the schooland the house.

1) 12 km 2) 1 km3) 10 km 4) 13 km

7. A man takes 5 hours 45 minutes in walking to a certain place and riding back. He couldhave gained 2 hours by riding both ways. The time he would take to walk both ways is

_________1) 12 hrs 2) 11 hrs 45minutes3) 7 hrs 45 minutes 4) 3 hrs

8. The ratio between rates of walking of two persons is 3:4. If the time taken by nd2 person

to cover a certain distance is 36 minutes, then the time taken by the first person to coverthe same distance is ___________

1) 36 minutes 2) 48 minutes3) 27 minutes 4) none

9. If the speed of a vehicle changes in the ratio a : b, then the ratio of times taken is

1) a : b 2)1b

a

3) b : a 4)1a

b

10. A car driver makes his journey by the speed of 75km/hr and returns to initial place with50 km/hr. Then his average speed of journey is ___________

1) 30 km/hr 2) 40 km/hr3) 50 km/hr 4) 60 km/hr

11. A vehicle travels 715 km at a uniform speed. If the speed of the car is 10 kmph more, ittakes 2 hours less to cover the same distance. The original speed was _______________

1) 45 kmph 2) 65 kmph3) 55 kmph 4) 75 kmph

12. Two persons P and Q run at 8 kmph and 12 kmph on a circular track of length 6 km inthe same direction starting at same time from same place. After how many hours will theymeet each other any where on the track?

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1) 1.5 hours 2) 2 hours3) 2.5 hours 4) 3.5 hours

13. A car driver driving at a speed of 68kmph locates a truck 40 meters ahead of him. After10 seconds, the truck is 60 meters behind. The speed of truck is ____________

1) 30 km/hr 2) 32 km/hr3) 23 km/hr 4) 3 km/hr

14. Rajan is traveling on his cycle and has calculated to reach a point at 2 p.m. if he travels at10 kmph. He would reach there by 12 noon if he travels at 15 kmph. At what speed musthe travel to reach the same place at 1.p.m?


15. Two persons start running simultaneously around a circular track of length 300m fromthe same point at speeds 15 and 25km/hr. When will they meet first time on the track,when move in opposite direction?

1) 21 sec 2) 22 sec3) 27 sec 4) 24 sec

16.

A robber steals a Maruthi car at 2.30 pm and drives at 60 kmph. The theft is discoveredat 3 p.m. and the owner sits in Police jeep running at 75 kmph. When will he catch thethief?

1) 5.30 pm 2) 5.15 pm3) 5 pm 4) 5.45 pm

17. Two planes move along a circle of circumference 1.2 km with constant speeds. When theymove in different directions they meet every 15 sec and then they move in the samedirection one plane over takes the other every 60 sec. The speed of slower plane is

1) 0.04 km/s 2) 0.03 km/s3) 0.05 km/s 4) 0.02 km/s

18. A 150 m long train crosses a man walking at a speed of 6 kmph in his opposite directionin 6 sec. The train (in kmph) is:

1) 66 2) 843) 96 4) 106

19. A train of length 150 m takes 10 sec to pass over another train 100 m long coming fromthe opposite direction. If the speed of the train is 30 kmph. Then the speed of the secondtrain in kmph is _________

1) 54 2) 603) 72 4) 36

20. If a train 110m long passes a signal pole in 3 sec. Then the time taken by it to cross arailway platform 165m long is :

1) 3secs 2) 4secs3) 7.5secs 4) 5secs

21. An Engine of 10 m length travels at 60 kmph. How long does it take to cross another train170 m long, running at 54 kmph in the same direction?

1) 16 sec 2) 16.8 sec3) 108 sec 4) none

22. Two trains starting at the same time from two stations 200 km apart and going inopposite directions cross each other at a distance of 110 km from one of the stations.What is the ratio of their speeds?

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1) 9:11 2) 11:93) 10:9 4) 9:10

23. A train M leaves Mumbai at 5am. And reaches Delhi at 9am. Another train leaves Delhi at7am. And reaches Mumbai at 11.00am. At what time do the two trains across each other?

1) 8 a.m. 2) 9 a.m.3) 7 a.m. 4) 6 a.m.

24. Train P leaves Hyderabad at 6.00am. And reaches Vijayawada at 10.00am. Train Q leavesVijayawada at 7.00am. And reaches Hyderabad at 1.00pm. At what time do the trainsmeet?

1) 8.48 a.m. 2) 8.12 a.m.3) 8.42 a.m. 4) 9.00 a.m.

25. A train running at 52kmph takes 36 seconds to pass a platform. Next it takes 24 secondsto pass a man walking at 10 kmph in the same direction. Find the length of the train andthat of the platform?

1) 800 m; 440 m 2) 280 m; 440 m3) 280 m; 240 m 4) 420 m; 300 m

26.

Two trains running in the same direction at 40 kmph and 22 kmph completely pass oneanother in 60 seconds. If the length of the first train is 125 meters, then the length ofsecond train is?

1) 125 m 2) 128 m3) 175 m 4) 900 m

27. Two trains 220 meters and 380 meters in length respectively are running in oppositedirection. One at the rate of 35 kmph and other at 25 kmph. In what time they will crosseach other?

1) 36 seconds 2) 30 seconds3) 60 seconds 4) None

28. A man misses a train by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph,then also he misses the train by 10minutes. What is the minimum speed required tocatch the train on time?


29. A boat traveled from A to B and back to A from B in 5 hours. If the speed of boat in stillwater and the speed of stream be 7.5 kmph and 1.5 kmph, then what is the distancebetween A and B?

1) 80 km 2) 45 km3) 18 km 4) 19 km

30. A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of theman in still water and the speed of stream (in kmph)

1) 13; 3 2) 15; 33) 12; 6 4) 14; 4

31. A man can row at 9 kmph in still water. He takes 4 ½ hours to row from P to Q and

back. What is the distance between P and Q if the speed of the stream is 1 kmph?1) 32 km 2) 28 km3) 20km 4) 24 km

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32. A man can row 30 km downstream in 3 hours 45 minutes, and 11 km upstream in 2hours 12 minutes. What is the speed of the man in still water and speed of stream (inkmph)?

1) 6; 2 2) 6.8; 1.83) 6.5; 1.5 4) 7; 3

33. A man rows 22 km upstream in 4 hours and 45 km downstream in 6 hours. In 10 hourshow much more distance can he row downstream than the distance he can rowupstream?

1) 24 km 2) 22 km3) 20 km 4) 18 km

34. A person can row 10 km in 1 hour in still water. If the speed of the water current is 2kmph and it takes two hours for him to go to a certain place and back. Find the distancehe traveled in upstream?

1) 9 ½ km 2) 9.6 km3) 48 km 4) 5 km

35. A person can row5

3 of a km in upstream in 10 minutes and return in 6 minutes. Find the

speed of man in still water?1) 4.4 kmph 2) 4.5 kmph3) 4.8 kmph 4) 4.9 kmph

36. A boat can travel 10 kmph in still water. It traveled 91 km downstream and thenreturned, taking altogether 20 hours. Find speed of the stream?


37. The time taken for a boat to cover certain distance in upstream is equal to the time takenby the boat to cover three times the distance in downstream. If the speed of current is 5kmph, what is the speed of boat in still water?

1) 14 kmph 2) 15 kmph

3) 10 kmph 4) 19 kmph

38. The time taken by a person to row upstream is twice the time taken by him to row thesame distance downstream. If the speed of the boat in still water is 42 kmph, find thespeed of current?


39. A man rows his boat to a certain place covering a distance of 72 km and back again in 15hours. He finds that he takes same time to row 3 km in downstream as much he takes for2 km in upstream. Find the speed of the stream?


40. A man can row 6 km/hr in still water. If the speed of stream is 2km/hr, it takes him 3hours to row to a place and back. How far is the place?

1) 16 km 2) 10 km3) 12 km 4) 8 km

Time and Work

If a person can complete a work in „n‟ days then he can do 1/n part of the work in one day.

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The amount of work done be a person in 1 day is called his efficiency.

Example:

A can do a work in 10 days. Then the efficiency of A is given by A = 1 / 10.

Note:

Number of days required to do a work = work to be done / work per day.

Example 1:

If A can do a work in 10 days, B can do it in 20 days and C in 30 days in how many days willthe three together do it?

Soln:

The efficiencies are A = 1/10, B = 1/20 and C = 1/30So work done per day by the three = 1/10 + 1/20 + 1/30 = 11/60 => No of days = 60/11 = 5.45

days.

Example 2:

If A and B can do a work in 10 days , B and C can do it in 20 days and C and A can do it in 40days in what time all the three can do it?

Soln:

A+B = 1/10B+C = 1/20C+A = 1/40Adding all the three we get 2(A+B+C) = 7/40 => A+B+C = 7/80 => No of days = 80/7 days.

Note:

If all the people do not work for all the time then the principle below can be used:

mA + nB + oC = 1. (1 is the total work)

Here, m=no of days A workedn=no of days B workedo=no of days C workedA,B,C = efficiencies

Example 3:

If A can do a work in 12 days, B can do it in 18 days and C in 24 days. All the three started thework. A left after two days and C left three days before the completion of the work. How manydays are required to complete the work?

Soln:

Let the total no of days be x.

A worked only for 2 days, B worked for x days and C worked for x-3 days.

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So, mA + nB + oC = 1 2(1/12) + x(1/18) + (x-3)(1/24) = 1 12 + 4x + 3(x-3) = 72 x = 69 / 7 days.

Note:

The ratio of dividing wages = ratio of efficiencies = ratio of parts of work done

Example 4:

A can do a work in 10 days and B can do it in 30 days and C in 60 days. If the total wages forthe work is Rs. 1800 what is the share of A?

Soln:

Ratio of wages = 1/10 : 1/30 : 1/60 = 6 : 2 : 1 (Multiplying each term by LCM 60)

So total 9 equal parts in Rs. 1800 => each part = Rs. 200 => share of A = 6 parts = Rs. 1200.

Note:

When pipes are used filling the tank they are treated similar to the men working but someoutlet pipes emptying the tank are present whose work will be considered negative.

Example 5:

A pipe can fill a tank in 5 hrs but because of a leak a the bottom it takes 1 hr extra. In whattime can the leak alone empty the tank?

Soln:

Let the filling pipe be A.

A = 1 / 5.

But with the leak L, A – L = 1 / 6 ( A-L because leak is outlet)

So, 1/L = 1 / 5 – 1/ 6 = 1/30 => Leak can empty the tank in 30 hrs.

Example 6:

A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All areopened at the same time. After how many hours shall the pipe B be closed such that the tank

can be filled in 10 hrs?

Soln:

Let the pipe B be closed after x hrs.

Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs.

mA + nB – oC = 1 (since C is outlet)

10(1/10) + x(1/20) – 10(1/40) = 1

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x = 5 hrs.

Exercise:1. A alone can complete the work in 12 days while A and B together can complete the same

work in 8 days. The number of days that B will take to complete the work alone is

___________1) 10 2) 243) 20 4) 9

2. A can do a work in 6 days and B in 9 days. How many days will both take together tocomplete the work.

1) 7.5 2) 5.43) 3.6 4) 3

3. A can do a piece of work in 4 hours, B and C can do it in 3hrs, A and C can do it in 2hrs.How long will B alone take to do it?

1) 10hrs 2) 12hrs3) 8hrs 4) 24hrs

4. 10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100days. In how many days will a woman finish the work?

1) 125 2) 1503) 90 4) 225

5. A completes a work in 12 days; B completes the some work in 15 days. A started workingalone and after 3 days B joined him. How many days will they now take together tocomplete the remaining work?

1) 5 2) 83) 6 4) 4

6. 10 men can complete a piece of work in 15 days & 15 women can complete the same work

in 12 days. If all the 10 men & 15 women work together, in how many days will the work getcompleted?

1) 6 2)3

27

3)3

26 4) None of these

7. A can do a certain work in the same time in which B & C together can do it. If A and Btogether could do it in 10 days and C alone in 50 days then B alone could do the work in

1) 15 days 2) 20 days3) 25 days 4) 30 days

8. A& B under took to do a piece of work for Rs.4,500. A alone could do it in 8 days and B

alone in 12 days. With the assistance of C they finished the work in 4 days. Then C‟s shareof the money is ____________1) Rs.2,250 2) Rs.1,5003) Rs.750 4) Rs.375

9. A can finish a work in 24 days, B in 9 days and C in 12 days. B & C start the work but areforced to leave after 3 days. The remaining work is done by A in _____________

1) 5 days 2) 6 days

3) 10 days 4)2

110 days

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10. If 3 men (or) 4 women can plough a field in43 days, how long will 7 men and 5 women taketo plough it.


11. A can doth

4

3 of a work in 12 days. In how many days can he finish

th

8

1 of work?

1) 1 day 2) 2 days3) 4 days 4) 8 days

12. If 72 men can build a wall 280m. long in 21 days, how many men will take 18 days to builda similar type of wall of length 100m.?

1) 30 2) 103) 18 4) 28

13. A takes twice as much time as B or thrice as much time as C to finish a piece of work.Working together, they can finish the work in 2 days. B can do the work alone in


14.

A does54 of a piece of work in 20 days; he then calls in B and they finish the remaining

work in 3 days. How long will B alone take to do the whole work?

1)2

137 days 2) 37 days

3) 40 days 4) 23 days

15. A does half as much work as B in 1/6 of the time. If together they take 10 days to completea work, how many days shall B take to do it alone?


16. A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone

can do it in 6 days and a boy alone can do it in 18 days, how long will a woman alone taketo complete the work.


17. If the wages of 6 men for 15 days be Rs.700, then the wages of 9 men for 12 days will be ___________

1) Rs.700 2) Rs.8403) Rs.1050 4) Rs.900

18. A man is paid Rs.20 for each day he works, and forfeits Rs.3 for each day he is idle. At theend of 60 days he gets Rs.280. Then he was idle for _____________

1) 20 days 2) 25 days

3) 30 days 4) 40 days

19. A team of 10 men can complete a particular job in 12 days. A team of 10 women cancomplete the same job in 6 days. How many days are needed to complete the job if the twoteams work together?

1) 4 2) 63) 9 4) 18

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20. A contractor undertook to finish a certain work in 124 days and employed 120 men on it.

After 64 days, he found that he had already donerd

3

2of the work. How many men he can

discharge now so that the work may finish in time1) 24 2) 563) 64 4) 80

21.

A work could be completed in 100 days. However, due to the absence of 10 workers, it wascompleted in 110 days. The original number of workers was ___________1) 100 2) 1103) 55 4) 50

22. A contractor under takes to make a road in 40 days and employs 25 men. After 24 days, hefinds that only one-third of the road is made. How many extra men should he employ sothat he is able to complete the work 4 days earlier?

1) 100 2) 603) 75 4) none of these

23. 30 men complete one third of a work in 30 days. How many more men should be employedto finish the rest of the work in 40 more days?

1) 15 2) 453) 20 4) 25

24. A and B under took to do a piece of work for Rs.900. A alone could do it in 60 days and B in30 days. If A & B work together and complete the work, then the share of B _______

1) Rs.600 2) Rs.4003) Rs.300 4) Rs.200

25. 5 men or 6 women or 10 boys can do a work in 15 days. How long will it take to completethe work by a group of 5 men, 6 women and 10 boys?


26.

A can do a piece of work in 30 days. B in 15 days and C in 10 days. They started the workall together but B put

2

1 time daily and C put

3

1 time daily to help A in doing the work. The

work will last in ______________1) 30 days 2) 10 days3) 20 days 4) 25 days

27. A can do a work in 15 days & B the same work in 12 days. B started the work and was joined by A, 5 days before the end of work. The work lasted for _____ days.

1) 8 2) 123) 13 4) 24

28.

A and B can do a piece of work in 40 days while C & A can do it in 60 days. If B is twice asgood as C, then C alone will do the work in ___________ days.

1) 120 2) 1003) 80 4) 24

29. A hostel has provision for 800 men for 24 days at the rate of 2 kg per man per day. For howmany men is the provision sufficient, for 20 days at the rate of 1.5 kg per man per day?

1) 1280 2) 10003) 1820 4) 1240

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30. 12 men can do a work in 15 days working 8 hours a day. In how many days can 9 men dothe same work, working 10 hours a day?

1) 10 2) 163) 18 4) 24

31. Two taps A and B can separately fill a tank in 20 and 30 hours respectively. If both thepipes are opened simultaneously, how much time will be taken to fill the tank?

1) 10 hrs 2) 11 hrs3) 18 hrs 4) 12 hrs

32. A tap can fill a tank in 12 minutes and another tap in 15 minutes, but a third tap canempty it in 6 minutes. The three taps are kept open together. Find when the cistern isemptied or filled?

1) 60 min. to fill 2) 30 min. to fill3) 60 min to empty 4) 30 min to empty

33. Two taps A & B can fill a cistern in 12 and 16 minutes respectively. Both fill taps areopened together, but 4 minutes before cistern is full, one tap A is closed. How much timewill the cistern take to fill?

1) 9 1/7 min. 2) 3 1/7 min.3) 11 1/7 min. 4) None.

34. A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 minutes.80 tonnes would suffer to sink her, but the pumps can throw out 12 tonnes an hour. Findthe average rate of sailing that she may just reach the shore as she begins to sink.

1) 5.5 kmph 2) 2.5 kmph3) 1.8 kmph 4) 4 kmph

35. A tap can fill a swimming pool in h hours. What part of the pool is filled in y hours?

1) yh 2) y

h

3)

h

y 4) h – y

36. Three pipes A, Band C can fill a tank in 30 min, 40 min and 60 min respectively. A and Bwork in alternative minutes, A beginning the work whereas C works continuously. In howmany minutes will the tank be filled?

1) 16.4 2) 21.83) 18.2 4) 19.6

37. A tank has a leak, which would empty it in 8 hrs. A tap is turned on which admits 6 litresof water a minute into the tank and it is now emptied in 12 hrs. How many litres does thetank hold?

1) 8640 2) 84603) 8064 4) 8406

38. A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill becauseof a leak in its bottom. If the cistern is full, then the leak will empty the cistern in

1) 20 hours 2) 40 hours3) 50 hours 4) 30 hours

39. Two pipes A and B can separately fill a cistern in 60 and 75 minutes respectively. There is athird pipe at the bottom of the cistern to empty it. If all the three pipes are simultaneouslyopened, then the cistern is full in 50 minutes. In how much time can third pipe alone emptythe cistern?

1) 110 minutes 2) 100 minutes

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40. A tap can fill a tank in 6 hours. After half the tank is filled, three more similar taps areopened. What is the total time taken to fill the tank completely?

1) 4 hours 2) 4 hours 15 minutes3) 3 hours 15 minutes 4) 3 hours 45 minutes

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Mensuration

Types of Plane Figures

1. Triangle2. Quadrilateral3. Polygon4. Circle5. Sector of a circle6. Rectangular Paths7. Circular paths

I. Triangle

(a). Any triangle

a, b and c are three sides of the triangle; h isthe altitude and AC is the base.

Perimeter (P) : P = a + b + c = 2s

Area (A) : A = 2

1 base altitude =2

1 any side

length of r dropped on that side =)cs()bs()as(s

(b). Equilateral

a is the length of each side

Perimeter (P) : P = 3a

Area (A) : A =4

3 a2

(c). Right-angled

b, c are the lengths of the two legs

Perimeter (P) : P = a + b + c = 2s

Area (A) : A = 2

1 product of two legs

(d). Isosceles

B

A C

a

a

a

B

A C

a

b

c

90o

B

A C

a

D

a

b/2b/2

B

A C

a

b

ch

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a is the length of two equal sidesb is the baseBD is the perpendicular dropped on base such that it divides the base equally AD =

CD =2

b

Perimeter (P) : P = 2a+b

Area (A) : A = 22 ba44

b

(e). Right-angled Isosceles

Perimeter (P) : P = 2 a ( 2 +1)

Area (A) : A = 2

1 (a)2

II. Quadrilateral

(a). Any Quadrilateral

AC is the diagonal = d, DE and BF are twoperpendicular drawn on the diagonal (AC) P1,and P2 are the lengths of the two perpendiculars

Perimeter (P) : P = sum of the four sides.

Area (A) : A = 2

1

d (p1+p2) = 2

1

any diagonal (sum of rs drawn on that diagonal)

(b). Rectangle

l = lengthb = breadthd = diagonal

Perimeter (P) : P = 2(l + b) =

2(l+ 22 ld ) = 2(b+Error! Objects

cannot be created from editing field

codes.) = 2 A2d2

Area (A): A = l b = l 22 ld = b Error! Objects cannot be created from editing

field codes., when p and A are known and l and b are unknown.

d

AB

C

D

E

F

P

P

d

A B

CD

b b

l

l

O

Hypotenuse - h

a

a

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The two values of x will give l and b.

(c). Square

a = length of side

d = diagonal

Perimeter (P) : P = 4a = 2d 2

Area (A) : A = a2 =16

p=

2

d 22

(d). Rhombus

a = each sided1 = one diagonald2 = another diagonalh = height

Perimeter (P) : P = 4a = 2 22

21 dd

Area (A) : A = 2

1 d1 d2 =2

121

2

da

2

d

=

2222

2

da

2

d

= a h

(e). Trapezium

a and b are two parallel sides, h is the height

Area (A) : A = 2

1

(a + b) h = 2

1

(sum ofparallel sides) (perpendicular distancebetween parallel sides)

(f). Parallelogram

b is the baseh is the perpendicular distance between the baseand its opposite side

Area (A) : A = b h = base (perpendiculardistance between the base and its opposite sides)

= 2 area of Δ ABD (or Δ BCD)

III. Polygon

Polygon is a n-sided closed figure bounded only by line segments.

In a polygon if the internal angle at each vertex is less than 180o then the polygonis a convex polygon, else a concave polygon.

D

A B

C

d

O

a

a

a

a

90

oa

90oa

A B

C

D

a

b

h

A B

C

D

b

h

A B

C

D

a

a

a

a

d

O

90o

90o

d

h

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Convex Polygon:

i. Area of a regular polygon =2

1 perimeter r distance from the center of the

polygon to any side.

ii. Number of diagonals in a polygon =2

)3n(n

iii. Sum of all interior angles of a polygon = (2n-4) 90o

iv.

Each interior angle of n-sided regular polygon =

n

2n 180o

v. Sum of all exterior angles of n-sided regular polygon = 360o

vi. Each exterior angle of n-sided regular polygon =n

360

IV. Circle

O is the center of the circle

OA = OC = OB = OD = radius of circle = r

AC = BD = diameter of circle = d = 2r

Circumference (or Perimeter) C = 2π r = πd

Area of circle A = π r2 = π4

d2

If C = circumference, A = area then

A =2

r

C

Aand

π4

C2

V. Sector of a circle

Area of sector AOB = 2o

rπ360

θ

Length of the Arc AB = rπ2360

θ

o

VI. Rectangular Paths

θ

A B

O

W

A

B

C

D

O

K

N

M

L

D

A

B

C

L

Rectangle Path

way

Case - I

K

N

M

L

D

A

B

C

L

W

Case - II

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Case - I

Pathway is outside the rectangle

The length of rectangle AB = l, Breadth BC = b and , Width of path way = W,

then

Area of Pathway = 2W (l+b+2w) (shaded portion)

Case – II

Path way is inside the rectangle

Area of Pathway = 2W(l+b-2W) (shaded portion)

VII. Circular Pathway

OAC is a circle of radius = r, there is pathway, outside the circle of width = W

Area of circular pathway = π W (2r+W)

When, the pathway is inside the circle,

Area of circular pathway = π W (2r - W)

Examples:1.

If three sides of a triangle are 5, 6 and 7 cm respectively, find the area oftriangle.

Sol: Area of = s(s a)(s b)(s c

W r

A

O

C

A

r

C

W

O

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Now, s = a b c 5 6 7

2 2

= 9

Area = 9 (9 5)(9 6)(9 7) 9 4 3

= 216 6 6 cm2.

2.

ABC is an equilateral triangle of side 24 cm. Find the in radius of thetriangle.

Sol: In a equilateral triangle, the altitude, median and perpendicular areequal.

AD = 3 /2 x 24 = 12 3

GD (in radius) = 1/3 x 12 3 = 4 3 cm

3. The base and other side of an isosceles triangle is 10 and 13 cm

respectively. Find its area.

Sol: Area of Isosceles = 2 2b4a b

4

Given, base b = 10 Other side a = 13

Area (A) = 2 210 104 (13) 10 676 100

4 4

= 10

4 24 = 60 cm2.

4.

In a right-angled triangle, the length of two legs are 12 and 5 cm. Find thelength of hypotenuse and its area.

Sol: In a right angled triangle,(Hypotenuse)2 = (one leg)2 + (other leg)2

= 122 + 52

Hypotenuse = 2 212 5 = 169 = 13 cm.

In a right angled triangle,

Area = 1 21 1

(leg) (leg) 12 52 2

= 30 cm2.

5. If the perimeter and diagonal of a rectangle and 14 and 15 cm respectively.Find its area.

Sol: In a rectangle,

2(Perimeter)

4 = (diagonal)2 + 2 x Area ;

2(14)

4= (5)2 + 2 x Area

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2 x Area = 196

4 - 25 Area = 49 25

2

= 12 cm2.

6. Find the length of the diagonal and the perimeter of a square plot if its areais 900 square metres.

Sol: In a square, A =2 2d p

2 16

(Diagonal)2 = 2 x Area = 900 Diagonal (d) = 2 900 30 2 = 42.42 metres

(Perimeter)2 = 16 x Area = 16 x 900

Perimeter (P) = 16 900 = 120 metres.

7.

A field in the shape of a rhombus has the distances between pairs ofopposite vertices as 14 m and 48 m. What is the cost (in rupees) of fencing

the field at Rs.20 per metre?

Sol: The diagonals are 14 m and 48 m

Sides of rhombus =2 2

14 48625

2 2

= 25

Perimeter of rhombus = 4 x 25 = 100 m.Cost of fencing the field = 100 x 20 = Rs.2000

8. In a trapezium, the length of parallel sides are 20 and 25 metresrespectively and the perpendicular distance between the parallel sides is 12metres. Find the area of trapezium.

Sol: One parallel side a = 20 metres. Second parallel side b = 25 metres.Height (perpendicular distance between a and b) = 12 metres.

Area = 1 1(a b) h (20 25) 12

2 2 = 270 m2.

9.

The distance between a pair of opposite vertices of a quadrilateral is 32units. The lengths of the perpendiculars drawn on to this diagonal from theother two vertices are 4 1/3 units and 6 2/3 units respectively. Find thearea (in sq units) of the quadrilateral?

Sol: Area of quadrilateral = 1/2 x 32 x 13 20

3 3

= 178 sq units.

A B

DC

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10.

In the above parallelogram ABCD, A = x + 30o and D = x – 40o, what is themeasure of DCB ?

Sol: In a parallelogram, sum of adjacent angles is equal to 180o

x + 30 + x – 40 = 180 x = 95o DAB = x + 30 = 95 + 30 = 125o

DCB = DAB = 125o (opposite angles of a parallelogram are equal)

11. In a circle of radius 49 cm, an arc subtends an angle of 36o at the centre.Find the length of the arc and the area of the sector.

Sol: Length of the arc = 2 r 2 22 49 36

360 7 360

θ

= 30.8 cm

Area of the sector =2r 22 49 49 36

360 7 360

θ

= 754.6 cm2

12.

A rectangular plot of dimensions 13 m x 17 m is surrounded by a garden ofwidth 5 m. What is the area (in sq m) the garden?

Sol: Let ABCD be the rectangular plot of given dimension. The shaded partis the surrounding garden. Now, the plot ABCD together with the gardenforms another rectangular form PQRS. Dimensions of PQRS, as can be seenfrom the diagram, are:

Length PQ = width of garden + AB + width of garden= 5 + 17 + 5 = 27 m

Similarly, breadth = PS = 5 + 13 + 5 = 23 mArea of garden = Area of PQRS – Area of ABCD

= (27 x 23) – (17 x 13) = 621 – 221 = 440 sq m.

13. There is a rectangular field of length 100 m and breadth 40 m. A carpet of 2m width is to be spread from the centre of each side to the opposite side.What is the area of the carpet?

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5. Find the area of a triangle whose sides are 66 cm, 88 cm and 1.1 m.1. 2640 sq cm 2. 2904 sq cm 3. 2940 sq cm 4. 1452 sq cm

6. Area of an equilateral triangle is 16 3 sq cm, Find its perimeter.1. 12 cm 2. 48 cm 3. 24 cm 4. 16 cm

7. What is the height of an equilateral triangle if its side is 8 3 cm?

1. 6 cm 2. 8 cm 3. 24 cm 4. 12 cm

8. In a quadrilateral, the length of its diagonals is 12 cm and the offsets drawn onthis diagonal measure 13 cm and 7 cm respectively. Find its area.1. 546 m2 2. 273 m2 3. 60 m2 4. 120 m2

9. In a parallelogram, the lengths of adjacent sides are 11 m and 13 mrespectively. If the length of one diagonal is 16 m, find the length of otherdiagonal.1. 18 m 2. 96 m 3. 18 m 4. 40 m

10. The two adjacent sides of a parallelogram are 12 m and 14 m respectively, andif the diagonal connecting the ends is 22 m respectively, find the area of theparallelogram.1. 151.87 m2 2. 115.78 m2 3. 151.78 m2 4. 115.87 m2

11. The base and the height of a parallelogram are 25 cm and 20 cm respectively.Find its area.1. 500 sq cm 2. 250 sq cm 3. 45 sq cm 4. 125 sq cm

12. If the perimeter and diagonal of a rectangle and 14 cm and 5 cm respectively.Find its area.1. 6 cm2 2. 19 cm2 3. 12 cm2 4. 9

cm2

13. The area and the perimeter of a rectangle are 84 m2 and 38 m respectively. Findits length and breadth.1. 12 m, 7 m 2. 14 m, 6 m 3. 42 m, 19 m 4. None

14. A rectangular grass field is 112 m x 78 m. It has a gravel path 2.5 m wide allround it on the inside. Find the area of gravel path.1. 8736 sq m 2. 925 sq m 3. 4368 sq m 4. 952 sq m

15. A rectangular lawn 70 m x 30 m has two roads each 5 m wide, running in themiddle of it, one parallel to the length and the other parallel to the breadth.Find the cost of gravelling the road at the rate of Rs.4 per sq m.1. Rs.1000 2. Rs.2700 3. Rs.1700 4. Rs.2100

16. The length of a rectangle is increased by 20% and the breadth is decreased by30%. Find the percentage change in its area.

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1. 10% increase 2. 16% decrease3. 8% decrease 4. 16% increase

17. The length and the breadth of a rectangle are in the ratio of 15 : 8 and itsperimeter is 230 cm. Find its area.1. 3000 sq cm 2. 2300 sq cm 3. 1500 sq cm 4. 6000 sq cm

18. There is a path of 1 m width around the outside of a rectangular field of 98 m x48 m. Find the area of the path.1. 148 sq m 2. 296 sq m 3. 598 sq m 4. 2352 sq m

19. The breadth of a rectangle is 4/5th of its length and its area is 720 sq cm. Findits length.1. 15 cm 2. 30 cm 3. 60 cm 4. 576 cm

20. The sides of a rectangle are in the ratio 4 : 3 and its area is 768 sq m. Find itsperimeter?

1. 56 m 2. 112 m 3. 96 m 4. None

21. The perimeter of a rectangle is 216m. If its sides are in the ratio 5 : 4 the area is _______1. 1140 sq m 2. 2880 sq m 3. 960 sq m 4. 1260 sq m

22. The sides of rectangular garden are 75 m x 48 m. What is the perimeter of asquare with same area?1. 60 m 2. 120 m 3. 240 m 4. None

23. Find the length of the diagonal of a square plot if its area is 900 sq m.

1. 10 2 m 2. 15 2 m 3. 30 2 m 4. 9 2 m

24. Find the perimeter of a square plot if its area is 1600 sq m.1. 80 m 2. 160 m 3. 320 m 4. 40 m

25. Find the ratio of area and the perimeter of a square of side 8 cm.1. 1 : 2 2. 4 : 1 3. 3 : 1 4. 2 : 1

26. Find the diagonal of a square whose perimeter is 128 2 sq m.1. 64 m 2. 32 m 3. 32 2 m 4. 64 2 m

27. The perimeter of a square is 88 cm. Find its area.1. 484 sq cm 2. 174 sq cm 3. 242 sq cm 4. None

28. There is a square shaped grass lane of 14 m side. Four cows are tethered withthe ropes of 3.5 m length each at one corner. Find the area of the grass laneover which the cows are unable to graze the grass.1. 157.5 sq m 2. 38.5 sq m 3. 175.5 sq m 4. 157.7 sq m

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29. The area of two squares is in the ratio of 16 : 49. Find the ratio of theirdiagonals.1. 7 : 4 2. 49 : 16 3. 4 : 7 4. None

30. If an error of 10% excess in made in calculating the side of square the % errorin its area is ___________

1. 20 2. 21 3. 22 4. None

31. The area of a square garden is 576 sq m. What is the cost of fencing, it at the rateof Rs.1.25 per m?

1. Rs.24 2. Rs.50 3. Rs.90 4. None

32. The area of a square garden is 625 sq m. What is the area of a path of width 2.5m around it, if the path is outside the garden?

1. 900 sq m 2. 275 sq m 3. 30 sq m 4. None

33. The diagonal of a square is 24 m. Its area is __________

1. 144 sq m 2. 576 sq m 3. 288 sq m 4. None

34. In a rhombus, the lengths of the two diagonals are 40 m and 30 m respectively.Find its area and perimeter.1. 600 sq m, 100 m 2. 100 sq m, 600 m3. 1200 sq m, 600 m 4. 600 sq m, 200 m

35. In a rhombus the side and one of its diagonals are 25 m and 40 m respectively.Find its perimeter.1. 50 m 2. 100 m 3. 200 m 4. 10 m

36. The side and one of the diagonals of a rhombus are 25 cm and 14 cmrespectively. Find its area.1. 350 sq cm 2. 390 sq cm 3. 168 sq cm 4. 336 sq cm

37. The diagonals of a rhombus are in the ratio of 8 : 3 and area is 432 sq cm., Findits diagonals.1. 18 : 48 2. 3 : 8 3. 48 : 18 4. None

38. If the side and the height of a rhombus are 12 m and 30 m respectively. Findthe cost of painting both the surfaces of an aluminum sheet of same shape and

size at the rate of Rs.5 per sq m.1. Rs.1200 2. Rs.3600 3. Rs.3000 4. Rs.4200

39. The cross-section of a canal is a trapezium in shape. If the canal is 7 m wide atthe top and 9 m at the bottom and the area of cross-section is 128 sq m, findthe height of the canal.1. 32 m 2. 8 m 3. 4 m 4. 16 m

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40. The parallel sides of a trapezium are 18 cm and 22 cm and the distancebetween them is 10 cm. Find its area.1. 100 sq cm 2. 250 sq cm 3. 200 sq cm 4. 150 sq cm

41. Find the area of a triangle having sides 3 m, 4 m and 5 m.

1. 60 sq m 2. 10 sq m 3. 12 sq m 4. 6 sq m

42. Find the area of a triangle whose base is 4.6m and height is 67 cm.1. 154.10 sq m 2. 15410 sq m 3. 15.410 sq m 4. None

43. Find the area of an equilateral triangle each of whose sides measures 6 cm.1. 36 sq cm 2. 3 3 sq cm 3. 9 3 sq cm 4. 12 sq cm

44. Length of the side of an equilateral triangle is3

4 cm. Find its height.

1. 2 cm 2. 4 cm 3. 6 cm 4. None

45. Height of an equilateral triangle is 4 3 cm. Find its area.

1. 4 3 sq cm 2. 2 3 sq cm 3. 16 3 sq cm 4. 8 3 sq cm

46. An isosceles right-angled triangle has two equal sides of length 6 m each. Findits area1. 8 sq m 2. 36 sq m 3. 18 sq m 4. None

47. The perimeter of an isosceles triangle is 80 cm. If the length of the equal sides isgiven by 0.15 m, find the length of the base.1. 40 m 2. 50 m 3. 12 m 4. 90.5 m

48. The perimeter of an isosceles triangle is 42 cm. If the base is 16 cm, find thelength of equal sides.1. 13 cm 2. 8 cm 3. 21 cm 4. 29 cm

49. The two adjacent sides of a parallelogram are 5 m and 6 m respectively, and ifthe diagonal connecting the ends is 9 m, find the area of the parallelogram(approximately).1. 29 sq m 2. 28 sq m 3. 58 sq m 4. 50 sq m

50. Find the area of a quadrilateral of whose diagonal is 38 cm long and the lengths

of perpendiculars from the other two vertices are 31 cm and 19 cm,respectively.1. 950 sq cm 2. 475 sq cm 3. 138 sq cm 4. 276 sq cm

51. Find the area of a parallelogram whose two adjacent sides are 130 m and 140 mand one of the diagonals is 150 m long.1. 8400 sq cm 2. 16,800 sq cm 3. 2100 sq cm 4. None

52. Find the diagonal of a rectangle whose sides are 8 cm and 6 cm.

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1. 14 cm 2. 5 cm 3. 20 cm 4. 10 cm

53. Find the perimeter of a rectangle of length 12 m and breadth 6 m.1. 18 m 2. 72 m 3. 36 m 4. 144 m

54. Calculate the area of a rectangular field whose length is 12.5 cm and breadth is

8 cm.1. 10 sq cm 2. 100 sq cm 3. 200 sq cm 4. 1 sq cm

55. Calculate the area of a rectangular field whose one side is 16 cm and thediagonal is 20 cm.1. 192 sq cm 2. 96 sq cm 3. 294 sq cm 4. 72 sq cm

56. A rectangular carpet has an area of 120 sq m and perimeter of 46 m. Find thelength of its diagonal.1. 34 m 2. 51 m 3. 93 m 4. 17 m

57. The perimeter of a rectangle is 82 cm and its area is 400 sq m. Find the length

of the rectangle.1. 8 m 2. 16 m 3. 32 m 4. 64 m

58. If the area of a square field be 6050 sq m, find the length of its diagonal.1. 220 m 2. 110 m 3. 55 m 4. None

59. Find the area of a square with perimeter 48 m.1. 288 sq m 2. 72 sq m 3. 144 sq m 4. 96 sq m

60. Find the diagonal of a square field whose side is of 6 m length.

1. 12 2 m 2. 6 2 m 3. 2 m 4. 3 2 m61. Perimeter of a square field is 16 2 cm. Find the length of its diagonal.

1. 16 cm 2. 4 cm 3. 8 cm 4. 64 cm

62. The area of a rhombus is 156 sq m. If one of its diagonals is 13 m, find thelength of the other diagonal.1. 12 m 2. 6 m 3. 48 m 4. 24 m

63. Find the area of a rhombus whose one side is 13 cm and one diagonal is 24 cm.1. 60 sq cm 2. 120 sq cm 3. 240 sq cm 4. 74 sq cm

64. If the perimeter of a rhombus is 73 cm and one of its diagonals is 27.5 cm, findthe other diagonal and the area of the rhombus.1. 24 cm, 330 sq cm 2. 20 cm, 115 sq cm 3. 30 cm, 660.8sq cm 4. 40 cm, 100.5 sq cm

65. In a rhombus, the lengths of two diagonals are 18 m and 24 m. Find itsperimeter.1. 15 m 2. 30 m 3. 60 m 4. 120 m

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66. The diagonally of Rhombus are 12 cm and 5 cm respectively. Find the side of

the Rhombus.1. 5 cm 2. 6.5 cm 3. 6 cm 4. 8.5 cm

67. What is the radius of a circular plot whose circumference is 176 m?

1. 14 m 2. 56 m 3. 88 m 4. 28 m

68. A circular plot covers an area of 154 sq m. How much wire is required forfencing the plot?1. 44 m 2. 22 m 3. 88 m 4. 77 m

69. Find the area of sector of a circle whose radius is 10 cm and the angle at thecenter is 36o.

1. 307

3 sq cm 2. 313

7 sq cm 3. 303

7 sq cm 4. 317

3 sq cm

70. Find the area of sector of a circle whose radius is 12 cm and the length of the

arc is 20 cm.1. 60 sq cm 2. 240 sq cm 3. 120 sq cm 4. 64 sq cm

Cuboid :

A right prism with a rectangular base is called a Cuboid.

The sides of the base are length (l) and breadth (b). The heightis h.

Lateral Surface Area = 2h(l + b)

Total Surface Area = 2h(l + b) + 2lb = 2(lb + bh + hl)Longest diagonal = 222 hbl Volume = lbh

Cube:

If the length, breadth and height of a cuboid are all equal, it iscalled a cube.

Then, if edge of the cube = a

Longest diagonal =3

aLateral Surface Area = 6a2 Total surface Area = 6a2 Volume = a3

Cylinder :

A cylinder can be considered to be a right prism except that insteadof identical polygons a cylinder has identical circles for its top and

hl

b

a

aa

r

h

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base and it has a single lateral surface also called curved surface, instead ofseveral rectangular surfaces. The basic measurements are the radius of the base (or top) r and the height h.

Curved Surface (Lateral Surface Area) = 2π rh Total surface Area = 2π rh+2 π r2 = 2π r(h + r)

Volume = π r2

h

Hollow Cylinder:

The cross section of a hollow cylinder is aring.Volume of the material of a hollow cylinder =πh(R2-r2)Here R is outer radius and r is inner radiusof the hollow cylinder.

Cone:

A cone can be formed from the sector of a circle by rolling it and joining together its two straight edges. If r is the radius of thecone, and R is the radius of the sector of angle θ , then

1. r = R360

θ

2. Relation between r, l and h. (the radius, the slant heightand height) is l2 = h2+r2

3. Curved Surface area of Cone = prl

4. Total Surface Area = π rl + π r2 = π r(l + r)

5. Volume =3

1π r2h

Sphere:

All points on the surface of a sphere are at the samedistance from the center of the sphere. This distance iscalled the radius, r.

Surface Area of Sphere = 4 π r2

Volume of a Sphere =

3

4 π r3

The sphere has only one surface and hence only one sur face area.

Hemisphere:

The radius is r.

r

R

h

h

r

r

r

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Curved Surface Area = 2 π r2 Total Surface Area = 2 π r2+π r2 = 3π r2

Volume =3

2rπ

3

4

2

1 3 π r3

Examples:

1. A cuboid is 20 m x 10 m x 8 m. Find the length of diagonal, surface area andvolume.

Sol: In a cuboid ,

Diagonal d = 2 2 2l b h = 2 2 220 10 8 = 23.75Surface are S = 2 (20 x 10 + 10 x 8 + 8 x 20) = 880 m2 Volume = l x b x h = 20 x 10 x 8 = 1600 m3.

2. A cube has edge 12 m. Find its length of diagonal, surface area and volume.

Sol: In a cubeDiagonal d = Edge x 3 = 12 x 3 = 20.78 mSurface area S = 6 x (Edge)2 = 6 x (12)2 = 864 m2 Volume V = Edge3 = (12)3 = 1728 m3.

3. The base of a right prism is a regular pentagon of side 18 cm. If the height ofthe prism is 2/3rd of the side of the base, how much is the lateral surface area(in sq cm) of the prism?

Sol: Perimeter of the base of the prism= number of sides x length of each side= 5 x 18 = 90 cm.

Lateral surface area of a right prism = (Base perimeter) x (height)

= (90) 218

3

= 1080 sq cm

4. If the radius of a sphere is increased by 50%, find the increase percent involume and the increase percent in the surface area.

Sol: Let original radius = R. Then new radius = 150 3RR

100 2 .

Original volume = 34R

3 , New volume

334 3R

9 R3 2

.

Increase % in volume = 33

19 3R 100

6 4 R

% = 237.5%

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Original surface area = 4 R2. New surface area =2

23R4 9 R

2

.

Increase % in surface area =2

2

5 R100

4 R

% = 125%.

5. A cylinder with base radius of 8 cm and height of 2 cm is melted to form a coneof height 6 cm. Find the radius of the cone?

Sol: Let the radius of the cone be r cm.

Then, 2 21 8 8 2 3r 6 8 8 2 r

3 6

= 64 r = 8 cm.

6. A brick measures 10 cm x 5 cm x 3 cm. How many bricks will be required for awall of 100 metre long 6 metre high and 1.5 metre thick?

Sol: Volume of the wall = 100 m x 6 m x 1.5 m = 900 m3

Volume of one brick = 31 1 3 3m m m m

10 20 100 20000

No. of bricks required =3900m

3 = 60,00,000

3

20000m3

7. What is the maximum length of a pencil which can be inscribed in a box oflength 24 units, breadth 3 units and height 4 units?

Sol: Maximum length in a cuboid is its diagonal

Length of main diagonal is 2 2 2length breadth height

= 2 2 2

24 3 2 576 9 4 589 units

8. The height and base-radius of a right circular cone are 10 cm and 24 cmrespectively. What is the area of the curved surface area (in sq cm) if the cone?

Sol: Curved surface area of a cone = rl,

R and l being radius and slant height.It is given that height h = 10 cm and radius = 24 cm.

L2 = h2 + r2 = 102 +242 l = 26 (10 and 24 are in the ratio of 5 : 12; hence l will be the 2 x 13 = 26

Hence, curved surface area = rl = x 24 x 26 624 sq cm.

Exercise:

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1. The surface area of cube is 96 sq cm. Find its volume.1. 48 cm3 2. 64 cm3 3. 16 cm3 4. 32 cm3

2. The volume of a cube is 125 cm3. Find its surface area.1. 25 cm2 2. 375 cm2 3. 150 cm2 4. 250 cm2

3. The diagonal of a cube is 3 cm. Find its surface area.1. 12 cm2 2. 102 cm2 3. 18 cm2 4. 36 cm2

4. A cube of 6 cm side melted and smaller cubes of 2 cm side are manufactured.Find the number of smaller cubes so formed.1. 12 2. 27 3. 24 4. 8

5. Two cubes have their volumes in the ratio 8 : 27. The ratio of their surface areasis ___________1. 2 : 3 2. 9 : 4 3. 2 : 9 4. 4 : 9

6. A cube of side 6 cm is cut into a number of cubes, each of side 3 cm. Find the

number of cubes.1. 8 2. 9 3. 24 4. 5

7. The percentage increase in the surface area of a cube when each side is doubledis ______________1. 100% 2. 200% 3. 300% 4. 400%

8. How many bullets can be made out of a cube of lead whose edge measures 22cm each bullet being 2 cm in diameter?1. 5324 2. 2662 3. 1347 4. 2541

9. The maximum length of a pencil which can be accommodated in a cubical boxof 10 cm side.1. 10 3 cm 2. 5 3 cm 3. 20 3 cm 4. 100 3 cm

10. The length, breadth & height of a cuboid are in the ratio of 4 : 3 : 2 and itsvolume is 3000 m3. Find its surface area.1. 1300 m2 2. 1500 m2 3. 1333 m2 4. 27000 m2

11. Two cubes each with 6 cm edge are joined end to end. The surface area of theresulting cuboid is ___________1. 360 cm2 2. 36 cm2 3. 216 cm2 4. 360 m2

12. Find the area of the four walls of a room of 6 m x 4 m x 3 m.1. 120 m3 2. 84 m3 3. 42 m3 4. 60 m3

13. The dimensions of a room are 200 m x 15 m x 10 m. What is the cost ofpainting its four walls at the rate of Rs.15 per 100 sq m?1. Rs.70 2. Rs.105 3. Rs.225 4. None

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14. The dimensions of a room are 16 m x 10 m. There are 2 doors 5 m x 4 m and 4

windows 5 m x 2.5 m. What is the cost of painting the wall and the top at thecost of Rs.1.50 per 10 sq m?1. Rs.96 3 Rs.112.5 3. Rs.126 4. None

15. A well with 14 m inside diameter is dug 10 m deep. Earth taken out of it hasbeen evenly spread all around it to a width of 21 m to form an embankment. The height of the embankment is ____

1.2

1 m 2.3

2 m 3.4

3 m 4.5

3 m

16. The radius and height of a cylinder are 6 cm & 14 cm respectively. Find theratio of its curved surface area and volume.1. 1584 : 528 2. 36 : 196 3. 528 : 1584 4. None

17. The radius and height of a cylinder are in the ratio of 2 : 1 and its volume is616 cubic cm. Find its curved surface area.1. 1848 cm2 2. 627 cm2 3. 612 cm2 4. 672 cm2

18. The radii of two cylinders are in the ratio 2 : 3 and the heights are in the ratio of3 : 4. Find the ratio of their volumes.1. 4 : 3 2. 3 : 1 3. 1 : 3 4. 6 : 12

19. A cylinder of radius 2 cm is melted and 11 cubes of 2 cm side aremanufactured. Find the height of the cylinder melted.1. 7 cm 2. 15 cm 3. 44 cm 4. 11 cm

20. Two circular cylinders of equal volumes have their heights in the ratio 2 : 1. Theratio of their radii is _________

1. 2 : 1 2. 1 : 2 3. 1 : 2 4. 2 : 1

21. If the radius of the base of a right circular cylinder is halved, keeping the heightsame, what is the ratio of the volume of the reduced cylinder to that of originalone?1. 1 : 4 2. 1 : 8 3. 1 : 2 4. 8 : 1

22. In what ratio are the volumes of a cylinder, a cone and a sphere, if each has thesame diameter and the same height?1. 1 : 3 : 2 2. 2 : 3 : 1 3. 3 : 1 : 2 4. 3 : 2 : 1

23. Two cylindrical jars have their diameters in the ratio of 3 : 1 and their heights

in the ratio of 1 : 3. The volumes are in the ratio of __________1. 1 : 2 2. 3 : 1 3. 6 : 1 4. 1 : 2

24. The radius of sphere is 21 cm. Find its surface area and volume.1. 5544 cm3; 38808 cm2 2. 5454 cm2; 38808 cm3 3. 5544 cm2; 38088 cm3 4. 5544 cm2; 38808 cm3

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25. Volumes of two spheres are in the ratio of 729 : 343. Find the ratio of theirsurface areas.1. 49 : 81 2. 343 : 729 3. 7 : 9 4. 81 : 49

26. A sphere and a cube have equal surface areas. Find the ratio of the volume ofthe sphere to that of the cube.

1. 2a : r 2. 2r : a 3. r : 2a 4. a : 21

27. The radius of a sphere is increased by 50%. The increase in the surface area ofthe sphere is _______1. 100% 2. 125% 3. 150% 4. None

28. If the radius of a sphere is doubled, then its surface area is increased by _______1. 50% 2. 100% 4. 300% 4. 200%

29. If the surface areas of two spheres are in the ratio of 4 : 25, then the ratio oftheir volumes is ________

1. 4 : 25 2. 25 : 4 3. 8 : 125 4. 125 : 8

30. The radius of a cylinder is the same as that of a sphere. Their volumes areequal. The height of the cylinder is how many times its radius?

1.3

4 2.3

2 3. 1 4. 2

Comprehensive Test – II(Chapters 5 – 7)

1.

Travelling at 3/5th of his actual speed a man is late by 20 min. What isthe actual time he takes?

a.

25 minb. 30 minc.

40 mind. 35 min

2.

A person covered 1/4th of the distance at 16kmph and the remaining at24 kmph. His average speed is

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a.

22.66b. 21.33c.

22.33d. 21.66

3.

A person takes 20 min to cover a distance by decreasing his speed by

20%. What time he takes at 50% speed?a.

24 minb. 30 minc.

32 mind.

36 min

4. Travelling from his house art 30 kmph a person reaches his office 5 minlate. If he increases speed by 10 kmph, he is early by 15min. Thedistance to the office is

a. 36 kmb.

32km

c.

30 kmd.

40 km

5. A train A started from X at 72 kmph and after 30s another train Bstarted from same station and meets A after 15s. The speed of B is

a. 50 kmphb.

135 kmphc. 144 kmphd.

None

6.

A train 180m long crossed 120m long platform in 20s and another train

at same speed crossed a pole in 10s. In what time can these trainscross each other in opposite directions?

a.

11sb. 13sc.

12sd. 14s

7. Two trains each of 100m long pass each other in same direction in 60sand in opposite directions in 10s. The speed of the slower train is

a.

30 kmphb. 42 kmph

c.

48 kmphd. 60 kmph

8. A boat travels 12 km downstream in 48min. If the speed of the streramis 2 kmph then the speed of the boat is

a. 13 kmphb. 15 kmphc.

17 kmphd. None

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9. A man rows 40 km upstream in 8 hrs and 36 km downstream in 6 hrs.

The speed in still water isa. 0.5b. 5.5c.

6

d.

5

10. In a stream running at 2kmph, a man goes 10 km upstream andcomes back in 55min. Find his speed in still water.

a.

20b.

22c. 24d. 28

11. A can do a work in 10 days and B can do it in 20 days. With thehelp of C they do it in 5 days. In how many days can C alone do it?

a.

20b.

10c. 35d. 15

12. 12 men complete a work in 18 days. 6 days after they start 4 men join them. How many more days are required to do it?

a. 10b.

15c. 12d.

9

13. A and B can do a work in 10 and 12 days. They start the workand B leaves after two days. If daily wages are Rs. 20 for each howmuch does A get?

a.

160b. 180c.

200d. None

14.

A and V together can do a work in 7 days. If A does twice as muchwork as V, how long does A alone take to do it?

a.

6.33 daysb. 10.5 daysc.

11 daysd. None

15. 24 men working 8hrs a day can do a work in 10 dyas. In howmany days 32 men working 10 hrs a day do it?

a.

10b. 6

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c.

5d. 8

16. Pipe A can fill a tank in 16min and pipe B can empty it in 24 min.If both are opened after how many min should B be closed to fill thetank in 30min?

a.

20b.

21c. 23d.

22

17.

Two pipes can fill a tank in 18min and 27min. A third pipe canempty it in 6 min. All three are opened with tank 2/3 full. In how manymin will it be empty?

a.

11b. 9c.

13

d.

7

18. A, B and C can fill a tank in 12, 24, 48 min. They are openedtogether but B is closed 3 min before and C closed 2 min before fillingthe tank. In how many min was the tank full?

a. 6b.

8c. 7d.

9

19.

P, Q and R can fill a ank n 20, 30 and 60 hrs. If they are opened

in rotation, one hour each starting with P in how many hrs will the tankbe full?

a.

28.33b. 30c.

32d. 34

20. Two pipes A and B can fill a tank in 10min and 15 min and C canempty it in 5 min. A and B are opened for 4 min and then C is alsoopened. In how many min tank will be empty?

a. 16

b.

18c. 20d.

25

21.

What is the ratio of areas of in-circle to that of circumcircle of asquare?

a. 1`:5b.

1:2c. 2:1

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d.

None

22.

The front wheels of a wagon are 3pi feet in circumference and therear wheels are 4pi feet. When the front ones make 12 more revolutionsthan the rear ones, how many feet will the wagon move?

a.

48pi

b.

56pic.

64pid. None

23.

Three circles of radius 4.2 cm are placed in such a way that eachtouches the other two. The are enclosed between them is

a. 28b. 29c.

30d. None

24.

A person uses a sheet measuring 30cmX40 cm. If margin of 3 cmis left on each side of the sheet the percentage of the paper used fortyping is

a. 50b.

68c. 80d.

None

25.

The length of a rectangle is increased by 20% and its breadth isdecreased by 8%. Then what is the % change in area?

a.

10

b.

20c. 30d.

40

26.

The radius of a cylinder is increased by 20% and height isdecreased by 33.33%, then what is the % change in volume?

a.

4b. 8c.

33d.

20

27.

The area of a square is increased by 69%. The % increase in itsside is

a.

13b. 15c.

30d. 40

28.

The base radius of a cone and cylinder are in the ratio of 2:3 andtheir heights are in the ratio of 3:2. The ratio of their volumes is

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Read this please:

Raju borrowed Rs.1000 from Ramesh. After some days Raju paid back Rs.1200to Ramesh. Means Raju paid Rs.200 excess than the amount he borrowed fromRamesh.

This excess amount is called interest.

The total amount of money borrowed by Raju from Ramesh is calledthe Principal or Sum.

The money paid back to Ramesh, which is the combination of bothPrincipal and interest is called the Amount.

So, Amount = Principal + Interest

Rate of interest: The interest is usually charged according to a specified term,which is expressed as some per cent of the principal and is called the rate ofinterest for the fixed period of time.

If the fixed period is a year, the rate of interest is charged annually. If the fixed period is six months, the rate of interest is charged semi-

annually.

If the fixed period is three months, the rate of interest is chargedquarterly.

If the fixed period is a month, the rate of interest is charged monthly.

Example: If the rate of interest is 10% per annum, then the interest payableon Rs.100 for one year is Rs.10.

Simple Interest: When the interest is payable on the principal only, it iscalled the simple interest. It is the interest calculated on the principal for theentire period it is borrowed. It is denoted by S.I.

Example: S.I. on Rs.100 at 10% per annum will be Rs.10 each year.At the end of one year, the total amount will be Rs.100+10 = Rs.110.At the end of second year, the total amount will be Rs.100+10+10 = Rs.120and so on.

Formulae:1. If P stands for Principal, R the rate per cent per annum, T the number of

years, A the amount and S.I. the simple interest then

S.I. =100

RTP

2. TR

.I.S100P

3. %TP

.I.S100R

4. R×P

.I.S×100=T years

5. Amount,

100

RT1PA

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6. If a certain sum in T years at R% per annum amounts to Rs.A, then the

sum will be)TR(100

A100P

.

7. The annual payment that will discharge a debt of Rs.A due in T years at

R% per annum =

2

)1T(RTT100

A100

.

8. If a certain sum is invested in n types of investments in such a manner

that equal amount is obtained on each investment where interest rates areR1,R2,…….,Rn respectively and time periods and time periods are T 1,T 2,…., T n respectively, then the ratio in which the amounts are invested is

nn2211 TR100

1........................:

TR100

1:

TR100

1

.

9. If a certain sum of money becomes n times itself in T years at S.I., then

the rate of interest per annum is, %T

)1n(100R

.

10. If a certain sum of money becomes n times itself at R% per annum S.I. in T

years, then 100(n 1)T

R

years.

11. If a certain sum of money becomes n times itself in T years at a simpleinterest, then the time 'T in which it will become m times itself is given

by =T' m 1T

n 1

years.

12. If the rate of interest (R) changes from R1 to R2 and P, T are constant, then

Change in S.I. = )RR(100

PT21 .

13. If Principal (P) changes from P1 to P2 and R, T are constant, then

Change in S.I. = )PP(100

RT21 .

14.

If Rate (R) Changes from R1 to R2 and time (T) changes from T 1 to T 2 butprincipal (P) is constant, then

Change in S.I. = )TRTR(100

P2211 .

15. If a debt of Rs.X is paid in n number of installments and if the value ofeach installment is a, then the borrowed (debt) amount is given

by2

)1n(n

b100

RanaX

.

Where, R is the rate of interest per annumb is the no. of installments per year

Note:b = 1, when each installment is paid yearly.b = 2, when each installment is paid half-yearly.b = 4, when each installment is paid quarterly.b = 12, when each installment is paid monthly.

16. If a certain sum of money P lent out at S.I. amounts to A 1 in T 1 years and

to A2 in T 2 years, then,12

1221

T~T

TATA=P

~ and %100×

TATA

A~A=R

1221

21

~

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17. If a certain sum of money P lent out for a certain time T amounts to A1atR1% per annum and to A2 at R2% per annum, then

21

2112

RR

RARA=P

~

~ and .years100×

RARA

AA=T

2112

21

~

~

18. If an amount P1 lent at S.I. rate of interest R1% p.a. and another amount

P2 at S.I. rate of R2% p.a., then the rate of interest for the whole sum is

21

2211

PP

RPRPR .

19. If a certain sum of money is lent out in n parts in such a manner thatequal sum of money is obtained as S.I. on each part where interest ratesare R1,R2,……,Rn respectively and time periods are T 1,T 2,…..,T n respectively, then the ratio in which the sum will be divided in n parts isgiven by

.TR

1........................:

TR

1:

TR

1

nn2211

20. If there is a change in principal (P), rate of interest (R) and time (T), thenthe value of S.I also changes and is given by

222

111

22

11

222

111

2

1

TRP

TRP

PA

PA

TRP

TRP

I.S

I.S

21. Out of a certain sum P,x

1 part is invested at R1%,y

1part is invested at R2%

and the remainder

y

1

x

11 say,

z

1 part at R3%. If the annual income from

all these investments is Rs.A, the original sum is given by

z

R

y

R

x

R

100AP

321

.

Examples:

1. Find the S.I. on Rs.3500 for 3 years at 5% per annum.

Sol: Here, P = Rs.3500, T = 3 years and R = 5% S.I. = 525..Rs

100

533500

2. Find the Principal, if S.I. = 624 for 2 years at 3% per annum.

Sol: 0400.1.Rs32

624100

TR

.I.S100P

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3. At what rate per annum will a sum of Rs.4000 amount to Rs. Rs.6000 in 5 years?

Sol: S.I. = 6000 – 4000 = 2000

%.1054000

2000100

TP

.I.S100R

4. In what time will Rs.1500 earn an interest of Rs.150 at 2% per annum?

Sol: .years521500

150100

RP

.I.S100T

5. Sunny borrowed Rs.2000 from his friend Praveen at 10% per annum for 5 years. Find the interest and money returned by Sunny to Praveen.

Sol: S.I. = 2000 5 101000

100

A = P + S.I. = 2000 + 1000 = Rs.3000

6. What sum will amount to Rs.420 at 2% per annum in2

12 years?

Sol: 400.Rs105

420100

)2

52(100

420100

)2

122(100

420100

)TR(100

A100P

7. Find the annual installment that will discharge a debt of Rs.16200 in 5 years at 4% per annum.

Sol: Annual installment =

2 )1T(RTT100

A100

= .3000.Rs540

16200100

2

80500

16200100

2

)15(54)5(100

16200100

8. A sum of Rs.3454 is divided among three such parts that amount obtainedon these three parts of money after 3, 4 and 5 years, respectively at rate of5% per annum remains equal. Find such three parts of the sum.

Sol: The three parts will be in the ratio

nn2211 TR100

1........................:

TR100

1:

TR100

1

=125

1:

120

1:

115

1

)55(100

1:

)45(100

1:

)35(100

1

= 552:575:600125

690001:

120

690001:

115

690001

[Since the L.C.M. of 115, 120 and 125 is 69000.]

Ratio = 552:575:600 Sum of proportional = 600 + 575 + 552 = 1727

8/20/2019 208666617 Total Book Rough


1st part = 1200.Rs34541727

600

2nd part = 1150.Rs34541727

575

3rd part = .1104.Rs34541727

552

9. A certain sum of money quadruples itself in 6 years S.I. Find the rate

percent per annum.

Sol: %.50=6

)14(100=%

T

)1n(100=R

10. In what time a sum of money will double itself at a rate of S.I. of 6% perannum?

Sol: years3

216

6

416100

6

)12(years100

R

1nT

11. A sum of money put on S.I. doubles itself in 10 years. In how many years

would it quadruple itself?

Sol: Required Time, 'T = 4 110

2 1

= 30 years.

12. If simple interest on Rs.500 increases by Rs.20, when the rate % increasesby 8% per annum, find the time.

Sol: Change in S.I. = )RR(100

PT21

.years2

1TT40208

100

T50020

13. If the S.I. on Rs.3500 be more than the interest on Rs.2000 by Rs.60 in 4 years, then find the rate per cent per annum.

Change in S.I. = )PP(100

RT21

%.1R1500100

R460)20003500(

100

R460

14. If the S.I. on a certain sum at 3% per annum for 5 years is Rs.90 morethan the interest on the same sum for 2 years at 6% per annum. Find thesum.

Sol: Change in S.I. = )TRTR(100

P

2211

.3000.RsP3

100

P90)6253(

100

P90

15. A sum of Rs.4 is lent to be paid back in 3 equal monthly installments ofRe.1 each. Find the rate percent.

Sol: Here, X = Rs.4, a = Re.1, n = 3, b = 12, R = ?

8/20/2019 208666617 Total Book Rough


2

)1n(n

b100

RanaX formula,Required

%.400R

1600R1200

400R12004

31200

R34

2

)13(3

12100

1R)1(34

16. Anitha deposits Rs.8000 in S.B.I at 2% per annum and Rs.6000 at 5% perannum in ICICI bank. Find the rate of interest for the whole sum.

Sol: Required rate,

21

2211

PP

RPRPR

%.14

5114000

19000

60008000

5600028000

17. If a sum of Rs.3800 is divided into two such parts that the S.I. on the first

part for2

11 years at the rate of 2% per annum, equals the S.I. on the

second part for 4 years at the rate of 4% per annum, then find two suchdivisions of the sum.

Sol: Required Ratio =2211 TR

1:

TR

1

1st part: 2nd part = 3:1616

1:

3

1

44

1:

2

112

1

Sum of proportionals = 16 + 3 = 19

So, 1st part = 3200.Rs380019

16

2nd part = 600.Rs380019

3 .

18. If Rs.50 amounts to Rs.85 in 2 years, what Rs. 340 amount to in 15 yearsat the same rate?

Sol: By using,222

111

22

11

TRP

TRP

PA

PA

we get

2

2 2

2

2

85 50 85 R 2

A 340 340 R 15

35 170 35 1

A 340 340 15 A 340 2 15

A 340 30 35 1050

A 1050 340 1390

19. From a certain sum Krishna invested, th4

1 at 2%, th5

1 at 4% and the rest at

6%. If the annual income of Krishna is Rs.1840 from all these investments,then find the original sum.

8/20/2019 208666617 Total Book Rough


Sol: Required formula is,

z

R

y

R

x

R

100AP

321

5

1

y

1,

4

1

x

1 and

20

11

20

4520

5

1

4

11

y

1

x

11

z

1

Original sum =

11

20

6

5

4

4

2

1001840

.000,40.Rs2092

1001840

20

661610

1001840

20

66

5

4

4

2

1001840

Exercise:

1.

Find the S.I. on Rs.16,000 for 3 years 3 months at 4 ½ % per annum?1. Rs.5200 2. Rs.1800 3. Rs.2340 4. None

2.

Find the S.I. on Rs.12,000 for 8 years 4 months at 3% p. a.?1. Rs.2000 2. Rs.15000 3. Rs.3000 4. None

3. On what Sum of money will the S.I. for 7 years 6 months at 5% p.a. be Rs.450?1. Rs.11,000 2. Rs.1200 3. Rs.13000 4. Rs.12,000

4. The S.I. on the certain Sum of money for 2 years at 8% p.a. is Rs.2560. What isthe Sum?1. Rs.16000 2. Rs.15000 3. Rs.13000 4. None

5. In what time will the S.I. on Rs.4000 at 7.5% be Rs.1050?1. 2 ½ years 2. 5 ½ years 3. 3 ½ years 4. None

6.

At what rate% per annum will the S.I. on Rs.2500 be Rs.750 for 3 years?1. 15% 2. 10% 3. 20% 4. None

7.

What Sum will amount to Rs.3300 in 2 years 6 months at 15% p.a. S.I.?1. Rs.2000 2. Rs.2400 3. Rs.2800 4. Rs.2500

8.

What Sum will amount to Rs.8160 in 4 ½ years at 8% p.a. S.I.?1. Rs.6600 2. Rs.5000 3. Rs.6000 4. 7000

9. In how many years will a Sum of money becomes double at 5% p.a. S.I.?1. 18 years 2. 20 years 3. 15 years 4. None

10.

At what rate% p.a. a Sum of money becomes four times of itself in 15 years?1. 8% 2. 10% 3. 15% 4. 20%

“The aim of education is the knowledge not of fact, but of values.”

8/20/2019 208666617 Total Book Rough


11. At what rate% p.a. a Sum of money becomes three times in 12 years 6 months?

1. 15% 2. 14% 3. 16% 4. None

12. A Sum of money becomes triple of itself in 8 years at S.I. In twelve years, it willbecome how many times at the same rate?

1. 6 times 2. 4 times 3. 5 times 4. None

13. A Sum of money becomes double itself in 4 years. In twelve years, it will becomehow many times at the same rate?1. 6 times 2. 4 times 3. 3 times 4. None

14. A man deposited Rs.9000 in a bank at 6% p.a. for 4 years. For how many years,must another man deposit an amount of Rs.5400 at 5% p.a. in another bank sothat both of them get the same interest?1. 6 years 2. 4 years 3. 3 years 4. None

15.

A Sum of Rs.450 amounts to Rs.495 in two years. In what time will the Sum ofRs.820 amounts to Rs.943 at the same rate?1. 3 years 2. 2 years 3. 6 years 4. None

16.

The S.I. on a Sum of money will be Rs.600 after 10 years. If the S.I. (orPrincipal) is tripled after 5 years find the total S.I. at the end of 10 years?1. Rs.3000 2. Rs.1200 3. Rs.1000 4. None

17.

A certain Sum of money amounts to Rs.1680 in 3 years and to Rs.1920 in 7 years. What is the Sum?1. Rs.3000 2. Rs.1200 3. Rs.1000 4. None

18.

A Sum of money amounts to Rs.3000 in 2 years and Rs.4250 in 7 years. Whatis rate% p.a.?1. 9% 2. 10% 3. 3% 4. 7%

19.

A Sum of money amounts to Rs.312 at 4% p.a. interest, Rs.324 at 8% interestp.a. Find the Principal and time period?1. Rs.300, 1 year 2. Rs.200, 1 year 3. Rs.100, 1 year 4. None

20. A Sum was put at S.I. at a certain rate for 3 years. Had it been at 1% higher

rate, it would have fetched Rs.36 more. What is the Sum?1. Rs.1000 2. Rs.1800 3. Rs.1200 4. Rs.1600

21. A man deposited certain amount in a bank at 4% p.a. for 7 years. However, hewould get Rs.380 less as interest, if he deposits the same amount at 3% p.a. for3 years. What is the Sum?1. Rs.2400 2. Rs.2600 3. Rs.2000 4. Rs.1500

8/20/2019 208666617 Total Book Rough


22.

A lent Rs.600 to B for 2 years and Rs.150 to C for 4 years and received Rs.90 asa S.I. in all. Find the rate% p.a.1. 4% 2. 6% 3. 5% 4. None

23. The S.I. on a certain Sum of money is 2/5 of the Principal. If the time period is4 years, what is the rate % p.a.?

1. 8% 2. 6% 3. 10% 4. None

24. The S.I. on a Sum of money is 4/9 of the Principal and its rate% p.a. is equal tothe number of years. What is the time period?1. 8 years 6 months 2. 6years 2 months 3. 6 years 8 months

4. None

25. A part of certain Sum of money is invested at 8% p.a. S.I. and the rest at 6%p.a. If the interests earned in each case for the same period are equal, the ratioof the Sum invested is _____.1. 3 : 5 2. 3 : 4 3. 5 : 3 4. 1 : 5

26.

Rs.15000 is invested partly at 5% and rest 8% p.a. The whole annual interestreceived was Rs.930. What is the amount lent at 8% per annum?1. Rs.9000 2. Rs.8000 3. Rs.6000 4. None

27. Rs.26,650 is lent into two parts so that the interest on first part for 3 years at5% may be equal to the interest for 8 years at 3% p.a. What is the second Sum?1. Rs.10,000 2. Rs.10,750 3. Rs.10,250 4. None

28. What annual payment will discharge a debt of Rs.2210 due at 7% p.a. in 4 years?

1. Rs.480 2. Rs.400 3. Rs.500 4. None

29.

A money lender finds that due to fail in the rate of interest from 8% to 7 ¾%,his yearly income diminishes by Rs.61.50. His capital at ______.1. Rs.24,600 2. Rs.24,000 3. Rs.3,000 4. Rs.35,000

30.

A man invested 1/3 of his capital at 7%, ¼ at 8% and the remaining at 10%. Ifhis annual income is Rs.561, find his capital.1. Rs.6000 2. Rs.6600 3. Rs.7000 4. None

31. Find the S.I. on Rs.200 for 7 months at 5 paise per rupee per month.

1. Rs.60 2. Rs.70 3. Rs.80 4. None

32.

If the interest on Rs.1200 be more than the interest on Rs.1000 by Rs.50 in 3 years. Find the rate%.1. 8% 2. 8 1/3% 3. 9% 4. None

33. Rs.1200 amount to Rs.1632 in 4 years at a certain rate of S.I. If the rate ofinterest increased by 1%, it amounts to how much S.I.?1. Rs.400 2. Rs.500 3. Rs.350 4. Rs.480

8/20/2019 208666617 Total Book Rough


34.

If the S.I. on Rs.2000 increased by Rs.40, then the rate% is increased by 2%p.a., find the time?1. 12 years 2. 3 years 3. 2 years 4. 1 year

35. If Rs.85 amounts to Rs.95 in 3 years, what Rs.102 will amount in 5 years at thesame rate%?

1. Rs.122 2. Rs.150 3. Rs.200 4. Rs.300

36. A father left a will of Rs.68,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attain 18 years. If the money reckoned at 10% p.a., find how much each gets at the timeof the will in thousands?1. 30, 38 2. 34, 34 3. 32, 36 4. None

37.

A Sum of money doubles itself in 7 years. In how many years it becomes four-fold?1. 11 years 2. 12 years 3. 21 years 4. 42 years

38.

If x is the S.I. on y, and y is the S.I. on z, rate% and time period being the samein both cases, what is the relation between x, y and z?1. z yx

2 = 2. z xy 2 = 3. y xz

2 4. xyz = 1

39.

What annual payment will discharge a debt of Rs.2160 due in 2 years at 16%p.a. S.I.?1. Rs.1000 2. Rs.1600 3. Rs.250 4. Rs.360

40. Ram lent Rs.750 to Raghu for 5 years and to Rs.800 to Raju for 4 ½ years andgot Rs.1470 S.I. from both the cases. Find the rate%.

1. 25% 2. 22% 3. 20% 4. 15%

Compound Interest: In this method, the interest for each period is added tothe principal before; interest is calculated for the next period. So, the principalgrows as the interest is added to it. It is denoted by C.I.

Formulae:

1. If a principal P is given on C.I. at the rate of interest R% p.a., then theAmount A after t years is

.100

R1PA

t

2. C.I. = A – P

=

1

100

R1PP

100

R1P

tt

3. Rate of interest (R) = .a.p%1P

A100

t1

8/20/2019 208666617 Total Book Rough


Note: S.I. and C.I. for 1 year at a given rate of interest per annum are alwaysequal.

4. If the interest is compounded half-yearly, then

a) Amount, .2100

R1PA

t2

b) C.I. =

12100

R1P

t2.

c) Rate (R) = .a.p%1P

A1002

2t

1

5. If the interest is compounded quarterly, then

a) Amount, .4100

R1PA

t4

b) C.I. =

1

4100

R1P

t4

.


A1004

4t

1

6. If the interest is compounded n times a year, then

a) Amount, .n100

R1PA

tn

b) C.I. =

1n100

R1P

tn

.


A

100n

nt

1

7. If the rate of interest is different for different years, say R1%, R2%, R3% forfirst, second and third years respectively, then

Amount, .100

R1

100

R1

100

R1PA 321

8. If the time is in the form of fraction, say z

y x years, then

Amount, .100

Rz

y

1100

R1PA

x

9. The difference between the C.I. and the S.I. on a certain sum of money for2 years at R% p.a., is

a) C.I. – S.I. =2

100

RP

if P and R are given

b) C.I. – S.I. =1002

.I.SR

if S.I. and R are given

10. The difference between the C.I. and the S.I. on a certain sum of money for3 years at R% p.a., is

8/20/2019 208666617 Total Book Rough


a) C.I. – S.I. =

23

100

R3

100

RP if P and R are given

b) C.I. – S.I. =

100

R3

100

R

3

.I.S 2

if S.I. and R are given

11. If a certain sum becomes n times in t years at C.I.,

a) Then the same sum becomes nt in mt years.

b) Rate of C.I., %.1)n(100R t

1

12. If a certain sum of money at C.I. amounts to Rs.x in A years and to Rs.y inB years, then the rate of interest p.a. is

%.1001x

yR

AB

1

13. If a loan of Rs.P at R% C.I. p.a., is to be repaid in n equal yearlyinstallments, then the value of each installment

= n2

R100

100........

R100

100

R100

100P.Rs

.

Examples

1. Ravi invested Rs.25000 at C.I. rate 4% p.a., for a period of 3 years. Whatamount will he receive at the end of 2 years?

Sol: P = Rs.25000, R = 4%, t = 3 years, A =?

.60.121,28.Rs25

26

25

26

25

2625000

100

4125000

100

R1PA

3

t

2. Find the C.I. on Rs.2000 for 2 years at 5% p.a.Sol: P = Rs.2000, R = 5%, t = 2 years, C.I. =?

C.I. =

1

100

R1P

t

=

1

20

2120001

100

512000

22

.205.Rs)1025.0(2000)1025.1(2000

3. Ram invested Rs.5548 for 3 years at C.I. and received an amount ofRs.6750 on maturity. What is rate percent?

Sol: P = Rs.5548, A = Rs.6750, t= 3 years, R =?

8/20/2019 208666617 Total Book Rough


Rate of interest (R) = .a.p%1P

A100

t1

%12774

3375100%1

5548

6750100

3

1

3

1

.a.p%.7

17

7

50

14

100

%114

15100%1

14

15100

313

4. Find the amount of Rs.16000 in2

11 years at 10% p.a., C.I. payable half-

yearly.

Sol: P = Rs.16000, R = 10%, t =2

11 =

2

3 years, A =?

Amount,

t2

2100

R1PA

.522,18.Rs926128000

)21(16000

20

2116000

2100

10116000

3

32

32

5. Find the C.I. on Rs.8192 at 50% p.a., compounded quarterly for 1 year.

Sol: P = Rs.8192, R = 50%, t = 1 year, C.I. =?

C.I. =

1

4100

R1P

t4

4930.Rs4096

24658192

4096

409665618192

18

981921

4100

5018192

414

6. Find the C.I. on Rs.2000 at 12% p.a. for 2 months compounded monthly.

Sol: P = Rs.2000, R = 12%, t = 2 months = years6

1

12

2 , C.I. =?

C.I. =

112100

R1P

t12

40.2..Rs0201.0200010201.12000

110010120001

121001212000

26

112

7. Lakshmi invests Rs.50000 in a mutual fund which gives interest at 2%p.a., during first year, 5% during the second year and 8% during the third year. How much does she get at the end of the third year?Sol: P = Rs.50000, R1 = 2%, R2 = 5%, R3 = 8%

8/20/2019 208666617 Total Book Rough


Amount at the third year,

100

R1

100

R1

100

R1PA 321

100

81

100

51

100

2150000

57834..Rs25000

2891750000

25

27

20

21

50

5150000

8. What will be the C.I. on Rs.93750 for 2

12 years at 4% p.a.?

Sol: P = Rs.93750, t=2

12 years, R = 4%.

Required C.I. =

1

100

Rz

y

1100

R1P

x

9678.Rs31250

322693750

15051

2526

252693750

1100

42

1

1100

4193750

2

9. Find the difference between C.I. and S.I. on a sum of Rs.6250 put for 2 years at 4% p.a.Sol: P = Rs.6250, t = 2 years, R = 4%

For 2 years, C.I. – S.I. =2

100

RP

if P and R are given

10.Rs25

1

25

16250

100

46250

2

10. The difference between C.I. and S.I. on a certain sum of money for 3 years,

at 4% p.a. is Rs.76. Find the sum.Sol: C.I. – S.I. = Rs.76, R = 3%

For 3 years, C.I. – S.I. =

23

100

R3

100

RP if P and R are given

76 =

23

100

43

100

4P

76 =

23

25

13

25

1P

76 =

23

2513

251P

76 =

252525

)253(1P

76 =

15625

76P

15625.RsP .

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11. Certain sum of money placed at C.I. doubles itself in 3 years. In how many years will it amount to eight times itself?

Sol: Here, n = 2, t = 3 years and m = 3 Then the same sum becomes mn in mt years = 3 x 3 = 9 years.

12. At what percent C.I. does a sum of money become eight-fold in 3 years.

Sol: Required Rate percent is, %.1001)8(1001)n(100R 3

1

t

1

13. A certain sum of money at C.I. amounts to Rs.800 in two years and toRs.1152 in four years. Find the rate of interest per annum.Sol: x = Rs.800, y = Rs.1152, A = 2 and B = 4

Required rate of interest, %1001x

yR

AB

1

%1001400

576%1001

800

1152 21

241

= %.2010020

2024%1001

20

24 2

12

14. If a sum of Rs.18120 is to be paid back in two equal installments at %3

11

per annum, what is the amount of each installment?

Sol: P = Rs.18120, R = %3

4=%

3

11

Each installment =2

R100

100

R100

100

P.Rs

=22

3

304

100

3

304

100

18120

3

4100

100

3

4100

100

18120

=

304

3001

304

300

18120

304

300

304

300

181202

=604300

30430418120

304

604

304

300

18120

= 9241.60.Rs10

304304

.

Exercise:

1. Find the C.I. on Rs.3000 for 3 years at 10% p.a.1. Rs.1000 2. Rs.1200 3. Rs.993 4. Rs.300

8/20/2019 208666617 Total Book Rough


2.

On what sum of money will be the C.I. be Rs.168 in 2 years at 10% p.a.?1. Rs.800 2. Rs.1000 3. Rs.1200 4. Rs.900

3. At what rate% p.a. will Rs.8000 amount to Rs.9261 in 3 years at C.I.?1. 6% 2. 7% 3. 5% 4. 10%

4.

At what rate% C.I. does a sum of money become 2 ¼ times itself in 2 years?1. 50% 2. 75% 3. 60% 4. 40%

5.

In what time will Rs.2000 amount to Rs.2420 at 10% p.a. C.I.?1. 3 years 2. 2 years 3. 5 years 4. 9 years

6. Find the C.I. on Rs.24,000 at 10% p.a. for 1 year 6 months, the interest beingcompounded half-yearly.1. Rs.12000 2. Rs.15000 3. Rs.14000 4. None

7.

In what time will Rs.64000 invested at 5% p.a. fetch an interest of Rs.4291 the

interest being compounded half-yearly?1. 3/2 years 2. 4/7 years 3. 3 years 4. 2 years

8. The difference between the C.I. and S.I. on a certain sum of money for 2 yearsat 5% p.a. is Rs.30. Find the sum.1. Rs.12000 2. Rs.15000 3. Rs.20000 4. None

9. The difference between the S.I. and C.I. on Rs.1250 for 2 years is 8. Find therate% p.a.1. 8% 2. 6% 3. 9% 4. None

10.

A and B borrowed equal sum for 3 years at 10% S.I. and C.I. respectively. At thetime of the repayment B has to pay Rs.15.50 more than A. Find the sumborrowed by each.1. Rs.500 2. Rs.600 3. Rs.800 4. None

11. The C.I. on a certain sum for 2 years is Rs.40.80 and the S.I. is Rs.40. Find therate% p.a. and the sum.1. 5%, Rs.500 2. 4%, Rs.500 3. 6%, Rs.600 4. None

12.

The S.I. on a sum at 4% p.a. for 2 years is Rs.80. Find the C.I. on the same sumfor same period.

1. Rs.90 2. Rs.96.60 3. Rs.84.60 4. Rs.81.60

13.

At a C.I. a sum becomes double itself in 3 years. In how many years will become8 times?1. 9 years 2. 10 years 3. 7 years 4. None

14. At a C.I. a sum becomes thrice itself in 8 years. In 16 years, it will become howmany times?1. 9 times 2. 10 times 3. 18 times 4. 27 times

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15. The annual increase in the population of a town is 5%. What will be the

population 3 years hence, if it is 80,000 now?1. 92,610 2. 12,000 3. 75,000 4. None

16.

Two cars A and B are of worth Rs.72,900 and Rs.1,33,100 respectively. After

how many years will the value of both be same, if the car A appreciates at 10%p.a. and the car B depreciates at 10% p.a.?1. 4 years 2. 5 years 3. 3 years 4. None

17.

A sum of money is borrowed and paid back in two equal installments of Rs.729allowing 8% C.I. What was the sum borrowed?1. Rs.1300 2. Rs.15000 3. Rs.16000 4. Rs.18000

18.

Find the difference between C.I and S.I on Rs.6400/- for 2 years at 12½% perannum?1. Rs.90 2. Rs.101 3. Rs.100 4. Rs.1000

19.

What annual payment will discharge a debt of Rs.50440 due in 3 years at 5%p.a. correspond annually?1. Rs.18,000 2. Rs.18,522 3. Rs.16,500 4. None

20. A tree increases annually by 1/8th of its height. By how much will it increaseafter 2 ½ years of it stands today 8 m high?1. 10.25 cm 2. 10.75 cm 3. 9.25 cm 4. 9.75 cm

21. A sum of money put at C.I. amounts to Rs.2809 in 2 years and to Rs.2977.54 in3 years. Find the sum.

1. Rs.2500 2. Rs.3000 3. Rs.4000 4. Rs.5000

22.

A man opened a restaurant with an initial investment of Rs.3200. In that first year, he incurred a loss of 5%. However during the second year, he earned aprofit of 10% which is third year rise to 12 ½ %. Calculate his net profit for theentire period for 3 years?1. Rs.5000 2. Rs.700 3. Rs.5620 4. None

23.

At what rate% C.I. does a sum of money become nine-fold in 2 years?1. 200% 2. 300% 3. 500% 4. 600%

24.

Arjun invested Rs.8000 for 3 years at 5% C.I. in a bank. If the interest iscompounded once in a year, what sum will get after 3 years?1. Rs.9261 2. Rs.8265 3. Rs.9365 4. Rs.9465

25.

Find the C.I. on Rs.2000 at 5% p.a. compounded yearly, for 2 years is1. Rs.315 2. Rs.425 3. Rs.205 4. Rs.215

26.

If the interest is compounded yearly the find at what rate% p.a. will Rs.1000amount to Rs.1331 in 3 years?

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1. 10% 2. 12% 3. 13% 4. 14%

27. What is the present worth Rs.9261 due 3 years hence 5% p.a. compounded yearly?1. Rs.7000 2. Rs.8000 3. Rs.9000 4. Rs.10,000

28.

The C.I. on Rs.10,000 at 20% p.a. at the end of 1 year 6 months if the interestis calculated half-yearly will be1. Rs.5320 2. Rs.3310 3. Rs.4340 4. Rs.2340

29.

A sum put out at 4% C.I. interest payable half-yearly amounts to Rs.6632.55 in1 ½ years. The sum is1. Rs.6530 2. Rs.6250 3. Rs.6470 4. None

30. The C.I. on Rs.12,000 for 9 months at 20% p.a. interest being compoundedquarterly is

1. Rs.1891.50 2. Rs.1901.50 3. Rs.1791.50 4. None

31. The difference of C.I. on Rs.800 for 1 year at 20% p.a. when compounded half- yearly and quarterly is ______1. Rs.4.40 2. Rs.5.40 3. Rs.6.40 4. None

32.

The difference between the S.I. and the C.I. on Rs.600 for 1 year at 10% p.a.,reckoned half-yearly is1. Re.1 2. Rs.1.5 3. Rs.2 4. None

33. Rs.800 at 5% p.a. C.I. amount to Rs.882 in _____.1. 6 years 2. 2 years 3. 4 years 4. None

34.

What will be the C.I. on a sum of Rs.1875 after 2 years if the rate of interest forthe first year is 4% and that for the second year is 8%?1. Rs.231 2. Rs.341 3. Rs.241 4. None

35.

What will be the amount if a sum of Rs.5000 is placed at C.I. for 3 years whilerate of interest for first, second and third years is 2, 3 and 4% respectively?1. Rs.5643.12 2. Rs.5463.12 3. Rs.6413.12 4. None

36. What sum will amount to Rs.15916.59 in 3 years at C.I., the interest for 1st, 2nd and 3rd year being 3, 2 and 1% respectively?1. Rs.18000 2. Rs.12000 3. Rs.15000 4. None

37. The C.I. on Rs.800 in 2 ½ years at 5% p.a. is1. Rs.105.05 2. Rs.104.05 3. Rs.106.05 4. None

38. On what sum will the C.I. for 2 ½ years at 10% amount to Rs.6352.50?

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1. Rs.7000 2. Rs.8000 3. Rs.5000 4. None

39.

The C.I. on a sum of money for 3 years at 5% is Rs.1324.05. What is the S.I.?1. Rs.1460 2. Rs.1365 3. Rs.1260 4. None

40.

On what sum of money will the compound interest be Rs.102 in 2 years at 4%

per annum?1. Rs.1250 2. Rs.1365 3. Rs.1200 4. None

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Clocks

In a clock the most important hands are the minutes hand and the hours hand.Whatever may be the shape of the dial they move in a circular track.

The total angle of 360 degrees in a watch is divided into 1 sectors, one for eachhour.

So one hour sector = 360 / 12 = 30 degrees.

For every one hour (60 min),

The minutes hand moves through 360 deg. The hours hand moves through 30 deg.

So for every minute,

The minutes hand moves through 6 deg The hours hand moves through 0.5 deg.

They move in same direction. So their relative displacement for every minute is 5.5deg.

This 5.5 deg movement constitutes the movements of both the hands.

So for every minute both the hands give a displacement of 5.5 deg.

Note:

1. Between every two hours i.e., between 1 and 2, 2 and 3 and so on the handsof the clock coincide with each other for one time except between 11, 12 and12, 1.

In a day they coincide for 22 times.2.

Between every two hours they are perpendicular to each other two timesexcept between 2, 3 and 3, 4 and 8, 9 and 9, 10.In a day they will be perpendicular for 44 times.

3. Between every two hours they will be opposite to each other one time exceptbetween 5, 6 and 6, 7.In a day they will be opposite for 22 times.

Examples:

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1. At what time between 5 and 6 will the hands of the clock coincide?

Soln:

At 5 the angle between the hands is 150 deg.

To coincide, they collectively have to travel this distance. Every minute theytravel 5.5 deg.

So no. of minutes required to coincide = 150 / 5.5 = 300 / 11 = 27 3/11 min.

2. At what time between 6 and 7 will the hands be perpendicular?

Soln:

At 6 the angle between the hands is 180 deg.

To form 90 deg they have to cover 90 deg (out of 180 if 90 is covered 90 willremain)

So no. of minutes required = 90 / 5.5 = 180 / 11 = 16 4/11 min.

But they will be perpendicular for two times. The second one will happen afterthe minutes hand crosses the hours hand and then for 90 deg.

So it has to travel 180+90 = 270 deg.

So time = 270 / 5.5 = 540 / 11 = 49 1/11 min.

3.

What is the angle between the hands of the clock at 3.45?

Soln:

At 3, the angle between the hands = A = 90 deg.

In 45 min the hands will move angle of B = 45 X 5.5 deg (since 5.5 deg for 1 min)

B = 247.5 deg.

Required angle = A ~ B = 157.5 deg.

4.

What is the angle between the hands at 4.40?

Soln:

At 4 the angle between the hands, A = 120 deg.

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In 40 min, B = 40 X 5.5 = 220 deg.

The required angle = A ~ B = 100 deg.

5.

A clock loses 5 min for every hour and another gains 5 min for every hour. If

they are set correct at 10 am on Monday then when will they be 12 hrs apart?Soln:

For every hour watch A loses 5 min and watch B gains 5 min.

So for every hour they will differ by 10 min.

For 12 hrs (720 min) difference between them the time required = 720 / 10 = 72hrs

So they will be 12 hrs apart after 3 days i.e., at 10 am on Thursday.

Exercise:1.

What is the angle between the hands of the clock at 2.45?

1)o

2

1180 2)

o

2

1182

3)o

2

1172 4)

o

2

1181

2.

At o9 clock find the angle between the hands of the clock.

1)o

2

1270 2)

o

2

1250

3)o

2

1150 4)

o

2

1220

3.

At what time between 6 O‟ clock and 7 O‟ clock the hands of the clock willcoincide?

1)11

830 min 2)

11

832 min

3)11

820 min 4)

11

825 min

4. At what time between 6 O‟ clock and 4 O‟ clock the hands of the clock will be

at right angles?1)

11

830 min 2)

11

810 min

3)11

832 min 4)

11

834 min

5. At what time between 1 O‟ clock and 2 O‟ clock the hands of the clock will bein opposite direction?

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1)11

830 min 2)

11

820 min

3)11

810 min 4)

11

432 min

6. At what time between 5 O‟ clock and 6 O‟ clock the hands of the clock will beat o

180 ?

1) 60 min 2) 50 min3) 40 min 4) 30 min

7. A clock which gains 6 minutes every three hours is set at 1.00 P.M. on acertain day. Find the time shown by the watch on next day at 13:50 hours.1) 15 hrs 21 min 40 sec 2) 15 hrs 11 min 40 sec3) 15 hrs 41 min 40 sec 4) 15 hrs 31 min 40 sec

8.

A clock which loses 5 minutes in every hour is set at 10.30 A.M. on a certainday. Next day at 18.00 hours what is the time shown by this watch?1) 15 hrs 12 min 30 sec 2) 15 hrs 22 min 30 sec3) 15 hrs 31 min 40 sec 4) 15 hrs 41 min 30 sec

9.

A clock, which loses 40 seconds every four minutes, is set at 18.00 hours on acertain day. What is the time shown by this watch if the current time is 4.00P.M.?1) 12:10 P.M. 2) 11:10 P.M.3) 10:10 P.M. 4) 9:10 P.M.

10. A clock, which gains 6 minutes in every three hours, is set at 6 P.M. ona certain day. If on next day, the time shown by this watch is 11 P.M. what is

the correct time?1) 8 hrs 2 min (PM) 2) 8 hrs 4 min (PM)3) 8 hrs 8 min (PM) 4) 8 hrs 6 min (PM)

11.

A clock, which loses 5 minutes in every two hours, is set at 9.00 A.M.on a certain day. Next day if the time shown by this watch is 11 P.M. what isthe correct time?

1)23

1510 min 2)

23

1511 min

3)23

159 min 4)

23

1512 min

12.

How many times in a day the hands of a clock are straight?1) 20 2) 223) 19 4) 18

13.

How many times do the hands of a clock point towards each other in aday?1) 18 2) 193) 22 4) 20

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14.

A clock which gains 5 minutes in every two hours is set at 12.00 P.M.on a certain day. Find the time shown by the watch on the next day 11 A.M.1) 12 hrs 47 min 30 sec 2) 12 hrs 45 min 30 sec3) 12 hrs 20 min 30 sec 4) 12 hrs 15 min 30 sec

15.

A clock which loses 10 seconds in every minute is set at 2.00 P.M. on a

certain day. Find the time shown by the watch on the next day 8 P.M.1) 1 P.M. 2) 2 P.M.3) 3 P.M. 4) 4 P.M.

16.

A clock which loses 50 seconds every two minutes is set at 6.00 P.M. ona certain day. What is the time shown by this watch if the current time is 3.00P.M.?1) 4 P.M. 2) 9 P.M.3) 5 P.M. 4) 6 P.M.

17.

A clock which gains 5 minutes in every two hours is set at 12 noon on a

certain day. If on the next day, the time shown by this watch is 1 P.M. thenfind the correct time.1) 10 P.M. 2) 12 P.M.3) 11 P.M. 4) 8 P.M.

18. A clock, which loses 3 minutes in every hour, is set at 10.00 A.M. on acertain day. Next day if the time shown by this watch is 2.30 P.M. What is thecorrect time?

1)29

119 min 2)

29

319 min

3) 29

4

19 min 4) 29

2

19 min

19. How many times do the hands of a clock coincide in a day?1) 22 2) 233) 24 4) 48

20. How many times are the hands of a clock at right angles in a day?1) 22 2) 483) 34 4) 46

21.

If a clock takes 22 seconds to strike 12, how much time will it take tostrike 6?1) 6 sec 2) 10 sec3) 8 sec 4) None

22. At what angle the hands of a clock are inclined when the time is 15minutes past five?

1)o

2

167 2) o

68

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3) o70 4) None

23. At what time between 3 and 4 O‟ clock are the hands of a clocktogether?

1) 18 min past 3 2)4

612 min past 8

3)11

416 min past 3 4) None

24. At what time between 8 and 9 O‟ clock are the hands of a clock be inthe straight line but not together?

1)11

510 min past 3 2)

11

1010 min past 8

3)

11


25. The minute hand of a clock overtakes the hour hand at intervals of 65minutes of correct time. How much in a day does the clock gain or lose?

1)143

1010 min 2)

11

1010 min

3)43

1010 min 4) None

26.

A watch gains uniformly, is 5 min slow at 8 O‟ clock in the morning ona Monday, and is 5 min.48 seconds fast at 8 P.M. on following Monday. Whenwas it correct?1) 3 days 11 hours 20 min 2) 8 min3) 6 days 10 hours 4) None

27.

A clock is set right at 8 A.M. The clock gains 10 minutes in 24 hours.What will be the true time when the clock indicates 1 P.M. on the followingday?1) 28 hours 2) 28 hours 48 min3) 30 hours 4) None

28. At what time between 7 A.M. and 7.30 A.M. will the two hands of a

clock be at right angle to each other?1)

11

921 min past 7 2)

11

55 min past 7

3)11


29.

At what time between 9 O‟ clock and 10 O‟ clock will the two hands of aclock be in a straight line but in opposite directions?

1)11

416 min past 9 2)

11

55 min past 9

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3)10


30.

A watch which gains uniformly is 6 minutes slow at 4 P.M. on a

Sunday and3

210 minutes fast on the following Sunday at 8 A.M. During this

period when (Day and Time) was the watch correct?

1) 1.30 A.M. , Tuesday 2) 1.36 P.M., Thursday3) 1.36 A.M. , Wednesday 4) None

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Calendars

Here you mainly deal in finding the day of the week on a particular givendate.

The process of finding this depends on the number of odd days.

Odd days are quite different from the odd numbers.

Odd Days: The days more than the complete number of weeks in a givenperiod are called odd days.

Ordinary Year: An year that has 365 days is called Ordinary Year.

Leap Year: The year which is exactly divisible by 4 (except century) is called

a leap year.

E.g. 1968, 1972, 1984, 1988 and so on are the examples of Leap Years.1986, 1990, 1994, 1998, and so on are the examples of non leap years.

Note: The Centuries divisible by 400 are leap years.

Important Points:

An ordinary year has 365 days = 52 weeks and 1 odd day.A leap year has 366 days = 52 weeks and 2 odd days.

Century = 76 Ordinary years + 24 Leap years.Century contain 5 odd days.200 years contain 3 odd days.300 years contain 1 odd day.400 years contain 0 odd days.Last day of a century cannot be Tuesday, Thursday or Saturday.First day of a century must be Monday, Tuesday, Thursday or Saturday.

Explanation:

100 years = 76 ordinary years + 24 leap years

= 76 odd days + 24 x 2 odd days= 124 odd days = 17 weeks + 5 days

100 years contain 5 odd days.

No. of odd days in first century = 5 Last day of first century is Friday.

No. of odd days in two centuries = 3 Wednesday is the last day.

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No. of odd days in three centuries = 1

Monday is the last day.

No. of odd days in four centuries = 0 Sunday is the last day.

Since the order is continually kept in successive cycles, the last day of acentury cannot be Tuesday, Thursday or Saturday.

So, the last day of a century should be Sunday, Monday, Wednesday or Friday. Therefore, the first day of a century must be Monday, Tuesday, Thursday or

Saturday.

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39. The no. of odd days in 400 years is _______.1. 1 2. 0 3. 3 4. 4

40. Smt. Indira Gandhi died on 31st October, 1984. The day of the week is _____.

1. Monday 2. Tuesday 3. Wednesday 4. Friday

41. What will be the day of the week on April 29, 2005?1. Friday 2. Tuesday 3. Saturday 4. Sunday

42. The first day of the year 1998 was Wednesday. If the birthday of Raju falls on25th June, then on which day of 1998 was his birthday?1. Friday 2. Tuesday 3. Wednesday 4. Sunday

43. If you are born on 13th April, 1992 which is a Saturday, then which day of theweek is your birthday in 1993?

1. Sunday 2. Monday 3. Tuesday 4. Wednesday

44. Find the day of the week on 15th July, 1776?1. Sunday 2. Monday 3. Tuesday 4. Wednesday

45. How many odd days are there in 352 days?1. 1 2. 2 3. 3 4. 4

46. If 9th March, 1988 is Tuesday, on what day of the week will 9th March, 1989falls?1. Sunday 2. Monday 3. Tuesday 4. Wednesday

47. What will be the day of the week on April 29, 2005?1. Saturday 2. Monday 3. Tuesday 4. Friday

48. On which day of the week does 5th June, 2001 fall?1. Thursday 2. Monday 3. Tuesday 4. Wednesday

49. If Ram was born on 29th June, 1988 which is Monday, on what day was yourbirthday in 1989?1. Friday 2. Monday 3. Tuesday 4. Wednesday

50. Find the day of the week of April 16th, 1976, if April 16th 1974 was Tuesday?

1. Friday 2. Monday 3. Tuesday 4. Saturday

51. Find the day of the week on 15th January, 1979?1. Sunday 2. Monday 3. Friday 4. Wednesday

52. If 23rd May, 2003 is a Friday, what day of the week will be 23rd December?1. Tuesday 2. Monday 3. Tuesday 4. Friday

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53. January 3rd, 1992 was a Friday. What day of the week was January 3rd, 1993?1. Sunday 2. Thursday 3. Friday 4. Saturday

54. On which day of the week does 28th May, 2003 fall?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

55. If your birthday is on 28

th

May, 1991, then what was the day it was?1. Tuesday 2. Wednesday 3. Friday 4. Sunday

56. What day of the week is 1st March, 1990?1. Sunday 2. Thursday 3. Tuesday 4. Friday

57. Which year will have the same calendar that of 2007?1. 2008 2. 2013 3. 2010 4. 2018

58. Which year will have same calendar that of 2001?1. 2002 2. 2005 3. 2006 4. 2007

59. You entered the college first time on 4th June, 2001. What was the day?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

60. The no. of odd days in an ordinary year is _______.1. 1 2. 2 3. 3 4. 4

61. If 3rd April, 2003 was Thursday then which day of the week is 28 th December ofthe same year?1. Sunday 2. Monday 3. Tuesday 4. Wednesday

62. Which among the following is a leap year?

1. 2600 2. 2700 3. 2800 4. 3000

63. What day of the week was 25th April, 1901?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

64. Raju‟s brother was born on 7th November, 1984. The day of the week was _____.1. Monday 2. Tuesday 3. Wednesday 4. Thursday

65. What was the day of the week on 23rd July, 1970?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

66. If today is Monday, then what day of the week will be 427th day from today?1. Sunday 2. Monday 3. Tuesday 4. Wednesday

67. Which day of the week was January 29th, 1601?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

68. If Sundays are holidays, and in a particular year 2nd April is Sunday. Is 30th September in that year a holiday?

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1. Yes 2. No 3. Insufficient Data 4. None

69. On what dates of September 1972 did Wednesday1. 6, 13, 20, 27 2. 4, 11, 18, 25 3. 5, 12, 19, 26 4. 3, 10, 17, 24

70. If 15th February, 1995 was a Wednesday then 15th February, 1994 was on

which day?1. Monday 2. Tuesday 3. Wednesday 4. Thursday

71. Today is Saturday. After 100 days it will be _______.1. Monday 2. Tuesday 3. Wednesday 4. Thursday

72. On which day this year (2008) you celebrated the Independence Day?1. Monday 2. Friday 3. Wednesday 4. Thursday

73. 4th April, 2002 was Thursday. The day of the week on 4 th April, 2003 was ______.

1. Monday 2. Friday 3. Wednesday 4. Thursday

74. 31st March, 2003 was Monday. The day of the week on 31st March, 2004 was _____.1. Monday 2. Friday 3. Wednesday 4. Thursday

75. 15th August, 1947 was Friday. Find the day of the week on 15th August, 1960.1. Monday 2. Tuesday 3. Wednesday 4. Thursday

76. 17th May, 1989 was Wednesday. The day of the week on 9th November, 1989was _______.

1. Monday 2. Tuesday 3. Wednesday 4. Thursday

77. 27th October, 1992 was Tuesday. The day of the week on 29th March, 1993 was ________.1. Monday 2. Tuesday 3. Wednesday 4. Thursday

40. The day of your birthday was __________

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PROBABILITY

ExperimentAn operation which results in some well-defined outcomes is called an experiment.

Random ExperimentAn experiment whose outcome cannot be predicted with certainty is called a random experiment. Inother words, if an experiment is performed many times under similar conditions and the outcome ofeach time is not the same, then this experiment is called a random experiment.Example: a) Tossing of a fair coin

b) Throwing of an unbiased diec) Drawing of a card from a well shuffled pack of 52 playing cards

Sample Space The set of all possible outcomes of a random experiments is called the sample space for that

experiment. It is usually denoted by S.Example:

f) When a die is thrown, any one of the numbers 1, 2, 3, 4, 5, 6 can come up. Therefore.Sample spaceS = {1, 2, 3, 4, 5, 6}

g) When a coin is tossed either a head or tail will come up, then the sample space w.r.t.the tossing of the coin isS = {H, T}

h) When two coins are tossed, then the sample space is

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Sample point / event point

Each element of the sample spaces is called a sample point or an event point.Example: When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6} where 1, 2, 3, 4, 5 and

6 are the sample points.

Discrete Sample SpaceA sample space S is called a discrete sample if S is a finite set.

EventA subset of the sample space is called an event.

Problem of Events Sample space S plays the same role as universal set for all problems related to the particular

experiment. is also the subset of S and is an impossible Event. S is also a subset of S which is called a sure event or a certain event.

Types of EventsA. Simple Event/Elementary Event

An event is called a simple Event if it is a singleton subset of the sample space S.Example:

a)

When a coin is tossed, then the sample space isS = {H, T}

Then A = {H} occurrence of head and B = {T} occurrence of tail are called Simple events.

b) When two coins are tossed, then the sample space isS = {(H,H); (H,T); (T,H); (T,T)}

Then A = {(H,T)} is the occurrence of head on 1st and tail on 2nd is called a Simple event.

B. Mixed Event or Compound Event or Composite EventA subset of the sample space S which contains more than one element is called a mixed event orwhen two or more events occur together, their joint occurrence is called a Compound Event.Example:When a dice is thrown, then the sample space isS = {1, 2, 3, 4, 5, 6}

Then let A = {2, 4 6} is the event of occurrence of even and B = {1, 2, 4} is the event of occurrence ofexponent of 2 are Mixed events

Compound events are of two type:a) Independent Events, andb) Dependent Events

C. Equally likely eventsOutcomes are said to be equally likely when we have no reason to believe that one is more likely tooccur than the otherExample: When an unbiased die is thrown all the six faces 1, 2, 3, 4, 5, 6 are equally likely tocome up.

D. Exhaustive EventsA set of events is said to be exhaustive if one of them must necessarily happen every time theexperiments is performed.Example: When a die is thrown events 1, 2, 3, 4, 5, 6 form an exhaustive set of events.

ImportantWe can say that the total number of elementary events of a random experiment is called theexhaustive number of cases.

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E. Mutually Exclusive Events

Two or more events are said to be mutually exclusive if one of them occurs, others cannot occur. Thus if two or more events are said to be mutually exclusive, if not two of them can occur together.Hence, A1, A2, A3,…, An are mutually exclusive if and only if A i A j = i j Example:

a) When a coin is tossed the event of occurrence of a head and the event of occurrence of a tailare mutually exclusive events because we cannot have both head and tail at the same time.

b) When a die is thrown, the sample space is S = {1, 2, 3, 4, 5, 6}Let A is an event of occurrence of number greater than 4 i.e., {5, 6}

B is an event of occurrence of an odd number {1, 3, 5}C is an event of occurrence of an even number {2, 4, 6}

Here, events B and C are Mutually Exclusive but the event A and B or A and C are notMutually Exclusive.

F. Independent Events or Mutually Independent events

Two or more event are said to be independent if occurrence or non-occurrence of any of them doesnot affect the probability of occurrence of or non-occurrence of their events.

Thus, two or more events are said to be independent if occurrence or non-occurrence of any of themdoes not influence the occurrence or non-occurrence of the other events.Example: Let bag contains 3 Red and 2 Black balls. Two balls are drawn one by one withreplacement.

Let A is the event of occurrence of a red ball in first draw.B is the event of occurrence of a black ball in second draw.

then probability of occurrence of B has not been affected if A occurs before B. As theball has been replaced in the bag and once again we have to select one ball out of 5(3R + 2B) givenballs for event B.

G. Dependent Events

Two or more events are said to be dependent, if occurrence or non-occurrence of any one of themaffects the probability of occurrence or non-occurrence of others.Example: Let a bag contains 3 Red and 2 Black balls. Two balls are drawn one by one withoutreplacement.

Let A is the event of occurrence of a red ball in first drawB is the event of occurrence of a black ball in second draw.

In this case, the probability of occurrence of event B will be affected. Because after theoccurrence of event A i.e. drawing red ball out of 5(3R + 2B), the ball is not replaced in bag. Now, forthe event B, we will have to draw 1 black ball from the remaining 4(2R + 2B) balls which gets affecteddue to the occurrence of event A.H. Complementary Events

Let S be the sample space for a random experiment and let E be the event. Also, Complement ofevent E is denoted by E‟ or E, where E‟ means non occurrence of event E. Thus E‟ occurs if and only if E does not occur.

n (E) + n (E‟) = n (S)Occurrence of an Event

For a random experiment, let E be an eventLet E = {a, b, c}. If the outcome of the experiment is either a or b or c then we say the event hasoccurred.Sample Space : The outcomes of any typeEvent : The outcomes of particular typeProbability of Occurrence of an event

Let S be the same space, then the probability of occurrence of an event E is denoted by p(E) and isdefined asP(E) = n(E)/n(S) = number of elements in E/number of elements in SP(E) = number of favourable/particular cases

total number of cases

Example:

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a) When a coin is tossed, then the sample space is S = {H, T}Let E is the event of occurrence of a head E = {H}

b) When a die is tossed, sample space S = {1, 2, 3, 4, 5, 6}Let A is an event of occurrence of an odd numberAnd B is an event of occurrence of a number greater than 4 A = {1, 3, 5} and B = {5, 6}

P(A) = Probability of occurrence of an odd number = n(A)/n(S) = 3/6 = ½and P(B) = Probability of occurrence of a number greater than 4 = n(B)/n(S) = 2/6 = 1/3

EXERCISE

Questions 1 – 7A coin is flipped three. Find the probability of getting

1. A head exactly once.1. 1/82. 1/ 43. 3/84. 1/ 2

2. tails exactly twice.

1.

1 /42. 3/83. 1/84. None of these

3. heads all three times.1. 1/82. ¼3. 3/84. 1/ 2

4. a tail at least once.1. 1 /42. 7/83. 1/8

4.

3/85. a head at least two times. S

1. 3/82. 1 /43. 1/84. 1 /2

6. a head in the first throw, a tail in the second, and a head in the third.1. 1 /82. 1/ 43. 3/8

4.

1 /27. a head in the third toss, if in the first two tosses the coin landed tails.

1. 1/ 22. 1/ 83. 7/84. 1 /4

Questions 8 – 11From a pack of 52 cards, a card is chosen at random. Find the probability of it being

8. a knave.

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3. 3/74. 4/7

19. if P (A)=0.3 P(B)=0.4 and P(AB)=0.6, then find P(AB).1. 0.32. 0.43. 0.14. 0.5

20. In throwing a fair dice, what is the probability of getting the number „3‟? 1.

1/32. 1/63. 1/94. 1/12

21. What is the number of throwing a number greater than 4 with an ordinary dice whose faces arenumbers from 1 to 6.1. 1 /32. 1/63. 1/94. 1/12

22. Three coins are tossed. What is the probability of getting(i) 2 Tails and 1 Head1. 1 /42.

3/83. 2/34. 1/ 8(ii) 1 Tail and 2 Heads1. 3 /82. 13. 2 /34. 3 /4

23. Three coins are tossed. What is the probability of getting(i) neither 3 Heads nor 3 Tails1. 1 /22. 1 /33. 2/34.

3 /4(ii) three heads1. 1 /82. 1 /43. 1 /24. 2/ 3

24. What is the probability of throwing a number greater than 2 with a fair dice1. 2 /32. 2/53. 14.

3/525. A can hit the target 3 times in 6 shots, B 2 times in 6 shots and C 4 times in 6 shots. They fire a

volley. What is the probability that at least 2 shots hit?1. 1 /22. 1/33. 2 /34. 1/ 4

26. If 4 whole numbers are taken at random and multiplied together, what is the chance that the lastdigit in the product is 1, 3, 7 or 9 ?1. 15/653

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2. 12/5423. 16/6254. 13/625

27. A life insurance company insured 25,000 young boys, 14,000young girls and 16,000youngadults. The probability of death within 10 years of a young boy, young girl and a young adult arte0.02, 0.03 and 0.15 respectively. One of the insured persons dices. What is the probability thatthe dead person is a young boy?1. 36/1652.

25/1663. 26/1654. 30/165

28. A team of 4 is to be constituted out of 5 girls and 6 boys. Find the probability that the team mayhave 3 girls.1. 4 /112. 3/113. 5/114. 2/11

29. 12 persons are seated around a round table. What is the probability that two particular personssit together?1. 2/112. 1/63.

3/114. 3/15

30. Six boys and six girls sit in a row randomly. Find the probability that all the six girls sit together.S1. 3/222. 1/1323. 1/15844. 1/66

31. A bag contains 5 red, 4 green and 3 black balls. If three balls are drawn out of it at random, findthe probability of drawing exactly 2 red balls.1. 7/222. 10/333. 7/124.

7/1132. A bag contains 100 tickets numbered 1, 2, 3,…., 100. If a ticket is drawn out of it at random,

what is the probability that the ticket drawn has the digit 2 appearing on it.1. 19/1002. 21/1003. 32/1004. 23/100

33. A fair coin is tossed repeatedly. If tail appears on first four tosses, then the probability of headappearing on fifth toss equals:1. 1 /22. 1/323. 31/324. 1/5

34.

Three mangoes and three apples are kept in a box. If two fruits are selected at random from thebox, the probability that the selection will contain one mango and one apple, is:1. 3/52. 5/63. 1/36 4.

None of these

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ANALYTICAL

Blood Relations

Examples 1. If Neena says, “Anita‟s father Raman is the only son of my father-in-law Mahipal”, then how is Bindu, who is the sister of Anita, related to Mahipal?

(a) Daughter(b)

Wife(c) Daughter-in-law(d)

None of these

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Solution. None of these. Only son of Neena‟s father-in-low Mahipal Neena‟shusband. So raman is Neena‟s husband and Anita and Bindu are his daughters. Thus, Bindu is the grand daughter of Mahipal.

Example 2. Pointing to a photograph, a woman says, “This man‟s son‟s sister is my

mother-in-law.” How is the woman‟s husband related to the an in the photograph? (a)

Son(b) Son-in-law(c)

Grandson(d) Nephew

Solution. Grand son. Man‟s son‟s sister-man‟s daughter. So, the man‟s daughter isthe mother of the woman‟s husband. Thus, the woman‟s husband is the grandson ofthe man in the photograph.

Example 3. Pointing towards a person in a photograph, Raman said, “She is theonly daughter of the mother of my brother‟s sister”. How is that person related toRaman?

(a) Uncle(b)

Father(c) Mother(d)

Sister

Solution. Sister. The mother of Roman‟s brother‟s sister is the mother of Ramanand only daughter of Raman‟s mother means Raman‟s sister. Therefore the personin the photograph is related as sister to Raman.

Example 4. A is father of C and D is son of B . e is brother of A . If C is sister of D ,how is B related to E ?

(a)

Husband(b) Brother-in-law(c)

Sister-in-law(d) Daughter

Solution. Daughter. A is father of C and C is sister of D . So A is father of D . But D isson of B . So, B is the mother of D and wife of A . Also, E is the brother of A So, B isthe sister-in-law of E .

Example 5. If P + Q means P is the husband of Q : P Q means P is the sister of Q and P × Q means P is the son of Q . Which of the following shows A is the daughterof B ?

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Solution. A D × B . A is the daughter of B means A is the sister of the son (say D )of B i.e., A D × B .

The standard definitions of relations are given below

A/An is related to a PERSON as

Grandfather The father of his/her mother or father

Grandmother The mother of his/her mother or father

Grandson The son of his/her daughter/son

Granddaughter The daughter of his/her daughters/son

Uncle The brother of his/her mother or father

Aunt The sister of his/her mother or fatherNephew The son of his/her brother or sister

Cousin The son or daughter of his/her aunt of uncle

Niece The daughter of his/her brother or sister

Spouse as her husband or his wife

Father-in-law the father of his/her spouse

Mother-in-law the mother of his/her spouse

Sister-in-law the sister of his/her spouse

Brother-in-law the brother of his/her spouse

Son-in-law the spouse of his/her daughter

Daughter-in-law the spouse of his/her son

Exercise:

1. When Amit saw Manoj, he recalled and said “He is the son of the father of themother of my daughter”. What is Manoj to Amit?

1. Brother-in-law 2. Brother 3. Cousin 4. Uncle

2. Introducing a girl, Vinod said, “Her mother is the only daughter of my mother-in-law”. How is Vinod related to the girl? 1. Uncle 2. Husband 3. Brother 4. Father

3. Pointing to an old man Karim said, “His son is my son‟s uncle”. How is the oldman related to Karim?

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1. Brother 2. Uncle 3. father 4. Grand father

4. Seetha told to Malini, “The girl I met yesterday in the market was the youngestdaughter of the brother-in-law of my friend‟s mother”. How is the girl related toSeetha‟s friend? 1. Cousin 2. Daughter 3. Niece 4. Aunt

5. Rohit told to Amit, “Yesterday I met the only brother of the daughter of mygrand father”. Whom did Rohit met? 1. Son 2. Father 3. Brother 4. Uncle

6. Showing the lady at the door, Kailash said, “She is the daughter of my grandfather‟s only son”. How is Kailash related to that lady?1. Brother 2. Cousin 3. Father 4. Uncle

7. Pointing a man in a photograph, Anuradha said, “His mother‟s only daughter ismy mother”. How is Anuradha related to that man?

1. Niece 2. Nephew 3. Sister 4. Wife

8. Pointing a person a man said to a woman, “His mother is only daughter of yourfather”. How was the woman related to that person? 1. Aunt 2. Mother 3. Wife 4. Daughter

9. Showing the man in the park, Sulthana said, “He is the brother of my uncle‟sdaughter”. What is the man to sulthana? 1. Son 2. Brother-in-law 3. Cousin 4. Uncle

10. C is A‟s father‟s Nephew. D is A‟s cousin but not the sibling of C. How is D

related to C?1. Cousin 2. Sister 3. Mother 4. Aunt

11. K is brother of N and X. Y is mother of N, and Z is father of K. Which of thefollowing statement is not true?1. K is the son of Z 2. Y is the wife of Z3. N is the brother of X 4. K is the father of X.

12. A woman walking with a boy meets another woman and on being asked abouther relationship with the boy, she says, “My maternal uncle and his maternaluncle‟s maternal uncle are brothers”. How is the boy related to the woman?

1. Father 2. Son 3. Brother 4. Father in law

13. Pointing to a person, a man said to a woman, “His mother is the only daughterof your father”. How was the woman related to the person?1. Sister 2. Mother 3. Wife 4. Daughter

14. Pointing to his son‟s portrait, a man said to a woman, “His mother is the onlydaughter of your mother”. How was the woman related to the man?

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1. Sister 2. Mother 3. Wife 4. Daughter

15. Pointing to a girl in the photograph Umesh said, “Her mother‟s brother is theonly son of my mother‟s father”. How is the girl‟s mother related to Umesh? 1. Mother 2. Sister 3. Aunt 4. Can‟t be determined

16. Introducing Kamala, Mahesh said, “Her father is the only son of my father”.How is Mahesh related to Kamala?1. Brother 2. Father 3. Uncle 4. Son

17. A man said to a woman, “Your only brother‟s sister is my mother”. How is thewoman related to the man‟s maternal grand mother? 1. Mother 2. Sister 3. Daughter 4. Mother in law

18. A man said to a woman, “Your only brother‟s son is my wife‟s brother”. How isthe woman related to the man‟s wife?

1. Mother 2. Aunt 3. Sister 4. Can‟t be explained

19. Pointing the man in the photograph, Reeta said, “He is the brother of my uncle‟sdaughter”. How is the man in the photograph is related to Reeta?1. Son 2. Brother in law 3. Nephew 4. Cousin

20. Introducing a girl in the photograph, Sunil said, “Her mother is the onlydaughter of my mother in law”. How is Sunil related to the girl in thephotograph?1. Uncle 2. Brother 3. Husband 4. Father

21. Pointing to a lady, a man said, “The son of her only brother is the brother of my

wife”. How is the lady related to the man? 1. Maternal Aunt 2. Mother in law 3. Mother‟s sister 4. Grand Mother

22. Pointing to a photograph, a person tells his friend, “She is the grand daughter ofthe elder brother of my father”. How is the girl in the photograph related to thisman?1. Aunt 2. Maternal aunt 3. Sister 4. None

23. Pointing to a man in a photograph a woman said, “His brother‟s father is onlyson of my grand father”. How is the woman related to the man in thephotograph?1. Mother 2. Aunt 3. Daughter 4. Sister

24. A is related to B and C, D is C‟s mother. Also D is B‟s sister and A is B‟s sister.How is C related to A?1. Niece 2. Cousin 3. Sister 4. Aunt

25. Sandhya is mother in law of Vrunda, who is sister in law of Dhanraj. Ravi is thefather of Ramana, the only brother of Dhanraj. How is Sandhya related to

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Dhanraj?1. Mother in law 2. Aunt 3. Mother 4. Wife

26. A, the son of B was married to C, whose sister D was married to E, the brotherof A. How is D related to B?1. Sister 2. Daughter in law 3. Sister in law 4.

Cousin

27. Introducing Swapna, Madhavi said, “She is the only daughter of my father‟sonly daughter”. How is Madhavi related to Swapna?1. Niece 2. Aunt 3. Cousin 4. None

28. Rohit said to Mohit, “The boy playing basket ball is younger brother of the twobrothers of the daughter of my father‟s wife”. How is the boy playing basket ballrelated to Rohit?1. Cousin 2. Nephew 3. Brother in law 4. Brother

29. Introducing a man to her husband, a woman said “His brother‟s father is theonly son of my grand-father”. How is the woman related to this man?

1. Mother 2. Sister in law 3. Sister 4. Aunt

30. A and B are brother. C and D are sisters. A‟s son is D‟s Brother. How is Brelated to C?1. Uncle 2. Brother 3. Father 4. Brother in law

Directions (Questions 31-35): Read the following information carefully and answerthe questions below:A family consists of six members P, Q, R, S, T and U. There are two married couples.

Q is a doctor and the father of T. U is the grandfather of R and is a contractor. S isgrandmother of T and is a housewife. There is one doctor, one contractor, onenurse, one housewife and two students in the family.

31. Who is the husband of P?1. R 2. U 3. Q 4. S

32. Who is the sister of T?1. R 2. U 3. T 4. Information insufficient

33. What is the profession of P?

1. Doctor 2. Nurse 3. Doctor of nurse 4. Housewife

34. Which of the following are two married couple?1. US, QT 22. US, QP 3. TS, RU 4. US, RP

35. Which of the following is definitely a group of male members?1. QU 2. QUT 3. QUP 4 UT

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47. Pointing towards a photograph of a girl, Ramu said, “she has no sisters ordaughters but her mother is the only daughter of my mother”. How is the girl inthe photograph related to Ramu‟s mother? 1. Sister in law 2. Grand Daughter 3. Daughter in law 4.Can‟t be determined

48. Pointing towards a person in a photograph, Raman said, “She is the onlydaughter of the mother of my brother‟s sister”. How is the person in photograph

related to Raman?1. Daughter 2. Sister 3. Wife 4. Cousin

49. Pointing to a man in a photograph, a woman said, “His brother‟s father is theonly son of my grandfather”. How is the woman related to the man in thephotograph?1. Sister 2. Mother 3. Grandmother 4. Aunt

50. If Monika says, “Rahul‟s father is the only son of my father”, how is Monika

related to Rahul?1. Daughter 2. Sister 3. Aunt 4. Can‟t be determined

51. If Vijay says, “Vinay‟s mother is the only daughter of my mother”, how is Vijayrelated to Vinay?1. Brother 2. Grandfather 3. Father 4. Maternal Uncle

52. Pointing towards a person in a photograph, Amrutha said, “He is the only son ofthe father of my sister‟s brother”. How is that person related to Amrutha? 1. Maternal uncle 2. Mother 3. Father 4. Brother

53. Introducing a man, a woman said, “His wife is the only daughter of my mother.”

How is the woman related with the man?1. Sister in law 2. Wife 3. Mother in law 4. Aunt

54. Pointing to Neha, Mahesh said, “Her mother‟s only daughter is my daughter”.How is Mahesh related to Neha?1. Brother 2. Uncle 3. Son 4. Father

55. Pointing to a boy in the photograph Manasa said, “His sister is the onlydaughter of my father”. How is the boy related to Manasa‟s father? 1. Father 2. Brother 3. Son 4. Cousin

56. Pointing to a lady in the photograph, Vinay said, “She is the daughter of mygrandfather‟s only son”. How is Vinay related to that lady? 1. Brother 2. Cousin 3. Father 4. Uncle

57. Introducing a man a woman said, “He is the only son of my mother‟s mother”.How is woman related to the man?1. Mother 2. Aunt 3. Niece 4. Sister

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58. Introducing a man, a woman said, “His wife is the only daughter of my father”.How that man was related to the woman?1. Maternal uncle 2. Father in law 3. Brother 4. Husband

59. Pointing to a man in photograph a woman said, “His brother‟s father is the only son of my grandfather”. How is the woman related to the man in the

photograph?1. Mother 2. Aunt 3. Sister 4. Daughter

60. Pointing to a person, a man said to a woman, “His mother is the only daughterof your father”. How was the woman related to the person?1. Sister 2. Mother 3. Wife 4. Daughter

61. Introducing a girl, Vishal said, “Her mother is the only daughter of my motherin law”. How is Vishal related to the girl? 1. Uncle 2. Husband 3. Brother 4. Father

62. Pointing to a lady, a man said “The son of her only brother is the brother of mywife”. How is the lady related to the man? 1. Mother‟s sister 2. Grand mother 3. Mother in law 4. Sister of father in law

63. Pointing to an old man, Karunakar said, “His son is my son‟s uncle”. How is theold man related to Karunakar?1. Brother 2. Uncle 3. Father 4. Grandfather

Directions (Questions 64-68): Read the following information carefully and answerthe questions that follow.

In a family, there are six members A, B, C, D, E and F. A and B are a marriedcouple, A being the male member. D is the only son of C, who is the brother of A, Eis the sister of D. B is the daughter in law of F, whose husband had died.

64. How is F related to A?1. Mother 2. Sister in law 3. Sister 4. Mother in law

65. How is E is related to C?1. Sister 2. Daughter 3. Cousin 4. Aunt

66. Who is C to B?

1. Brother 2. Brother in law 3. Son in law 4. Nephew

67. How many male members are there in the family?1. Two 2. Three 3. Four 4. Five

68. How is F related to C?1. Mother in law 2. Sister in law 3. Mother 4. Aunt

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Directions (Questions 69-73): Read the following information carefully and answerthe questions given below. A family consists of six members P, Q, R, X, Y, Z. Q is theson of R but R is not the mother of Q. P and R are a married couple. Y is the brotherof R, X is the daughter of P, Z is the brother of P.

69. Who is the brother in law of R?

1. P 2. Z 3. Y 4. X

70. Who is the father of Q?1. P 2. Z 3. R 4. Can‟t be determined

71. How many children does P have?1. Four 2. Two 3. Three 4. One

72. How many female members are there in the family?1. One 2. Two 3. Three 4. Four

73. How is Q related to X?

1. Uncle 2. Brother 3. Father 4. Husband

Directions (Questions 74-77): In a family there are 6 members A, B, C, D, E and F.A is Husband of B. D is only son of C, who is the brother of A. E is the sister of D. Bis daughter-in-law of F, whose husband has died.

74. How is F related to A?1. Mother 2. Sister-in-law 3. Sister 4. Mother-in-law

75. How is E related to C?

1. Sister 2. Son-in-law 3. Brother-in-law 4. None

76. Who is C to B?1. Brother 2. Brother in law 3. Nephew 4. Son in law

77. How many male members are there in the family?1. 2 2. 3 3. 4 4. 5

Directions (Question 78-80): There are 6 persons P1, P2, P3, P4, P5 and P6. P3 isthe sister of P6. P2 is brother of P5‟s Husband. P4 is the father of P1 and grandfather of P6. There are 2 fathers, 1 mother and 3 brothers in the family.

78. How many male members are there?1. 4 2. 3 3. 2 4. 1

79. Who is the mother in given options?1. P5 2. P3 3. P1 4. P2

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80. Who is P5‟s husband? 1. P3 2. P6 3. P1 4. P4

Directions

Examples

Example 1. Ravi traveled 4 km straight towards south. He turned left and traveled 6 km straight,then turned right and traveled 4 km straight. How far is he from the starting point?(e) 8 km(f) 10 km(g) 18 km(h) 12 km

Solution. 10 km. B is the finishing point and A is starting point. The distance of A from B is

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Example 2. A is to the South-East of C, B is to the East of C and North-East of A. If D is to the Northof A and North-West of B. In which direction of C is D located?(a) North-West(b) South-West(c) North-East(d) South-East

Solution. North-East D is located to the North-East of C.

Example 3. A rat runs 20‟ towards East and turns to right, runs 10‟ and turns to right, runs 9‟ andagain turns to left, runs 5‟ and then runs to left, runs 12‟ and finally turns to left and runs 6‟. Now,which direction is the rat facing?

(e)

East(f)

West(g) North(h) South

Solution. North. The movements of the rat from A to G are as shown in the fig. It is clear, rat iswalking in one direction FG, i.e., North.

Example 4. From his house, Lokesh went 15 km to the North. Then he turned west and covered 10km, then he turned South and covered 5 km. Finally, turning to East, he covered 10 km. In whichdirection is he from his house?(a) East(b) South(c) North(d) West

Solution. North. Starting point is A and ending point is E. E is to the north of his house at A.

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Exercise

1. After starting from office Ravendra turns left twice and then turns right. Now he turns towardsSouth. In which direction Ravendra had started walking?(a) East(b) West(c) North

(d)

South

2. Facing towards south Varun walked 50 mts. He then turned to his right and walked 30 mts. Heagain turned right and walked 50 mts. How for was he from his original position and towardswhich direction?(a) 20m, East(b) 30m, South(c) 30m, West(d) 20m, North

3. Lalit walks 8 km east, turns South-West and walks another 8km. He again takes a turn towardsNorth-West and walks another 8m. In which direction from his starting point is he standing now?In which direction from his starting point is he standing now?

(a)

North-East(b) North(c) East(d) West

4. Six persons are playing a game sitting in a circle facing the centre. Vijay was to the left of Sudhir.Amar was between Rakesh and Sarv, Neerav was second to the left of Amar. Which of thefollowing is the position of Amar from Neerav?(a) Second from right(b) Second to the left(c) Third from the left(d) Third from right

5.

Ankit started walking towards North. After walking 30 metres, he turned towards left and walked40 metres. He then turned left and walked 50 metres. How far is he from his original position?(a) 50 metres(b) 40 metres(c) 30 metres(d) None of these

6. Rahim started from point X and walked straight 5 km West, then turned left and walked straight2 km and again turned left and walked straight 7 km. In which direction is he from the point X?(a) North-East(b) South-West(c) South-East(d) North-West

7. B is to the South-west of A,C is to the East of B and South-East of A and D is to the North of C inline with B & A. In which direction of A is D located?(a) North(b) East(c) South-East(d) North-East

8. A walks 10 metres towards East and then 10 metres to his right, then every time turning to hisleft, he walks 5.15 and 15 metres respectively. How far is he now from his starting point?(a) 5 metres

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(b) 10 metres(c) 15 metres(d) 20 metres

9. A man walks 1 km towards. East and then he turns so South and walks 5km. Again he turns toEast and walks 2 km, after this he turns to North and walks 9 km. Now how far is he from hisstarting point?(a) 7 km(b)

5 km(c) 4 km(d) 3 km

10. I am facing South. I turn right and walk 20 m, then I turn right again and walk 10 m. Then I turnleft and walk 10 m and then turning right walk 20 m. Then I turn right again and walk 60metres. In which direction am I from the starting point?(a) North(b) East(c) North-West(d) North-East

11. A man is facing North-West. He turns 900 in the clock wise direction, then 1350 in theanticlockwise direction which direction is he facing now?(a) North(b) East(c) North-West(d) North-East

12. One day, Ravi left home and cycled 10 km Southwards, turned right and cycled 5 km and turnedright and cycled 10 km and turned left and cycled 10 km. How many kilometers will he have tocycle to reach his home straight?(a) 10 km(b) 20 km(c) 15 km(d) 25 km

13. A Child is looking for his father. He went 90 metres in the east before turning to his right. Hewent 20 metres before turning to his right again to look for his father at his uncle‟s place 30metres from this point. His father was not there. From there, he went 100 metres to his northbefore meeting his father in a street. How far did the son meet his father from starting point?(a) 180 metres(b) 100 metres(c) 140 metres(d) 120 metres

14. Varun walks 20 m North, then he turns right and walks 30 m, then he turns right and walks 35m, then he turns left and walks 15 m. Then he again turns left and walks 15 m. In whichdirection and how many metres away is he from his original position?(a)

15 metres West(b) 30 metres East(c) 45 metres East(d) 30 metres West

15. I am facing East. I turn 1000 in the clockwise direction and then 1450 in the anticlockwisedirection which direction and I facing now?(a) South-West(b) North(c) North-East(d) East

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16. A man is facing North-West. He turns 900 in the clockwise direction, then 1800 in theanticlockwise direction and then another 900 in the same direction. Which direction is he facingnow?(a) South-East(b) West(c) South-West(d) South

Directions (Questions 17-20) : P, Q, R and S are standing on the four corners of a square field.Study the following questions which are based on the figure.

17. P, Q, R and S from the position shown in the above fig., walk across the field along the diagonalsto reach the opposite end from where Q and R walk anticlockwise and P and S walk clockwisealong the sides. Each one covers ½ side. Now indicate which one of the following statements is

true?(a) P is to the North-West of Q(b) Q is to the North-East of P(c) P is to the South-West of S(d) R is to the North-West of Q

18. From the position in question 17, P,Q and S walk clockwise and R walks anticlockwise along thesides and cover one side each assuming that they walk with the same speed, indicate which oneof the following statements is true.(a) P will meet Q on the North-Eastern corner.(b) S will meet P on the North-Western corner.(c) Q will meet R on the South-Eastern corner.(d) S will meet R on the South-Western corner.

19. From the position in question 18, P and R walk across field to reach the opposite side from wherethey turn of their right and cover 1 ½ sides each. Now indicate which one of the followingstatements is not true?(a)

R and Q are not opposite to each other.(b) R and S are not opposite to each other.(c) P and Q are not opposite to each other.(d)

Q and S are opposite to each other.

20. From the position in question 18, P and R walk across field to reach the opposite side from wherethey turn of their right and cover 1 ½ sides each. Now indicate which one of the followingstatements is not true?(a) P will reach the North-Western corner after Q

(b)

P and R will cross each other at the centre.(c) S and P will cross each other on the Southern side.

(d) R and Q will not cross each other on Northern side.

21. A is 40 m. South-West of B. C is 40 m South-East of B. Then C is in which direction of A?(a)

South(b) North-East(c)

West(d)

East

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22. Ravi wants to go to the university. He starts from his home which is in the East and comes to acrossing. The road to the left ends in a theatre, straight ahead is the hospital. In which directionis the university?(a)

West(b) East(c) North(d)

South

23.

P, Q, R and S are playing a game of carom. P,R and S,Q are partners. S is to the right of R who isfacing West. Then, Q is facing(a)

East(b) West(c)

North(d)

South

Directions (Qs24-27): Read the following information carefully and answer the question given belowit:

(i) Six flats on a floor in two rows facing North and South are allotted to P, Q, R, S, T and U(ii) Q gets a North facing flat and is not next to S.(iii) S and U get diagonally opposite flats.(iv) R, next to U, gets a South facing flat and T gets a North facing flat.

24. Which of the following combinations get South facing flats?a) Q T Sb) U R Pc) U P Td) None of these

25. Whose flat is between Q and S?(a)

P(b)

R(c) U(d)

T

26.

If the flats of T and P are interchanged, whose flat will be next to that of U?(a) T

(b) R

(c) Q(d)

P27. The flats of which of the other pairs SU, is diagonally opposite to each other?

(a) TS

(b) PT(c)

QR(d)

QP

28. One evening before sunset, two friends Sumit and Mohit were talking to each other face to face. IfMohit‟s shadow was exactly to his right side, which directions was Sumit facing?

(a)

North(b) West

(c) South

(d) None of these

29. One morning after sunrise, Daya and Bhavna were talking to each other face to face at Tilaksquare. If Bhavna‟s shadow was exactly to the right of Daya, which direction Bhavna was facing?(a) North(b)

East(c)

South(d) None of these

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30. After walking 6 km, I turned right and covered a distance of 2 km, then turned left and covered a

distance of 10 km. In the end, I was moving towards the North. From which direction did I startmy journey?(a) West(b) East(c)

South(d) North

Directions (31-32): Stady the information given below carefully and answer the questions that followon playing ground, Dinesh, Kunal, Nitin, Atul and Prashant are standing as described below facingthe North

(i) Kunal is 40 mts to the right of Atul(j) Dinesh is 60 mts to the south of Kunal(k) Nitin is 25 mts to the west of Atul(l) Prashant is 90 mts tot eh North of Dinesh

31. Who is to the North-East of the person who is to the left of Kunal?(a) Atul(b)

Dinesh(c)

Nitin(d)

None of these

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32. If a boy walks from Nitin, meets Atul followed by Kumal. Dinesh and then Prashant, how manymetres has he walked is he has traveled the straight distance all through?

(a) 215 m

(b) 155 m(c) 185 m(d)

245m

33.

Vikas starts walking straight towards east. After walking 75meters, he turns to the left and walks 25 meters straight. Again, he turns toleft walks a distance of 40 meters straight, again he turns to left and walks adistance of 25 meters. How far is he from the starting point?1. 40 m 2. 30 m 3. 35 m 4. 50 m

34.

A is standing at P. He walks 10 meters towards the south;then he walks 20 meters towards the west; then he walks 10 meters towardsthe south; then he walks 20 meters towards the North and reaches Q. What isthe straight distance between P and Q in meters?1. 15 m 2. 8 m 3. 9 m 4. None

35. Facing towards north, Goel walks 20 meters, he turns leftand walks 40 meters, he again turns left and walks 20 meters, then he turnsright and walks 20 meters. How far is he now from his original position?1. 30 m 2. 40 m 3. 45 m 4. 60 m

36. Facing towards north, Rajesh walked 30 meters. He thenturns left and walks 50 meters. He again turns left and walks 30 meters. Howfar is he from his original position and towards which direction?

1. 50 m, west 2. 60 m, west 3. 50 m, east 4. 60 m, east

37.

In the Olympic Games, the flags of 6 nations were flown onthe masts in the following way. The flag of America was found to the left ofIndian Tricolor and to the right of the flag of France. The flag of Australia wason the right of the Indian flag but was to the left of the flag of Japan, whichwas to the left of the flag of China. Find the two flags which are in the center.1. America and India 2. Japan and Australia

3. America and Australia 4. India and Australia

38.

One day Jack left home and cycled 10 km southwards,turned right and cycled 5 km and turned right and cycled 10 km and turnedleft and cycled 10 km. How many kms will he have to travel to reach his homestraight?1. 10 km 2. 15 km 3. 20 km 4. 25 km

39. Anil travels from a point to east 10 km and turned right andtraveled 8 km and turned right traveled 6 km and turned right traveled 5 km.How far is he from the starting point?

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1. 4 km 2. 6 km 3. 5 km 4. 22 km

40.

A person walks facing north 10 m and then he turns left andwalks 5 m. He again turns left and walks 10 m. How far is he from his originalposition and towards which direction?1. 20 m, south 2. 15 m, west 3. 10 m, south 4. 5 m, west

41.

One morning after sunrise, Mahender and Manoj werestanding in a chowk in Delhi with their backs towards each other. Mahender‟sshadow fell exactly towards his left hand side. Which direction was Manojfacing?1. East 2. West 3. South 4. North

42. Mr. S. Bharat goes 30 meters North, then turns right andwalks 40 meters, then again turns right and walks 20 meters, then againturns right and walks 40 meters. How many meters is he from his originalposition?

1. 10 2. 15 3. 20 4. 18

43. Saurav travels 5 km to the north. Then turn to his right andtravel 12 km. How many kms away is he from the starting point?1. 2 2. 13 3. 10 4. 12

44.

Suman is 40 meters south-west of Ashok. Prakash is 40meters south-east of Ashok. Prakash is in which direction of Suman?1. South 2. West 3. East 4. North-east

45.

Niraj who is facing south turns to his left and walks 8 meters.

Then he faces North and walks 25 meters, and then turning to his left hewalks a few meters so that he is 25 meters away from the original position.What is the total distance in meters covered by him in west?1. 25 2. 8 3. 41 4. Can‟t be determined

46. A man goes five kilometers towards east, then he takes a turnto south-west and goes five kilometers. He again takes a turn towards north-east and goes five kilometers with respect to the point from where he started.Where is he now?1. at the starting point 2. in the west 3. in the east 4. in thenorth-east

47. Starting from a point, Raju walked 12 meters towards north,he turned right and walked 10 meters, he again turned right and walked 12meters, then he turned left and walked 5 meters. How far is he now and inwhich direction from the starting point?1. 27 m, east 2. 5 m, east 3. 10 m, west 4. 15 m, east

48.

Mr. X travels towards north 3½ km. Then he turns left andtravels towards west for 1½ km, then turns left and travels for 3½ km. How

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far is he from the starting point?1. 7 km 2. 4½ km 3. 2½ km 4. 1½ km

49. I went 15 m to the North, then I turned west and covered 5m, and then I turned east and covered 10 m. In which direction am I from thehouse?

1. North-East 2. South-West 3. North-East 4. South-East

50. Yugal started walking towards south. After walking 15 metershe turned to the left and walked 15 meters. He again turned to his left andwalked 15 meters. How far is he from his original position and in whichdirection?1. 15 m, north 2. 15 m, south 3. 15 m, east 4. 15 m, west

51.

A is east of B and west of C. H is south-west of C. B is south-east of X. Which is the farthest west?1. A 2. B 3. C 4. X

52.

If Shiny starts from point A and walks 5 miles, then turns leftand walks 4 miles towards north, turns left again and walks 3 miles, in whichdirection is she going at the end?1. West 2. North 3. South 4. East

53.

While going northwards a police-Inspector turns right andwalks 5 km straight. Then, he turns right and walks 8 km. In the end heturns left to reach his office. In which direction is his office from startingpoint?1. North 2. South 3. East 4. West

54. A walks 10 m in front and 10 m to the right. The everytimeturning to his left, he walks 5, 5, 15 meters respectively. How far is he nowfrom his starting point?1. 10 m 2. 20 m 3. 5 m 4. 15 m

55.

A man walks 10 km towards north. From there he walks 6km towards south. Then he walks 3 km towards east. How far and in whichdirection is he with reference to his starting point?1. 5 km towards west 2. 7 km towards east

3. 5 km towards north-east 4. 7 km towards west

56.

Lalith walks 7 km east, turns south-west and walks another8 km. He again takes a turn towards north-east and walks another 8 km. Inwhich direction from his starting point is he standing now?1. North-east 2. South-east 3. West 4. East

57.

One day John left home and cycled 10 km southwards,turned right and cycled 5 km and turned right and cycled 10 km. How many

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km will he have to cycle to reach his home straight?1. 10 km 2. 5 km 3. 20 km 4. 25 km

58. Girish walks 8 km towards east and turns right and walks 3km straight. Again he turns right and walks 12 km straight. Now how far ishe from the starting point?

1. 5 km 2. 6 km 3. 8 km 4. 10 km

59. Ramesh walked 5 km towards east then he turned right andwalked 8 km. He then turned left and walked 5 km. He again turned left andwalked 8 km. At what distance is he now from the starting point?1. 13 km 2. 10 km 3. 16 km 4. 20 km

60. A man walks 30 meters towards south. Then turning to hisright he walks 30 meters. Then turning to his left he walks 20 m. Againturning to his left he walks 30 meters. How far is he from his startingposition?

1. 30 m 2. 40 m 3. 50 m 4. 60m

61. Samir started from his police station on inspection duty.After traveling straight for a distance of four km, he turned left for the marketand traveled straight for another 200 meters, and turned left and traveledstraight for 600 meters. How far is Samir from the police station?1. 3.4 km 2. 3.8 km 3. 4.4 km 4. 4.8 km

62.

A boy rode his bicycle northwards, then turned left andmoved 1 km and again turned left and rode 2 km. He found himself exactly on1 km west of his starting point, How far did he ride northwards initially?

1. 1 km 2. 3 km 3. 2 km 4. 5 km

63.

Deepu went 20 meters to the east, he turned left and walked15 meters. He turned again right and went 35 meters. He again turned rightand walked 15 meters. How far was he from his starting point?1. 35 m 2. 50 m 3. 55 m 4. 60 m

64. From a point P, Samir started walking towards South andwalked 40 meters. He turned towards his left and walked 30 meters andreached a point Q. The point Q is at what minimum distance and at whatdirection from the point P?

1. 50 m, south-west 2. 45 m, south-east 3. 50 m, south-east 4. 35 m, south-east

65. I traveled 35 km to the west, then turned right and traveled 7km, then turned left and traveled 8 km, then turned back and traveled 11 km,then turned right and traveled 7 km. How far is he from the starting point?1. 3 km 2. 6 km 3. 7 km 4. 9 km

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66.

Soni traveled 9 km to the west, then turned right andtraveled 7 km, then turned left and traveled 8 km, then turned back andtraveled 11 km, then turned right and traveled 7 km. How far is he from thestarting point?1. 3 km 2. 6 km 3. 7 km 4. 9 km

Directions : A, B, C and D are standing on four corners of a square piece of plot asshown in the given figure. They start moving and the movements are explained ineach of the questions. Read the questions and select the right alternative.

67. From the original position, D starts crossing the fielddiagonally. After walking half the distance he turns right, walks some distanceand turns left. Which direction is D facing now?1. South-east 2. North-west 3. South-west 4. North

68. B traveled straight to C, a distance of 10 km. He turned rightand walked 7 km towards D, again he turned right and walked 8 km and thenfinally turned right and walked 7 km. How far is he from his original position?1. 7 km 2. 8 km 3. 2 km 4. 3 km

69.

A, B, C and D walk diagonally to opposite corners and fromthere B and C walk one and a half side anti clock-wise while A and D walkone side clock-wise along the sides. Where is D now?1. At the north-west corner 2. At the north-east corner3. At the south-west corner 4. At the north corner

70.

A and D walk one and a half length of the side clockwise andanti-clockwise respectively. Which one of the following statements is true?1. A is at midpoint between B and C and D at the corner originally occupied

by A2. A and D are both at the midpoint between C and D3. A and D are both at the midpoint between B and C4. None of these

Directions: -)

Seven Villages A, B, C, D, E, F and G are situated as follows:a) E is 2 km to the West of B

W E

S

NC

DA

B

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b)

F is 2 km to the North of Ac) C is 1 km to the West of Ad)

D is 2 km to the South of Ge) G is 2 km to the East of Cf) D is exactly in the middle of B and E

71.

Which two villages are farthest from one another?1. F and E 2. G and E 3. D and C 4. F and B

72.

How far is E and F as the Crow Flies?1. 5 2. 26 3. 4 4. 20

73. Suman walks 15 meters towards west, then turns to her rightand walks 15 meters and then turns to her left and walks 10 meters. Againshe turns left and walks 15 meters. What is the shortest distance between herstarting point and her present position?1. 25 m 2. 35 m 3. 30 m 4. 20 m

74.

Ashok started walking towards north. After walking 30meters he turned left and walked 40 meters. He then turned left, and walked30 meters. He again turned left and walked 50 meters. How far was he fromhis original position?1. 12 m 2. 15 m 3. 10 m 4. 20 m

75. A rat runs 20‟ towards east and turns to right runs 10‟ andturns to right, runs 9 and again turns to left, runs 5‟ and then turns to leftruns 12‟ and finally turns to left and runs 6‟. Now which directions is the ratfacing?

1. East 2. North 3. West 4. South

76.

Two towns A and B are 60 km apart. A school has to be builtto serve 150 students of A, 50 students of town B. If the total distance to betraveled by all the 200 students is to be small as possible, then where is theschool to be built?1. In town B 2. 45 km from town B 3. In town A 4. 45 kmfrom town A

77.

I went 10 m to the east, then turned North and walkedanother 15 m, then I turned west and covered 12 m and then turned south

and covered 15 m. How far am I from my house?1. 0 m 2. 2 m 3. 3 m 4. 5 m

78. Ramesh started from a point A towards south and traveled 5km, then he turned right and traveled 2 km, then he turned right and traveled5 km, then he turned left and traveled 5 km. How far was he from point A?1. 7 km 2. 17 km 3. 46.5 km 4. 60.5 km

The question is not whether we will die but how we will live.

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79.

I traveled 3 km southwards, then turned right and traveled 5km. Then turned right and traveled 7 km. In which direction was I travelinglast?1. South 2. East 3. North 4. West

80.

After walking 6 km, I turned right and covered a distance of

2 km, then turned left and covered a distance of 10 km. In the end, I wasmoving towards the North. From which direction did I start my journey?1. North 2. South 3. East 4. West

81.

Arun started walking positioning his back towards the sun.After some time, he turned left, then turned right and then towards the leftagain. In which direction is he going now?1. East or South 2. West or North 3. North or South 4. South or West

82. A policeman goes straight seven kilometers eastwards, thenturns right and goes straight three kilometers and turns right again and goes

straight ten kilometers. In which direction is he from the starting point?1. South-west 2. North-west 3. North-east 4. South-east

83. Sub-Inspector Jatin traveled from his police station straightfor 400 meters. He then turned left and traveled 500 meters straight afterwhich he turned left again and traveled for 400 meters straight. He thenturned right and walked for another 600 meters straight. How far is he fromthe police station?1. 1 km 2. 1.1 km 3. 1.4 km 4. 1.8 km

84.

Rakesh is standing at a point. He walks 20 m towards the

east and further 10 m towards the south, then he walks 35 m towards thewest, and further 5 m towards the east. What is the straight distance inmeters between his starting point and the point where he reached last?(approximately)1. 12 2. 14 3. 10 4. 18

85.

P, Q, R and S are playing cards, P and Q are partners, S facestoward north. If P faces towards west, then who faces towards south?1. P 2. Q 3. S 4. R

86. Facing towards South, Ram started walking and after

covering 40m he turned left and walked further 30 meters. How far is he fromhis starting position and in which direction?1. 50 m South-west 2. 25 m South-west3. 50 m South-east 4. 25 m South-east

87. Radha‟s school bus is facing north when she reaches herschool. After starting from Radha‟s house, it turns right twice and then leftbefore reaching the school. What direction was the bus facing when it left thebus stop in front of Radha‟s house?

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1. South 2. North 3. East 4. West

88.

Starting from point P satish walked 20 meters towards south.He turned left and walked 30 meters. He then turned left and walked 20meters. He again turned left and walked 40 meters and reached at point Q.How far and in which direction is the point Q from the point P?

1. 20 m, west 2. 10 m, east 3. 10 m, west 4. 10 m, north

89. Facing towards south, Pramod walked 25 meters. He thenturned to his right and walked 13 meters. He again turned right and walked25 meters. How far was he from his original position and towards direction?1. 20 m, east 2. 13 m, south 3. 20 m, north 4. 13 m, west

90. Starting from a point Raju walked 12 meters towards northhe turned right and walked 10 m, he again turned right and walked 12 mthen he turned left and walked 5 m. How far is he now and in which directionfrom the starting point?

1. 27 m towards east 2. 5 m towards east 3. 10 m towards west 4. 15 m towards west

91. Ram traveled 35 km from starting point towards south andthen turned left and traveled 17 km and finally turned left again and traveled35 km. How far was Ram from the starting point?1. 17 km 2. 18 km 3. 35 km 4. 70 km

92.

Somi traveled 9 km to the west then turned right andtraveled 7 km, then he turned left and traveled 8 km, then turned back andtraveled 11 km, then turned right and traveled 7 km. How far is he from the

starting point?1. 3 km 2. 6 km 3. 7 km 4. 9 km

93. A boy rode his bicycle northwards then turned left and moved1 km and again turned left and traveled 2 km. He found himself correctly 1km west of his starting point. How far did he ride northwards initially?1. 1 km 2. 3 km 3. 2 km 4. 5 km

94.

Ramesh started from a point A towards south and traveled 5km, then he turned left and traveled 5 km, then he turned right and traveled5 km. How far was he from point A?

1. 7 km 2. 17 km 3. 11 km 4. 5 km

95.

Facing towards south Pramod walked 50 meters. He thenturned to his right and walked 30 meters. He again turned right and walked50 meters. How far was he from his original position and towards whichdirection?1. 20 m, east 2. 30 m, south 3. 20 m, north 4. 30 m, west

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96.

Mohan starts from his home and walks 4 km straight, heturns towards his right and walks 2 km. He turns again to his right and walks2 km again. If he is in north-west, then in which direction did he start in thebeginning?1. North-west 2. South-east 3. North-east 4. South-west

97.

A goes 100 m to the south and then 100 m to the east toreach B‟s house. From there they together go to the market which is to thenorth-east of B‟s house. If the market be to the east of A‟s house, how far is itfrom his house?1. 100 m 2. 200 m 3. 300 m 4. 400 m

98. From my house I went 15 km to the North, then I turned westand covered 10 km, then I turned south and covered 5 km and then turnedeast and covered 10 km. In which direction am I from my house?1. West 2. East 3. North 4. South

99.

A police-Inspector drove 30 km towards west and then 40 kmtowards South. From this place, he drove 60 km towards east and then 40 kmtowards north. At what distance is he from the starting point?1. 30 km 2. 50 km 3. 60 km 4. 130 km

100. Mohit walks a distance of 5 km towards south, then turns to his right andwalks 3 km. He again turns right and walks 5 km. He then turns to his leftand walks 5 km. How far is he from the starting point and in what direction?1. 5 km, west 2. 3 km, north 3. 3 km, east 4. 8 km,west

101.

A man proceeding to the north turns to the right. After some time he takes aturn to the left and again to the left. Then he goes to his right and after somedistance again turns towards his right. The direction in which he is nowmoving is ___________1. East 2. North 3. South 4. West

102.

The time on Rita‟s watch is a quarter to three. If the minute hand point tonorth-east, in which direction does the hour hand point?1. South-west 2. South-east 3. North-west 4. East-west

103.

A man walks 7 miles eastwards, turns right and travels 3 miles and furtherturns right and travels 11 miles. How far is he from the starting point?1. 5 miles 2. 3 miles 3. 6 miles 4. 8 miles

104.

A and B start walking in opposite directions. A covers 3 miles and B 4 miles. Then A turns right and walks 4 miles and B turns left and walks 3 miles. Howfar each is from the starting point?1. 4 miles 2. 6 miles 3. 8 miles 4. 5 miles

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105.

A man started walking from a point towards south. He turned right at rightangles, then again right at right angles. In what direction was he ultimatelywalking?1. East 2. West 3. North 4. South

106.

Ravi went 10 m to the east, then turned north and walked another 5 m.

Then he turned west and covered 15 m. How far is he from the starting point?(approximately)1. 5 m 2. 2 m 3. 3 m 4. 7m

107.

A watch show 8.30. If the minute hand point towards east, in whichdirection will the hour hand point?

1. South-West 2. West 3. North-West 4. South-East

108.

Venu walked 7 km towards west from Annapurna Studio. Then he tooko90 to his left and walked 4 km, again he had taken another left turn witho

90 and walked 2 km, then he turned to his right and walked towards south 1km. Finally he walked 5 km towards east. How far is Venu from his startingpoint and in which direction?

1. 6 km South 2. 5 km North 3. 5 km South 4. 8 km North

109.

Harish, Sai, Shanker and Raghu are in play ground. Harish stands South-west to shanker. Sai stands North-east to Harish and is between Harish andShanker‟s way, but south to Raghu. Find in which direction Raghu toShanker?

1. South 2. North-East 3. North-West 4. South-East

110. One evening, A was standing and facing a pole. The shadow of the pole fell

exactly to his left. In which direction was he facing?1. North 2. South 3. East 4. South-East

111. A clock is so placed that at 2 P.M. the minute hand points towardsnorthwest. In which direction does the hour hand point at 6 P.M.

1. North-West 2. West 3. North-East 4. South-East

112. Ramana started from his college and walked 1 km forward, then hereturned to his left and walked 1.5 km. Again he turned to his left and walked1 km. Finally he walked 1.5 km towards his right. How far is he from hisstarting point?1. 5 km 2. 2.5 km 3. 3.5 km 4.3km

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Coding – Decoding

Examples

Example1. In a certain code, PAPER is written as SCTGW. How is MOTHER written in that code?(a) POXJJT(b) ORVLGW(c) PQXKJV(d) PQVJGT

Solution. PQXKJV. The letters at the odd positions are moved three, four and five steps forward,while the letters at the even positions are each moved two steps forward, to get the corresponding

letters of the code.

Example 2. In a certain code, SIKKIM is written as THLJJL. How is TRAINING written in that code?(a) SQBHOHOH(b) UQBJOHHO(c) UQBHOHOF(d) UQBJOHOH

Solution. UQBHOHOF. The letters at the odd position are moved one step forward while the lettersat the even positions are moved one step back to get the corresponding letters of the code.

Example 3. If in a certain language. CALCUTTA is coded as GEPGYXXE, which word would be codedas FSQFCE?

(a)

BOMBYA(b) BOMYAB(c) BOMBAY(d) BOBAMY

Solution. BOMBYA. Each letter of the word is four steps behind the corresponding letter of the code.

Example 4. If D = 4 and COVER = 63 then BASIS = ?(a) 55(b) 54(c) 50

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(d) 49

Solution. 50. In the given code A = 1, B = 2, C = 3 … so that, COVER = 3 + 15 + 22 + 5 + 18 = 63BASIS = 2 + 1 + 19 + 9 + 19 = 50

Example 5. In a certain code, 15789 is written as XTZAL and 2346 is written as NPSU. How is23549 written in that code?(a)

NPTSL(b) NPTUL(c) NBTSL(d) PNTSL

Solution. NPTSL. The numbers coded as1 5 7 8 9 2 3 4 6X T Z A L N P S U

That is 2 as N, 3 as P, 5 as T, 4 as S and 9 as L. Thus 23549 coded as NPTSL.

Example 6. If cloud is called white, white is called rain, rain is called green is called air, air is calledblue and blue is called water, where will the birds fly?(a) Air(b)

Cloud(c) Blue(d) Rain

Solution. Blue. The birds fly in the „air‟ and „air‟ is called „blue‟. So the birds fly in the „blue‟.

Example 7. In a certain code language, „dom pul ta‟ means „bring hot food‟; „pul fir sop‟ means „foodis good‟ and „tak da sop‟ means „good bright boy‟, which of the following does mean „hot‟ in thatlanguage?(a) dom(b) pul(c) ta(d) can‟t determined

Solution. Can‟t determined. The code for „food‟ from the first and second statements can bedetermined. To find the code for hot, we need the code for „bring‟ which can not be determined fromthe given information.

Example 8. In a certain code, „37‟ means „which class‟ and „583‟ means „caste and class‟. What is thecode for „Caste‟? (a) 3(b) 7(c) 8(d) Either 5 or 8

Solution. Either 5 or 8. In the both statements, the common code digit is 3 and common word is

„class‟ so „3‟ means „class‟. Thus in the second statement, either 5 or 8 stands for „caste‟.

Exercise

1. IF LEARNING is written as MGDVSOUO then SURPRISE would be:(a) TWUTWOAL(b) TWUTWOZM(c) TWVUXPAN(d) TWUSVNZK

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2. If SUNDAY is coded as XZCMTR then PAYMENT would be:(a)

RPNDZOJ(b) QBZNFOU(c)

SMDLXZO(d)

TNEMYAP

3. If TAP is coded as SZO, then how is FREEZE coded?

(a)

EQDDYD(b) ESDFYF

(c) GQFDYF

(d) EQDFYG

4. In a certain code, FORGE is written as FPTJI. How is CULPRIT written in that code?(a)

CXOSULW(b)

CVNSVNZ(c) CVMQSTU(d)

CSJNPGR

5. If victory is coded as YLFWRUB, how can success be coded?(a) VXFFHVV(b)

VXEEIVV

(c)

VYEFIVV(d) VYEEHVV

6. In a certain code SOCIAL is written as TQFMER, then how you will code DIMPLE?(a)

EKPTQK(b)

EKPQPJ(c) EKPSPJ(d) EKPSOH

7. In a certain code SOCIAL is written as TQFMER, then how you will code DIMPLE?(a)

wtzyv(b) twxyz(c)

tqwvm(d)

mtuvw

8. If PAINTER is written in a code language as NCGPRGP, then REASON would be written as :(a) PCYQMN(b)

PGYQMN(c)

PGYUMP(d) PGYUPM

9. If CIGARETTE is coded as GICERAETT. Then DIRECTION will be coded as :(a)

RIDTCENOI(b)

NORTECDII(c) IRDCTIONE(d)

NOIETCRID10. If DIAMOND is coded as VQYMKLV, how is FEMALE coded as:

(a)

UVNZOV(b) TUMYNU

(c) TUMZOU

(d) TVNYNV

11. If in a certain language, REMOTE is coded as ROTEME, which word would be coded as PNIICC?(a) PICCIN(b)

PINCIC(c)

PICNIC(d) PICINC

12. If in a certain code, COVET is written as FRYHW, which word would be written as SHDUO?

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(a) REPAY

(b) PEARL(c)

QUAKE(d)

STINK

13. If PAINT is coded as 74128 and EXCEL is coded as 93596, then how would you encode ACCEPT?(a) 547978(b)

554978

(c)

735961(d) 455978

14. If ENGLAND is written as 1234526 and FRANCE is written as 785291, how is GREECE coded?(a)

832252(b)

835545(c) 381191(d) 381171

15. If LINGER is 123456 and FORCE is 56789, then FIERCE is:(a)

345667(b) 345677(c)

456678

(d)

556789

16. If SHARP is coded 58034 and PUSH as 4658, then RUSH is coded as :(a) 3583(b)

3685(c) 3658(d) 3568

17. If MASTER is coded as 411259, then POWDER will be coded as:(a)

765459(b)

765439(c) 765549(d)

765439

18.

In certain code language 35796 is written as 44887. How is 46823 written in that code?(a) 55934(b) 55914(c)

55714(d)

57914

19. In a certain code language 24685 is written as 44887. How is 35791 written in that code?(a) 44880(b)

46682(c)

44682(d) 44826

20. If AT = 20, BAT = 40 then CAT will be equal to:(a)

30

(b)

60(c) 50(d)

70

21. If ROSE is coded as 6821, CHAIR is coded as 73456 and PREACH is coded as 961473, what willbe the code for SEARCH?(a)

246173(b)

216473(c) 214673(d)

214763

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22. If in a certain language, 943 is coded as BED, and 12448 is coded as SWEET, how is 492311coded in that language?(a)

EDSWBS(b) DSWTEE(c) EBWDSS(d)

TSWBDD

23.

If according to a certain code, PAINTER is written as 3528617, then TANRPEI is coded as?(a)

6587312(b)

6583721(c) 9385472(d)

9385427

24. If PLANETS is written as 4823579, then SNLEPAT would be coded as:(a) 9385247(b)

9384527(c)

9385472(d) 9385427

25. If water is called food, food is called is tree, tree is called sky, sky is called wall, on which of the

following grows a fruit?(a) sky(b)

tree(c)

water(d) food

26. If sky is called sea, sea is called water, water is called air, air is called cloud and cloud is calledriver, then what do we drink when thirsty?(a) sky(b) water(c)

air(d) sea

27.

In a certain code language „389‟ means „run very fast‟ „964‟ means „come back fast‟ and „487‟means „run and come‟. Which digit in the language means „come‟? (a)

9(b) 4(c)

7(d)

8

28. In „nitco sco tingo‟ means „softer than flower”; „tingo rho mst‟ means „sweet flower fragrance‟ and„mst‟ sco tmp‟ means „sweet than smile‟, what would „fragrance‟ stand for? (a) rho(b)

tmp(c)

sco(d) mst

29. If „nso pir kli chn‟ stands for „Sapna‟ gets marriage gift? „ptr lnm wop chn‟ stands for „wife gives

marriage gift‟, „tti wop nhi‟ stands for „he gives nothing‟, what would means „gives‟?(a) wop(b)

ptr(c)

nhi(d) chn

30. In a certain code language „bi nie pie‟ means „some good jokes‟; „nie bat tik; means „some realstories‟ and „pie lik tal‟ means „many good stories‟. Which word in that code means „jokes‟? (a) nie(b)

pie

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(c) bi

(d) None of these

31. In a certain code language, „Tom Kun Sub‟ means „Dogs are barking‟; „Kun Jo Mop; means „Dogsand horses‟ and „Must Tom Ko‟ means „Donkeys are mad‟. Which word in that language means„barking‟? (a)

Kun(b) Sud(c)

Tom(d)

Ko

32. If „isn lto inm‟ stands for „neat and tidy‟; „qpr inm sen‟ stands for „small but neat‟ and „hsm senrso‟ stands for „good but erratic‟, what would „but‟ stand for? (a)

qpr(b)

sen(c) inm(d)

hsm

33. If „col tip mot‟ means „singing is appreciable‟; „mot baj min‟ means „dancing is good‟ and „tip nopbaj‟ means singing and dancing‟. Which of the following means „good‟ is that code language? (a)

min(b)

baj(c)

not(d)

None of these

Directions (Qs.34-37) : According to a certain code : „I received a letter,‟ we saw an aircraft‟. „Johnloves long letters‟, means „captain saw blue flag‟. „I like long one‟, means „we believe the captain‟.

34. What does the word „received‟ in the code mean? (a) we(b) saw(c)

aircraft(d) blue

35.

What word is coded as „believe”? (a) I(b) Like(c)

Long(d)

one

36. What does John mean?(a)

aircraft(b)

captain(c) blue(d)

is

37. What will be the code for „The captain‟?

(a)

Long letter(b)

Received one(c) Loves long(d)

Long me

38. In a certain code language, „po ki top ma‟ means „usha is playing cards‟; „Kop ja ki ma‟ means„Asha is playing is tennis‟; „ki top sop ho‟ means „they are playing football; and „po sur kop ho‟means „cards and tennis‟. Which word in that language means „Asha‟? (a)

Kop(b) Top(c)

Ja

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(d) Ki

Directions (Qs. 39-41) : In a certain code, „il be pee‟ means „ roses are blue ‟; „sik hee means „ red flowers ‟ and „ pee mit hee‟ means „ flowers are vegetables‟.

39. How is „red‟ written in that code? (a) Be(b)

Hee

(c)

Sik(d) None of these

40. How is „roses‟ written in that code? (a) il(b)

Pee(c)

Be(d)

Pee

41. How is „vegetables are red flowers‟ written in this code? (a)

Pee sik nut hee(b) Sik pee hee be(c) il sik mi thee

(d)

None of these

Directions (Qs. 42-43) : According to certain code; „po be co fo‟ means „ some students are sharp ‟ „ lomo jo bo‟ means „ many teachers are dull ‟ „ wo co lo zo‟ me ans „Dull students need training „mo zo ho po‟means „some teachers need test‟.

42. The code for „many students‟ would be (a)

Co mo(b)

Co jo(c) Jo fo(d)

Fo zo

43. The code „ zo wo jo mo‟ means(a) Some teachers need training

(b)

Some students need rest(c) Some teachers are sharp(d) Many teachers need training.

Directions (Qs.44-45) : if according to a certain code : „mar tar gar zar‟ means „Can we startimmediately‟. „har zar par dar‟ means „No you start tomorrow‟. „dar sar kar tar‟ means „Can you comehere‟. „yar par mar sar‟ means „No we stay here‟.

44. What is the code for „stay‟? (a) Yar(b)

Par(c)

Mar(d) Sar

45. What does „dar‟ mean? (a)

No(b)

Can(c)

You(d)

Start

46. In a certain code, „467‟ means „leaves are green‟; „485‟ means „green is good‟ and „639‟ means „theyare playing‟. Which digit stands for „leaves‟ in that code?(a)

4(b) 6(c)

7(d)

3

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47. In a certain code language, 479‟ means „fruit is sweet‟; „248‟ means „very sweet voice‟ and „637‟means „eat fruit daily‟. Which digit stands for „is‟ in that code?(a)

9(b)

7(c) 4(d) None of these.

48. In a certain code „786, means „study very hard‟. „958‟ means „hard work pays; and „645‟ means„study and work‟. Which of the following is the code for „very‟? (a)

8(b)

6(c) 7(d)

None of these

49. In a certain code language, „3a, 2b, 7c‟ means „truth is Eternal‟; „7c, 9a, 8b, 3a‟ means „Enmity isnot Eternal and „9a, 4d, 2b, 8b‟ means „truth does not Peresh‟. Which of the following means„enemity‟ in that language:(a)

3a(b) 7c(c)

8b(d)

9a

Directions

(A) „134‟ means „you are well‟; (B) „758‟ means „they go home‟; (C) „839‟ means „we are home‟;

50. Which of the following represents „they‟ in that code language?(a)

5(b) 7(c) 3(d)

Data inadequate

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51.

In a certain code language CENTRAL is written as LARTNEC.How will SEMINAR be written in that code language?

1. NARIMES 2. MESIRAN 3. RANIMES 4. NARISEM

52. In a certain code language INACTIVE is written as VITCANIE.How will COMPUTER be written in that code language?

1. UTEPMOCR 2. ETUPMOCR 3. MOCPETUR 4. PMOCRETU

53. In a certain language KNIFL is coded as IFLKN, how isDOCTOR coded in that language?

1. ROTCOD 2. ROTDOC 3. CODTOR 4. TORDOC

54. In a certain code HUMIDITY is written as UHMIIDTY. How isPOLITICS written in that code?

1. OPLIITCS 2. OPLITICS 3. POLIITCS 4. OPLIITSC

55.

In a certain code language LEARNING is written as

LGNINRAE. How will SURPRISE be written in that code language?1. ESIRPRSU 2. RUSEPSIR 3. SESIRPRU 4. ESRIPRUS

56. In a certain code language TELEPHONE is written asENOHPELET. How is ALIGATOR written in that code?

1. ROTAGIAL 2. ROTAGILA 3. ROTAGILE 4. ROTEGILA

57. In a certain code CALANDER is written as CLANAEDR. Howis CIRCULAR written in that code?

1. ICCRLURA 2. CRIUCLRA 3. ICCRULRA 4. CRIUCALR

58.

In a certain code MEDICAL is written as MEIDCAL. Howwould POLICE be written in that code?

1. PCELIO 2. POICLE 3. POILCE 4. PCELIO

59.

In a certain code MOUNTAIN is written as OMNUATNI. How isREADER written in that code?

1. ERDARE 2. ERADRE 3. REDAEL 4. RAEDER

60.

In a code, EDITION is written as IDETNOI. How willMEDICAL be written in that code?

1. DEMILAC 2. LACIDME 3. DIEMCAL 4. CAMDILE

61. If VAIN is written as WBJO. Which word is written as UPOF?1. TONE 2. TOMB 3. ROSE 4. ROPE

62.

In a code language „ABHIJIT‟ is written as CEJLLLV. How isBROTHER written in that code?

1. DUQWJTH 2. DUQWTSH 3. DUQTWSH 4. DUQWJHT

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63.

In a certain code language PARENTS is written as RCTGPVU.How will CHILDREN be written in that code language?

1. EFJKCPCM 2. EJKNFTGP 3. EJKNFTPG 4. EJKNFPTG

64. If in a certain language GRASP is called as BMVNK, whichword would be coded as CRANE?

1. FUDSJ 2. HWFSJ 3. HWFJS 4. XMVIZ

65. If QOSCFLBIO is the code for PORCELAIN, which word iscoded as BKMOUSPP?

1. ALTOLROPY 2. ALLOTROPY 3. ALOTROLPY 4. None

66. If CANT is written as BZMS which word is written as JHKM?1. MILK 2. LIKE 3. KITE 4. KILN

67. In a certain code GOODNESS is coded as HNPCODTR. How isGREATNESS coded in that code?

1. HQFZUODTR 2. HQFZUMFTR 3. HQFZUMFRT 4. HQFZSMFRT

68. If in a certain language SALE is coded as PAIE, how isCASUAL coded in that code?

1. FAVUDL 2. DBTVBM 3. ZAPUXL 4. BARUZK

69.

If CANOE is coded as IFRRG, how is MUSIC written in thatcode?

1. SZWEL 2. SQWLE 3. SWZLE 4. SZWLE

70.

If CAB is coded as WUV. How is DEAF coded in that

language?1. XYZU 2. XWUY 3. XYUZ 4. XZVU

71. If ROSE is coded as 6821, CHAIR is coded as 73456 andPREACH is coded as 961473. What will be the code for SEARCH?

1. 216473 2. 214637 3. 214673 4. 246173

72. If GIVE is coded as 5137 and BAT is coded as 924. How isGATE coded?

1. 5427 2. 5247 3. 5724 4. 2547

73.

If HID is written ad B4C3B2. How will URN be written as?1. C7B9B7 2. C3B9B7 3. C7B9B5 4. B9C3C7

74. If in a certain code SISTER is coded as 535301, UNCLE iscoded as 84670 and BOY as 124, how is SON coded in that code?

1. 524 2. 643 3. 353 4. 846

75.

If ROPE is coded as 6821 and CHAIR is coded as 73456 thenwhat will be the code for CRAPE?

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1. 73456 2. 76412 3. 77246 4. 76421

76.

If MINJUR is coded as 312547 and TADA as 6898, how canMADURAI be coded?

1. 3498178 2. 389487 3. 3849781 4. 3894781

77.

If in a certain code language A is coded as 1, B is coded as 2and so on, how is BIDDIC coded in that code?1. 294439 2. 294493 3. 294349 4. 249439

78.

If FUN is written as B3C7B7 which word is written asB2C3B7?

1. PIN 2. RUN 3. DIN 4. PUN

79.

If in a certain code TWENTY is written as 863985 andELEVEN is written as 323039, how is TWELVE written in that code?

1. 863203 2. 823230 3. 823032 4. 863903

80.

If in a certain language PRIVATE is coded as 1234567 andRISK is coded as 2398, how is RIVETS coded in that language?

1. 687543 2. 234769 3. 496321 4. 246598

Directions Calculate the value of each word by the following formula. All theconsonants are coded as 2n-1 and vowels are coded as 3n+1, where n is theposition of the letter?

81. CHIRU1. 67 2. 152 3. 147 4. None

82. REASONING1. 233 2. 234 3. 250 4. None

83.

MATHS1. 117 2. 116 3. 120 4. None

84. ARITHMETIC1. 263 2. 231 3. 235 4. None

85. ICET

1. 80 2. 85 3. 88 4. 87

86.

If rain is called water, water is called air, air is called cloud,cloud is called sky, sky is called sea, sea is called road, then where do theaero planes fly?

1. water 2. road 3. sea 4. cloud87. If rain is called pink, pink is called cloud, cloud is called

water, water is called breeze and breeze is called moon. With what do youwash your hands?

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1. water 2. rain 3. breeze 4. room

88.

If cushion is called pillow, pillow is called mat, mat is calledbed sheet, and bed sheet is called cover. What can be spread on the floor?

1. cover 2. bed sheet 3. mat 4. pillow

89.

If light means red, red means green, green means white,white means yellow. What is the colour of blood?1. red 2. yellow 3. blue 4. light

90.

If pen is called pencil, pencil is called scale, scale is calledbag and bag is called book, which is used to carry the books?

1. scale 2. pen 3. book 4. bag

Directions (Questions 41-43): In a certain code “il be pee” means “roses are blue”,“sik hee” means “red flowers” and “pee mi hee” means “flowers are vegetables”.

91.

How is red written in that code?1. hee 2. sik 3. be 4. Can‟t be determined

92. How is “roses” written in that code?

1. il 2. pee 3. be 4. Can‟t be determined

93. How is “vegetables are red flowers” written in this code? 1. sik pee hee be 2. il sik mi hee 3. pee sik mi hee 4. Can‟t be determined

94.

In a certain language “pre not bis” means “smoking is

harmful”, “vog dor not” means “avoid harmful habit”, and “dor bis yel” means“please avoid smoking. Which of the following means “habit” in that language?

1. vog 2. not 3. dov 4. bis

95.

“bis” stand for 1. please 2. avoid 3. harmful 4. smoking

96. In a certain code “253” means “books are old”, “546” means“man is old”, “378” means “buy good books”. What does “are” mean in thatcode?

1. 2 2. 3 3. 4 4. 3

97. In a certain code “37” means “which claws” and “583” means“caste and claws”. What is the code for “caste”?

1. 3 2. 7 3. 8 4. Either 5 or 8

98. In a certain code „289‟ means „read from paper‟, „276‟ means„tea from field‟ and „85‟ means „wall paper‟. Which of the following is the codefor „tea‟?

1. 2 2. 6 3. Either 7 or 6 4. Either 5 or 8

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99. In a certain code language “123” means “how are you”, “423”means “how are they”, and “356” means “how is she”. In that code language 3stands for which of the following?

1. how 2. are 3. you 4. she

100.

In a certain code language “123” means “hot filter coffee”,“356” means “very hot day” and “589” means “day and night”. Which digit inthat language means “very”?

1. 8 2. 6 3. 9 4. 5

101.

In a certain code, MPOEPO means LONDON. What is CPNCBZ?1. DQODCA 2. BOMBAY 3. MADRAS 4.RAJKOT

102. In a certain code, CLOCK means KCOLC. How is STEPS written in thatcode?

1. SPEST 2. SPSET 3. SPETS 4. SEPTS

103. In a certain code, GAMESMAN means AGMEMSAN. How is DISCLOSEwritten in that code?

1. IDSCOLSE 2. IDCSOLES 3. IDSCOLES 4.IDSCLOSE

104. In a certain code, PRACTICE is written PARTCCIE. How is TRAINS written inthe same code?

1. TRAINS 2. TANRIS 3. TAIRNS 4. TARNIS

105.

In a certain code, BAD is written as YZW, SAID is written as HZRW, thenLOVE will be written as

1. WXMN 2. MRSU 3. BRTP 4. OLEV

106.

In a certain code, GOLFER is written as H N M E F Q. HUNGER will becoded as

1. I T O F F Q 2. I V O H F S 3. I T O D F Q 4. T I D OQ F

107.

In a certain code, GOLFER is written as IRPKKY, then decode HRVHK1. FORTS 2. FORCE 3. FIRST 4. FEWER

108. In a certain code, ROUNDS is written as RONUDS. How is PLEASE writtenin that code?

1. LPAESE 2. PLAESE 3. LPAEES 4. PLASEE

109. In a certain code, SCALE is written as ELACS. How is CREAM written inthat code?

1. MACER 2. MEARC 3. MERAC 4. MAERC

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110.

In a certain code, CHAIR is written as HAIRC. How is BRIDE written in thatcode?

1. RIDEB 2. BRIEB 3. EBRID 4. RIDBE

111. In a certain code, VACATE is written as AVACET. How is LITERATE writtenin that code?

1. ILETRAET 2. ILTEARTE 3. ILTREATE 4.ILETARET

112.

In a certain code, RUSTIC is written as CSUITR. How is DUSTER written inthat code?

1. RUSETD 2. CSUETR 3. RESTUD 4.RSUETD

113.

In a certain code, QUIET is written as TXLHW. How is FLOAT written in thatcode?

1. TORDW 2. HNQCV 3. INRCW 4. IORDW

114.

In a certain code, TRINOLI is written as SSHONMH. Write SICILY in thesame code.

1. RJBJKA 2. RHJCZP 3. RJBJKZ 4. TJDJMZ

115.

In a certain code, BANANA is written as ANANAB : write MELON in the samecode.

1. KENDM 2. NFMPO 3. NPOKS 4. NOLEM

116.

If HOBBY is coded as IOBY; LOBBY is coded as MOBY; code BOBBY.

1. BOBY 2. COBY 3. DOBY 4. COBBY

117.

If SUCCESS is coded as TVDDFTT, then how will you code RETREAT?1. SBUSFBS 2. SFUSFBS 3. SFUSFSB 4.SFUSFBU

118.

If MAN is written as NZM, then GIRL will be written as1. TRIO 2. RTIO 3. HJLM 4. GIKL

119.

If SWEET is written as WSTEE, then BOOKS will be written as1. OBOSK 2. OBSOK 3. OBKSO 4. BOSOK

120. If MALT is written as NBMU, then ZEBRA will be written as1. AFCSB 2. ACFSB 3. YFCSB 4. AFSCB

121.

If TABLE is coded as ABTEL, then STOOL is coded as1. TOSLO 2.TOLSO 3. OTSLO 4. TOSOL

122.

If SHIP is written as VKLS, then PENCIL will be written as

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1. SHQFLO 2. RIPGHO 3. SHFQLO 4.SHQFOL

123. If ZAT is written as RAT, then MAT will be written as1. RAT 2. SAT 3. BAT 4.TAT

124.

If PAGES is written as GESPA, then TIGHT will be written as1. GHITT 2. GHTTI 3. GHTIT 4. HGTTI

125.

If SING is written as UKPI, then TAKE will be written as1. VCMG 2. WDNH 3. VCGM 4. WDHN

126. If ARMY is written as HYTF, then SICK will be written as1. ZRJP 2. ZPRJ 3. ZJPR 4. ZPJR

127. If COBRA is coded BOCAR, then GROUP will be coded as1. ORPGU 2. OGRPU 3. ORTAU 4. ORGPU

128.

If PAGES is written as APEGS, then TOUCH will be written as1. OCTUCH 2. OTUCH 3. OTCUH 4. OTUHC

129.

If SELF is coded as RDKE, then STATE will be coded as1. RSZSD 2. RSZDS 3. RZSZD 4. RSZSC

130. If MOSCOW is written as JLPZLT, then LONDON will be written as1. ILKALA 2. ILKALK 3. ILKLAK 4. ILKLKA

131.

If NEWS is written as WENS, then MATE will be written as

1. TAME 2. META 3.MTAE 4. EATM

132.

If ZEBRA is written as EZRBA, then BRISK will be written as1. RBSIK 2. BRSKI 3. RBIST 4. RBSKB

133. If SELF is written as TELF, then COW will be written as1. MOW 2. TOW 3. WOW 4. DOW

134.

If NEW is written as WEN, then TWO will be written as1. OWT 2. SOW 3. WTO 4. WTV

135.

If WATCH is written as AWCTH, then TABLE will be written as1. ATLBE 2. ATBLE 3. ATBEL 4. ELBAT

136. If MATCH is written as OCVEJ, then SCORE will be written as1. UEQGT 2. UEQTG 3. UETQG 4. TDPFS

137. If WATER is written as XBUFS, then SALT will be written as1. UCNV 2. TBMU 3. WZKS 4. WZSK

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138.

If PAGES is written as SEGAP, then STATE will be written as1. ETATS 2. STTAE 3. ETSAT 4. TATSE

139. If WOLF is written as YQNH, then SENT will be written as1. GUPV 2. GUVP 3. UGPT 4. UGPV

140.

If REPORT is written as MZKJMO, then MODEL will be written as1. GIXYF 2. GIXYT 3. HJYZG 4. GJYZG

141.

If WFITE is written as YHKVG, then EXAM will be written as1. GCZO 2. GYBO 3. GZCO 4. GZBO

142. If PAPER is written as REPAP, then ENGLISH will be written as1. HSILGNE 2. HSLIGNE 3. HSLIGEN 4.HSLIENG

Directions: If A = 5, B = 6, C = 7, D = 8 and so on, what do the following numbers

or letters stand for

143. 22, 25, 8, 22, 51. Priya 2. Neema 3. Meena 4. Rudra

144. 6, 22, 19, 27, 181. Brown 2. White 3. Green 4. Black

145.

22, 5, 14, 5, 181. Rajan 2. Badal 3. Rajiv 4. Bimal

146.

6, 5, 22, 19, 8, 51. Cochin 2. Baroda 3. Madras 4. Bombay

147. 17, 19, 20, 9, 81. Plane 2. Moped 3. Motor 4. Tonga

Directions: For the following questions, calculate value of each word by using thefollowing formula:

Consonants : (2 x position of the letter inalphabet) – 1

Vowels : (3 x position in alphabet) + 1

148. BREAD1. 67 2. 62 3. 59 4. 65

149.

FLUTE1. 153 2. 157 3. 151 4. 149

150.

CHANGE1. 77 2. 79 3. 83 4. 80

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151. In a certain code, PAN is written as 31 and PAR is written as 35; code PAT inthe same pattern.

1. 30 2. 37 3. 39 4. 41

152.

If BLOOD is coded as 24113, BURST is coded as 20678; code ROBUST.

1. 620781 2. 612078 3. 678102 4. 610732

153. If CINEMA is written as 395541, then PICTURE will be written as1. 16932021185 2. 79311295 3. 2967694 4.7932395

154. If BALL is coded as 211212, how will you code the word LATE?1, 121205 2. 122195 3. 123205 4. 101205

155. If MEALS is coded as 13511219, how will you code the word WATER?1. 13120518 2. 23120518 3. 23120519 4.

23121518

156. If CABLE is coded as 312125, how will you code the BUTTER?1. 22120201518 2. 22120202319 3. 2212020518 4.32120212128

157.

If LETTER is coded as 1252020518, how will you code the word VOWEL?1. 2215234 2. 221523512 3. 221523513 4.2115235

158.

If TERM is coded as 722914, how will you code the word RECT?

1. 92247 2. 92237 3. 92217 4. 92238

159.

If CAP is coded as 242611, how will you code the word POT?1. 11127 2. 11137 3. 11128 4. 11138

160. If FIVE is coded as 2118522, how will you code NIKE?1. 13181622 2. 13181722 3. 12181622 4.12181722

161.

If DATE is coded as 2326722, how will you code ZEAL?1. 1222615 2. 1222515 3. 1242615 4.

1242516

162.

If COME is coded as 24121422, how will you code MEAN?1. 14222614 2. 14212614 3. 14222613 4.14212613

163. If MATHS is coded as 14267198, how will you code PHYSICS?1. 11192818228 2. 11192818248 3. 11193818238 4.11193818238

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164. If MALE is coded as 25132417, how will you code SEAL?1. 5161324 2. 5161234 3. 5171324 4.5171424

165.

If ADVENTURE is coded as ERUTNEVDA, how is GREEN coded in that

language?1. NEERG 2. ENEGR 3. GEREN 4. NEEGR

166.

In a certain code JODHPUR is written as RUJODHP, how is CANDIDATEwritten in that code?

1. TECANDIDA 2. TECANDIAD 3. ETCANDIDA 4.ETCANDIAD

167.

If PEOPLE is coded as PLPOEE, how is TREND coded?1. TREDN 2. DNERT 3. TRDNE 4. TNERD

168.

In a certain code language STUDENT is written as TUTDNES. How willSOURCES be written in that code language?

1. SUORCES 2. SUORECS 3. SOURSEC 4. SOUCRES

169.

In a certain code HUMIDITY is written as UHIMIDTY. How is POLITICSwritten in that code?

1. OPILITCS 2. OPLITCS 3. POLITISC 4. OPLITISC

170.

In a certain code GIGANTIC is written as GIGTANCI. How is MIRACLESwritten in that code?

1. RIMLASCE 2. RIMLACSE 3. RMLIASCE 4. RIMLSCAE

171. In a certain code JUDICIAL is written as a JUDICILA. How will GLORIOUSbe written?

1. GLOORSIU 2. GLOOIRSU 3. GOLOIRSU 4. GOLORSIU

172. In a certain code MAN is written as SANM and WORD is written as SORDW.How would SALE be written in that code?

1. SEALS 2. LEASS 3. LEASAS 4. SALES

173.

In a certain code INSTITUTION is written as NOITUTITSNI. How isPERFECTION written in that code?

1. NOICTEFREP 2. NOITCEFERP 3. NOITCEFREP 4. NOITCEFRPE

174.

If REACH is written as TGCEJ which word is written as VQYGT?1. STAND 2. SOWER 3. TOAST 4. TOWER

175. In a certain code SENSITIVE is written as QHLVGWGYC. How isMICROSOFT written in that code?

1. KGAPMQMDT 2. OKETQUQHV3. KLAUMVMIR 4. KLAUMUMIR

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176. If CURE is written as BTQD. How will MAIL be written in that code?1. LZGS 2. LZKH 3. LZHK 4. LYHK

177. If SKIP is written as VHLM. How is NAME written as1. QXBP 2. QXPB 3. XQPB 4. QXOB

178.

If the word NATION is written as OCWMTT, how the word COUNTRY wouldbe written in that code?

1. DQXRYXF 2. DQXRYFX 3. DQXRXYF 4.DPXRYXF

179. In a certain code TABLE is written as WDEOH. How would SKY be written inthat code?

1. VNB 2. TBN 3. BNY 4. NYB

180.

In a certain language BLEMISH is coded as AODPHVG, how is CHAPTER

coded in that code?1. DEBOUTDR 2. BKZSSHQ 3. CAHTPRE 4.

BKZSSOH

181.

If in a certain language CASUAL is coded as GEWYEP, how is PEOPLE codedin that code?

1. SHRSOH 2. TISTPI 3. SIRTOI 4. THSTOI

182.

In a certain language TRIANGLE is coded as SQHZMFKD. Which word wouldbe coded as DWZLOKD?

1. EXAMPEL 2. EXAMFL 3. EXAMPLE 4. NONE

183. If in a certain code, COVET is written as FRYHW, which word would bewritten as SHDUO?

1. QUAKE 2. REPAY 3. REAPL 4. PEARL

184. If LOSE is coded as 1357 and GAIN is coded as 2468, then the figures84615 stand for ____?

1. SNAIL 2. LANES 3. NAILS 4. NALIS

185.

In a certain code RIPPLE is written as 613382 and LIFE is written as 8192.How is PILLER written in that code?

1. 318826 2. 318286 3. 618826 4. 328816

186.

If PALE is coded as 2134. EARTH is coded as 41590, how is PEARL coded inthat language?

1. 29530 2. 24153 3. 25413 4. 25430

187. If CASE is coded as 5231, CHAIR is coded as 58206, and TEACH is coded as71258. What does 586037 stand for?

1. CHRSIT 2. CHASTE 3. CHEESE 4. CHRIST

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188. If PLAY is coded as 8123 and RHYME is coded as 49367. How is MALEcoded?

1. 6198 2. 6395 3. 6217 4. 6271

189.

In a certain code RIPSLE is written as 613082 and WIFE is written as 4192,

how is PEWSLE written in that code?1. 324082 2. 698241 3. 416328 4. 356124

190.

In a certain code language 24685 is written as 33776. How is 35791 writtenin that code?

1. 44882 2. 44880 3. 46682 4. 44828

191. If HORN is written as B4C5B9B7 which word is written as B3C7B7B2?1. FUND 2. HIND 3. FERN 4. FILM

192.

If MATH is coded as E8A0G13C5. Which word is written as A2J5C1B3?

1. COME 2. CONE 3. CODE 4. CAVE

Directions: In a particular language every rth letter is coded as (14-r)th letter forr=1,2,3…….13 and for r=14, 15…..26. rth letter is coded as (40-r)th letter.

193. What is the code for ICET?1. EKIT 2. EKTI 3. FKIT 4. ELIT

194.

What is the code for RANK?1. VMCZ 2. VNCZ 3. VMCY 4. VMZC

195.

What is the code for MATHS?1. AMTFV 2. AMTFU 3. ANTFU 4. AMTUF

196. What is the code for „CODE‟? 1. KZII 2. KZJL 3. KYJI 4. KZIJ

197.

If sand is called air, air is called rock, rock is called well, well is called ruby,ruby is called table, table is called gauge, gauge is called bangle and bangle iscalled bed then from where a woman can draw water?

1. bed 2. gauge 3. ruby 4. well

198.

If bat is called racket, racket is football, football is shuttle, shuttle is judo, judo is carom. What is cricket played with?

1. racket 2. football 3. bat 4. shuttle

199.

If black means white, white means red, red means yellow, yellow meansblue, blue means green, green means violet and violet means orange. What isthe colour of the sky?

1. blue 2. yellow 3. orange 4. green

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200.

If paper is called eraser, eraser is called bag, bag is called scale, scale iscalled pencil, pencil is called paper. What will a person write with?

1. scale 2. pencil 3. paper 4. eraser

201. If banana is apple, apple is grape, grape is mango, mango is nuts, nuts isguava. Which of the following is yellow fruit?

1. mango 2. nuts 3. grapes 4. banana

202. If lead is called stick, stick is called nib, nib is called needle, needle is calledrope, rope is called thread, what will be fixed in a pen to write with it?

1. stick 2. needle 3. thread 4. lead

203. If air is called water, water is called green, green is called dust, dust is called yellow and yellow is called cloud, where do fish live in?

1. air 2. water 3. green 4. dust

204.

If sky is called sea, sea is called water, water is called air, air is called cloud

and cloud is called river, then what do you drink in thirst?1. sky 2. air 3. water 4. river

205. If wall is called window, window is called door, door is called floor, floor iscalled roof and roof is called ventilator, on what will a person stand?

1. window 2. wall 3. floor 4. roof

206. If paper means wood, wood means straw, straw means grass, grass meansrubber, rubber means cloth, then the furniture made up of?

1. cloth 2. straw 3. paper 4. wood

Directions In a certain code language “ in jee loo” means “you did it”, “joo ip an” means “how are things”, “loo sam” means “you sing” and “an pee joo” means “thingsare sweets”.

207.

Which of the following is the code for how?1. joo 2. ip 3. am 4. joo

208. What is the code for “you sing sweet” 1. loo sam an 2. loo pee joo3. pee sam loo 4. loo ip pee

209.

Which of the following is the code for “it”? 1. in 2. jee3. loo 4. Can‟t be determined

210.

If 9144 means CHENNAI, 9122 means MUMBAI, 9111 means DELHI, thenhow do you code HYDERABAD?

1. 9133 2.9155 3. 9140 4. 9177

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Series and Sequences

Number Series:

1.

2, 3, 5, 7, 11, _____, 171. 9 2. 15 3. 13 4. 14

2.

21, 32, 45, 60, _____, 96, 117, 1401. 75 2. 73 3. 74 4. 77

3. 1, 2, 5, 10, 17, 26, 37, ______1. 51 2. 50 3. 49 4. 65

4. 43, 44, 48, 57, 73, _____

1. 98 2. 97 3. 87 4. 99

5.

13, 17, 21, 25, _______1. 28 2. 31 3. 27 4. 29

6. 2, 2, 4, 12, 48, ________1. 96 2. 250 3. 240 4. 230

7. 1, 2, 10, 37, _______1. 101 2. 100 3. 102 4. 103

8.

291, 170, _____, 40, 15, 61. 76 2. 112 3. 89 4. 100

9.

21, 23, 26, ____, 351. 28 2. 30 3. 37 4. 29

10. 10, 12, 16, 24, 40, 72, 136, ____1. 272 2. 382 3. 264 4. 292

11.

1, 5, 11, 19, 29, ____, 551. 45 2. 39 3. 41 4. 47

12.

6, 10, 18, 34, ______1. 44 2. 55 3. 66 4. 80

13. 1, 8, 16, 25, _______1. 30 2. 35 3. 40 4. 50

14.

5, 10, 17, 26, 37, 50, ___

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1. 64 2. 82 3. 65 4. 101

15.

37, 38, 34, 43, 27, 52, ____1. 16 2. 64 3. 74 4. 18

16.

10, 14, 22, 38, 70, ____

1. 130 2. 134 3. 140 4. 142

17. 10, 11, 13, 16, 20, 25, ____1. 30 2. 31 3. 32 4. 33

18.

10, 15, 40, 165, ___1. 700 2. 725 3. 760 4. 790

19.

21, 29, 43, 55, 73, ____1. 88 2. 89 3. 90 4. 101

20.

2, 6, 6, 14, 30, 62, ______, 2541. 142 2. 128 3. 126 4. 132

21. 4, 8, 7, 14, 12, 24, 19, ____, 281. 12 2. 38 3. 36 4. 24

22.

2, 7, 9, 3, 8, 11, 4, 9, 13, _____, 10, 151. 4 2. 7 3. 5 4. 6

23. 3, 9, 5, 25, 7, 49, 9, ______1. 81 2. 64 3. 100 4. 121

24. 8, 8, 9, 9, 11, 10, 14, 11.1. 15 2. 18 3. 17 4. 12

25.

1, 8, 9, _____, 25, 216, 491. 64 2. 60 3. 70 4. 75

26. 3, 4, 15, 16, ______, 36, 63, 641. 30 2. 25 3. 34 4. 35

27. 1, 3, 1, 9, 1, 81, 1, _____

1. 243 2. 324 3. 6561 4. 5641

28.

2, 4, 7, 14, 17, 34, 37, _____1. 74 2. 76 3. 47 4. 72

29. 20, 18, 19, 16, 18, 14, _____1. 16 2. 17 3. 15 4. 13

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30.

3, 12, 4, 16, 5, 20, 6, _______1. 30 2. 36 3. 24 4. 18

31. 5, 20, 6, 24, 7, 28, _____1. 8 2. 9 3. 32 4. 10

32.

5, 4, 10, 8, 15, 12, 20, _____, 251. 13 2. 18 3. 15 4. 16

33.

8, 24, 12, ____, 18, 541. 28 2. 46 3. 36 4. 48

34. 10, 15, 20, 30, 40, 60, 80, ____1. 90 2. 100 3. 110 4. 120

35. 6, 42, 12, 35, 18, 28, 24, 21, __ , 14, 36, 71. 30 2. 35 3. 36 4. 18

36.

2, 9, 30, ____, 2821. 90 2. 91 3. 92 4. 93

37.

1, 4, 12, 2, 5, 15, 3, 6, 18, 4, ______1. 21 2. 7 3. 5 4. 6

38. 2, 8, 4, 3, 18, 6, 4, 32, 8, _______50, 101. 7 2. 6 3. 5 4. 9

39.

1278, _____, 314, 152, 70, 28

1. 634 2. 636 3. 632 4. 656

40.

7, 5, 2, 14, 3, 1, 2, 6, 8, 5, 3, 24, 6, 2, 4, ___1. 10 2. 36 3. 12 4. 24

41. 2, 3, 6, 3, 4, 12, 4, 5, 20, 5, 6, ___1. 35 2. 30 3. 25 4. 35

42.

5, 7, 12, 6, 8, 14, 7, _____, 16, 8, 10, 181. 8 2. 10 3. 6 4. 9

43.

5, 2, 11, 6, 3, 12, 7, 4, 13, ____1. 8 2. 9 3. 10 4. 11

44. 3, 4, 12, 6, 2, 9, 18, 3, 6, ___, 24, 12, 21. 3 2. 8 3. 4 4. 9

45. 51, 17, 3, 16, 48, 12, 4, 10, 40, ____, 5, 13, 651. 9 2. 7 3. 6 4. 8

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62. 6, 10, 18, 34, ______1. 44 2. 55 3. 66 4. 80

63. 1, 8, 16, 25, _______1. 30 2. 35 3. 40 4. 50

64.

5, 10, 17, 26, 37, 50, ___1. 64 2. 82 3. 65 4. 101

65.

37, 38, 34, 43, 27, 52, ____1. 16 2. 64 3. 74 4. 18

66. 3, 4, 10, 33, 136, ____, 41161. 136 2. 685 3. 32 4. 680

67.

10, 14, 22, 38, 70, ____

1. 130 2. 134 3. 140 4. 142

68. 10, 11, 13, 16, 20, 25, ____1. 30 2. 31 3. 32 4. 33

69. 10, 15, 40, 165, ___1. 700 2. 725 3. 760 4. 790

70.

21, 29, 43, 55, 73, ____1. 88 2. 89 3. 90 4. 101

71.

2, 3, 5, 7, ?1. 17 2. 15 3. 11 4. 19

72. 1, 5, 11, 19, 29, 41, ?1. 49 2. 51 3. 55 4. 59

73.

11, 32, 53, 74, 95, 116, ?1. 137 2. 125 3. 120 4. 138

74.

2, 5, 9, 10, 13, 17, 18, 21, 25, 26, ?1. 27 2. 28 3. 29 4. 30

75. 3, 5, 9, 15, 23, 33, 45, ?1. 59 2. 60 3. 61 4. 62

76.

0, 1, 8, 27, 64, ?1. 91 2. 125 3. 128 4. 256

77.

2, 4, 7, 11, 16, ?1. 20 2. 21 3. 22 4. 23

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78. 5, 14, 27, 44, 65, ?1. 88 2. 90 3. 109 4. 130

79. 1, 4, 10, 22, 46, ?1. 48 2. 68 3. 82 4. 94

80.

3, 5, 9, 17, 33, ?1. 48 2. 49 3. 63 4. 65

81.

1, 4, 9, 16, 25, ?1. 30 2. 31 3. 32 4. 36

82. 17, 13, 11, 7, 5, 1, ?1. 2 2. - 1 3. 0 4. 1

83.

30, 24, 19, 15, 12, ?

1. 8 2. 9 3. 10 4. 1184.

?,24

1,

36

1,

54

1,

81

1

1.32

3 2.15

1 3.16

1 4.18

1

85.

2, 6, 11, 17, ?, 321. 22 2. 24 3. 28 4. 23

86.

3, 7, 15, ?, 631. 31 2. 42 3. 35 4. 34

87.

128, 110, 90, ?, 441. 56 2. 72 3. 68 4. 70

88. 7, 15, 29, 59, 117, ?1. 235 2. 233 3. 234 4. 335

89.

6, 8, 9, 12, 14, 18, ?1. 19 2. 21 3. 23 4. 25

90. 5, 6, 10, 19, 35, ?1. 50 2. 55 3. 60 4. 71

91. 999, 727, 509, 339, ?1. 211 2. 208 3. 120 4. 205

92.

5, 14, 41, 122, 365, ?1. 1194 2. 1094 3. 1095 4. 1093

93. 17, 19, 15, 23, 7, 39, ?1. 18 2. 9 3. - 25 4. 25

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94. 3, 5, 8, 13, 20, ?1. 29 2. 31 3. 33 4. 39

95. 3, 6, 12, 15, 30, 33, ?1. 50 2. 60 3. 44 4. 66

96.

0, 2, 6, ?, 20, 30, 421. 8 2. 10 3. 12 4. 14

97.

5, 7, 11, 13, 17, 19, 23, 25, ?1. 25 2. 27 3. 29 4. 31

98. 1, 2, 9, ?, 65, 1261. 28 2. 82 3. 99 4. 108

99.

97, 86, 73, 58, 45, ?

1. 54 2. 55 3. 34 4. 56

100. 3, 5, 7, 9, ?1. 11 2. 12 3. 13 4. 14

101. 1, 4, 9, 16, ?1. 18 2. 23 3. 25 4. 36

102.

3, 10, 19, 30, 43, ?1. 60 2. 58 3. 55 4. 50

103.

5, 6, 14, 45, 184, ?1. 952 2. 925 3. 529 4. None

104. 5, 7, 11, 19, 35, ?1. 60 2. 62 3. 67 4. 70

105.

2, 2, 4, 12, 48, ?1. 240 2. 420 3. 480 4. 220

106.

8, 9, 20, 63, ?1. 100 2. 252 3. 256 4. 120

107. 7, 8, 12, 21, ?1. 42 2. 25 3. 37 4. 35

108.

1, 5, 19, 81, ?1. 162 2. 231 3. 411 4. 352

109.

3, 7, 15, 31, ?1. 52 2. 45 3. 60 4. 63

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110. 3, 8, 18, 33, ?1. 52 2. 53 3. 60 4. 63

111. 43, 60, 94, 145, ?1. 213 2. 201 3. 190 4. 205

112.

0, 2, 6, ?, 20, 30, 421. 13 2. 15 3. 12 4. 14

113.

3, 6, 18, 72, ?1. 108 2. 360 3. 164 4. 320

114. 215, 182, 149, 116, ?1. 83 2. 73 3. 58 4. 92

115.

4, 9, 13, 22, 35, ?

1. 57 2. 70 3. 63 4. 75

116. 2, 4, 7, 11, 16, ?1. 18 2. 20 3. 22 4. 25

117. 11, 13, 17, 19, 23, 29, 31, 37, 41, ?1. 43 2. 47 3. 51 4. 53

118.

2, 6, 12, 20, 30, 42, 56, ?1. 60 2. 64 3. 70 4. 72

119.

11, 12, 17, 18, 23, 24, ?1. 12 2. 29 3. 30 4. 35

120. 5, 6, 8, 11, ?, 20, 261. 15 2. 17 3. 14 4. 16

121.

840, 168, 42, 14, 7, ____1. 1 2. 7 3. 9 4. 12

122.

13, 32, 24, 43, 35, ?, 46, 65, 57, 761. 45 2. 52 3. 54 4. 55

123. 0, 2, 3, 5, 8, 10, 15, 17, 24, 26, ?1. 28 2. 30 3. 32 4. 35

124.

15, 14, 16, 13, 17, ?1. 18 2. 19 3. 15 4. 12

125.

17, 18, 14, 15, 11, ?1. 12 2. 15 3. 17 4. 19

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126. 3, 5, 5, 19, 7, 41, 9, ?1. 71 2. 61 3. 72 4. 69

127. 3, 2, 6, 8, 18, 40, 72, 240, ?1. 360 2. 320 3. 440 4. 432

128.

4, 6, 6, 15, 8, 28, 10, ?1. 36 2. 39 3. 45 4. 38

129.

23, 32, 49, 94, 73, ?1. 64 2. 87 3. 95 4. 37

130. 67, 61, 59, 53, 47, ?1. 43 2. 41 3. 37 4. 31

131.

5, 8, 9, 14, 16, 23, 26, ?

1. 29 2. 33 3. 35 4. 39

132. 3, 6, 8, 16, 19, ?1. 35 2. 38 3. 21 4. 36

133. 6, 3, 12, 6, 18, ?1. 9 2. 12 3. 24 4. 36

134.

5, 9, 6, 11, 7, ?1. 13 2. 15 3. 17 4. 19

135.

0.1, 0.9, 0.01, 0.09, ?, 0.0091. 0.01 2. 0.005 3. 0.001 4. 0.0101

136. 1, 2, 3, 6, 9, 18, ?, 541. 18 2. 36 3. 81 4. 27

137.

1, 2, 7, 7, 13, 12, ?1. 19 2. 18 3. 12 4. 14

138.

2, 3, 10, 15, 26, 35, 50, 63, ?1. 80 2. 82 3. 83 4. 84

139. 6, 24, 12, ?, 18, 8, 24

1. 4 2. 8 3. 16 4. 6140.

1, 0, 3, 2, 5, 4, ?1. 7 2. 6 3. 5 4. 4

141.

4, 2, 5, 1, 6, ?1. 5 2. 2 3. 4 4. 0

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142. 0, 2, 6, 6, 12, 10, ?1. 12 2. 14 3. 15 4. 18

143. 50, 50, 60, 40, 70, 30, 80, 20, 90, 10, 100, ____1. 10 2. 20 3. 0 4. 5

144.

200, 300, 212, 288, 236, 264, 284, 216, __, __1. 380, 120 2. 188, 360 3. 388, 178 4. 380, 130

145.

0, 2, 3, 5, 8, 10, ?1. 9 2. 11 3. 13 4. 15

146. 8, 24, 12, ____, 18, 541. 28 2. 46 3. 36 4. 48

147.

10, 15, 20, 30, 40, 60, 80, ____

1. 90 2. 100 3. 110 4. 120

148. 6, 42, 12, 35, 18, 28, 24, 21, __ , 14, 36, 71. 30 2. 35 3. 36 4. 18

149. 5, 20, 6, 24, 7, 28, _____1. 8 2. 9 3. 32 4. 10

150.

5, 4, 10, 8, 15, 12, 20, _____, 251. 13 2. 18 3. 15 4. 16

151.

1, 8, 9, _____, 25, 216, 491. 64 2. 60 3. 70 4. 75

152. 3, 4, 15, 16, ______, 36, 63, 641. 30 2. 25 3. 34 4. 35

153.

1, 3, 1, 9, 1, 81, 1, _____1. 243 2. 324 3. 6561 4. 5641

154.

2, 4, 7, 14, 17, 34, 37, _____1. 74 2. 76 3. 47 4. 72

155. 20, 18, 19, 16, 18, 14, _____1. 16 2. 17 3. 15 4. 13

156.

3, 12, 4, 16, 5, 20, 6, _______1. 30 2. 36 3. 24 4. 18

157.

8, 8, 9, 9, 11, 10, 14, 111. 15 2. 18 3. 17 4. 12

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158. 2, 6, 6, 14, 30, 62, ______, 2541. 142 2. 128 3. 126 4. 132

159. 4, 8, 7, 14, 12, 24, 19, ____, 281. 12 2. 38 3. 36 4. 24

160.

2, 7, 9, 3, 8, 11, 4, 9, 13, _____, 10, 151. 4 2. 7 3. 5 4. 6

161.

3, 9, 5, 25, 7, 49, 9, ______1. 81 2. 64 3. 100 4. 121

162. 14, 60, 28, 45, ?, 30, 561. 40 2. 35 3. 36 4. 42

163.

7, 5, 2, 14, 3, 1, 2, 6, 8, 5, 3, 24, 6, 2, 4, ___

1. 10 2. 36 3. 12 4. 24

164. 1, 4, 12, 2, 5, 15, 3, 6, 18, 4, ______1. 21 2. 7 3. 5 4. 6

165. 2, 8, 4, 3, 18, 6, 4, 32, 8, _______50, 101. 7 2. 6 3. 5 4. 9

166.

1278, _____, 314, 152, 70, 281. 634 2. 636 3. 632 4. 656

167.

2, 3, 6, 3, 4, 12, 4, 5, 20, 5, 6, ___1. 35 2. 30 3. 25 4. 35

168. 5, 7, 12, 6, 8, 14, 7, _____, 16, 8, 10, 181. 8 2. 10 3. 6 4. 9

169.

5, 2, 11, 6, 3, 12, 7, 4, 13, ____1. 8 2. 9 3. 10 4. 11

170.

3, 4, 12, 6, 2, 9, 18, 3, 6, ___, 24, 12, 21. 3 2. 8 3. 4 4. 9

171. 51, 17, 3, 16, 48, 12, 4, 10, 40, ____, 5, 13, 651. 9 2. 7 3. 6 4. 8

172.

4, 5, 9, 20, 5, 6, 11, 30, 6, 7, _____, 421. 12 2. 11 3. 13 4. 8

173.

1, 7, 11, 13, 11, ?1. 12 2. 7 3. 9 4. 10

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174. 1, 2, 3, 5, 4, 5, 9, 14, 13, 14, 27, ?1. 80 2. 82 3. 40 4. 41

175. 1, 4, 9, ?, 8, 271. 1 2. 4 3. 6 4. 2

176.

8, 17, 9, 21, 12, 27, 15, ?, 211. 18 2. 16 3. 36 4. 10

177.

1, 3, 4, 8, 15, 27, ?1. 37 2. 55 3. 50 4. 44

178. 1, 2, 4, 7, 13, 24, 44, ?1. 62 2. 81 3. 73 4. 69

179.

1, 1, 1, 2, 4, 8, 3, 9, ?

1. 18 2. 17 3. 15 4. 27

130. 10, 40, 90, 61, 52, 63, ?1. 54 2. 94 3. 14 4. 72

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Letter Series

1. AZXBVTCR _______1. P, D 2. E, O 3. Q, E 4. O, X

2. C-3, E-5, G-7, I-9, _______

1. X-24, M-21 2. K-11, M-13 3. O-15, X-14 4. M-18, K-14

3. C, e, G, i, K, _____1. O 2. m 3. k 4. U

4. BA, YZ, DC, WX, _______1. DE 2. EF 3. FE 4. FG

5. A, C, E, G, I, _____1. J, L 2. K, N 3. K, M 4. L, N

6. ACE, FHJ, KMO, PRT, _____1. TVX 2. RTU 3. UWY 4. ZBG

7. ADG, GJM, MPS, ____, YBE1. SVX 2. SYX 3. SWZ 4. SVY

8. AK, CM, EO, GQ, ______1. JT 2. IS 3. JP 4. HR

9. SJA, TKB, ULC, VMD, WNE, _____1. XPF 2. XNF 3. XOG 4. XOF

10. QIA, SKC, UME, ______1. XOH 2. WOG 3. TLD 4. VPG

11. AJQ, BHR, CLS, DMT, ENU, ______1. VOF 2. IOT 3. FOV 4. FOW

12. EIMQ, FJNR, GKOS, _____1. IMQU 2. KOSW 3. HLPT 4. HLPU

13. ABCDE, FGHIJ, KLMNO, PQRST, UVWXY, _______1. ABCDE 2. ZABCD 3. ZYXWV 4. None

14. YUSP; UROL; QNKH, ______1. MIGD 2. MJFC 3. MJGD 4. MKHE

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15. J Z I Y H _____1. A 2. X 3. U 4. Z

16. A Z B Y C ______1. A 2. W 3. Y 4. None

17. Z Y X A B C W V U D E F T S R G H _____1. L 2. M 3. R 4. P

18. P Q U R Q Q U R R Q U R ______1. I 2. R 3. V 4. Z

19. P Q U R Q U R N Q U R _______1. M 2. N 3. O 4. Q

20. Z A S G S F Z J Z _____1. Z 2. I 3. O 4. Q

21. A C F J O ______1. U 2. B 3. V 4. W

22. AB, DC, EF, HG, ____1. I 2. V 3. W 4. N

23. D F I M R _____1. V 2. X 3. W 4. Y

24. B E I _____

1. W 2. M 3. N 4. Z

25. DMP, FLN, HKL, JJJ, ______1. MII 2. LIH 3. III 4. MIF

26. A, Z, D, X, G, V, J, T, M, ____1. R, P 2. S, N 3. P, R 4. N, S

27. B, D, G, K, P, _____1. S 2. V 3. T 4. W

28. MKP, WSZ, KGN, ____

1. LIP 2. MIP 3. TMQ 4. HLE

29. C4X, F9U, I 16R, ____1. L 25P 2. L 25 O 3. L 27 P 4. None

30. EJOT, DHLP, CFIL, ___1. BDFH 2. BHLM 3. DEIJ 4. DGKC

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46. ACF acf G______ _______1. IL, giL 2. JL, giL 3. IL, giL 4. LL, gli

47. Z X V z x v U ____ ______1. Ust UST 2. SQ usq 3. USQO 4. USTrs

48. accce, ACCCE, _______ _______1. GJJJK, gjjjjjk 2. giiik, GIIIK 3. GIIIK, ghhk 4. None

49. CFL, EIK, GLJ, IOI, __1. KRH 2. KRJ 3. JRH 4. KQH

50. A, CD, GHI, ___, VUWXY1. LMNO 2. MNO 3. NOPQ 4. MNOP

51. A/2, B/4, C/6, D/8, ________1. E/16 2. F/32 3. F/12 4. E/10

52. ZXVTR ______1. O 2. N 3. K 4. P

53. B, A, Z, D, C, Y, F, E, _____1. W 2. X 3. U 4. G

54. A, E, J, O, T, ______1. U 2. Y 3. W 4. Z

55. AG, CI, MS, R___

1. V 2. U 3. X 4. Y

56. AG, BH, CI, ______1. DJ 2. DI 3. EL 4. HM

57. AGM, BHN, CIU, DJP, ______1. EPR 2. EKP 3. EMS 4. EKQ

58. CJQ, DKR, ELS, FMT, ______1. GNU 2. GOV 3. GNW 4. HOV

59. GPW, FOV, ENU, _______, CLS, BKR

1. DMT 2. DKR 3. DMR 4. DLT

60. NIFA, OJGB, PK___1. HD 2. LC 3. HC 4. TU

61. YMA, ZNB, AOC, ____1. BND 2. CPC 3. BPQ 4. BPD

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62. AGPU, BHQV, CIRW, ____1. DOSX 2. DJSY 3. DJSX 4. DISX

63. XSNI, TOJE, _____1. LGBZ 2. PKFA 3. HCYU 4. JGBX

64. A E I L P _____1. V 2. W 3. N 4. T

65. A C E D F ______1. H 2. J 3. E 4. W

66. A J E B U Q I Y E P A ______1. J 2. K 3. W 4. Y

67. B C D Y X W F G H U T S ________1. C 2. D 3. F 4. J

68. G I J J L M M O P P _________1. M 2. R 3. N 4. O

69. A D B E C F D _______1. W 2. G 3. U 4. U

70. W U S Q O _____1. O 2. N 3. M 4. W

71. B C F G J K ____

1. P 2. O 3. M 4. N

72. B, F, K, Q, _____1. X 2. R 3. T 4. Y

73. A, B, D, G, ____, P1. J 2. I 3. K 4. L

74. POQ, SRT, VUW, _____1. XYZ 2. XZY 3. YXZ 4. YZX

75. AD, EH, IL, ______, QT

1. MP 2. MN 3. LM 4. OM

76. ADG, HKN, _____1. ORU 2. VXZ 3. JLN 4. BEG

77. AZ, CX, FU, _____1. KP 2. JQ 3. IR 4. IV

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78. CDE, HIJ, OPQ, XYZ, _____1. IJK 2. JKL 3. KLM 4. LMN

79. CDE, IJK, RST, DEF, _____1. RST 2. STU 3. GRS 4. PQR

80. C4X, F9U, I16R, _____1. K25P 2. L25P 3. L25O 4. L27P

81. OPQ, WXY, ______, RST, EFG1. HIJ 2. IJK 3. KLM 4. LMN

82. CD, HI, MN, _____1. QS 2. RS 3. OP 4. PQ

83. AU, BY, CZ, _______1. BC 2. KL 3. MN 4. DX

84. C F I L O _____1. P 2. Q 3. R 4. S

85. E G J L O Q ____1. S 2. R 3. U 4. T

86. A I P V A E _____1. F 2. G 3. H 4. I

87. I M Q U Y C _____

1. C 2. D 3. F 4. G

88. X U S P N K ____1. I 2. L 3. M 4. Q

89. T Q N K H _____1. I 2. J 3. S 4. E

90. D I L Q T Y B G _____1. H 2. I 3. O 4. J

91. X U S P N K I ____

1. J 2. K 3. M 4. F

92. D F I M R ____1. S 2. U 3. M 4. X

93. B D G I L N ____1. O 2. Q 3. S 4. U

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94. D I L Q T Y B G _1. H 2. J 3. R 4. I

95. T S Q N J ______1. S 2. E 3. K 4. L

96. S P L G _____1. R 2. S 3. U 4. A

97. B E I N T _____1. R 2. S 3. U 4. A

98. B F K Q ______1. R 2. S 3. W 4. X

99. R T P R N P ____1. Q 2. L 3. S 4. F

100. W T P M I F B ____1. W 2. P 3. F 4. Y

101. X W V U T S ____1. R 2. T 3. E 4. X

102. AD, EH, IL, ______, QT, UX1. AY 2. VB 3. CW 4. MP

103. AY, BZ, CW, _____

1. EF 2. GH 3. MN 4. DX

104. BC, FG, JK, ____, RS, VW1. LM 2. OP 3. QR 4. NO

105. AI, BJ, CK, ____1. LM 2. GH 3. QR 4. DL

106. Z W S P L I E____1. D 2. F 3. G 4. B

107. AC, EG, BD, FH, IK, _____1. LM 2. OP 3. IJ 4. JL

108. ABC abc DEF _____1. ghi 2. GHI 3. ABC 4. def

109. AGMS, agms, _____1. ABCD 2. abcd 3. BHNT 4. bhnt

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110. CYD, FTH, IOL, LJP, ______1. OFT 2. LET 3. OEK 4. OET

111. BXF, DVI, FTL, HRO, _____1. JPL 2. KPL 3. JOL 4. JPR

112. ZGL, XHN, VIQ, TJU, _____1. QKZ 2. RKY 3. RLZ 4. RKZ

113. BXJ, ETL, HPN, KLP, _______1. NHR 2. MHQ 3. MIP 4. NIR

114. AaD, BeF, DiH, _____, KuL1. FmI 2. GoJ 3. HlK 4. GiJ

115. OAL, MZN, KBP, IYR, _______1. GCT 2. QXT 3. QXJ 4. GET

116. BY, IQ, NK, QG, ____1. RF 2. TF 3. RE 4. SE

117. DKM, FJP, HIS, JHV, _____1. HGY 2. IGZ 3. IGY 4. LGY

118. AZ, IY, OW, SS, ____1. QA 2. KU 3. OU 4. UK

119. AX, BY, CX, ____

1. EF 2. GH 3. IJ 4. DW

120. GHJM__V1. T 2. S 3. R 4. Q

121. AYD, BVF, DRH, ______, KGL1. FMI 2. GMJ 3. HLK 4. GLJ

122. MHZ, NIW, OKT, PNQ, _______1. RRN 2. QRN 3. QRM 4. QQN

123. LXF, MTJ, NPN, OLR, ___1. PHV 2. PIU 3. PJW 4. PKX

124. shg, rif, qje, pkd, _____1. ole 2. olc 3. nmc 4. nlb

125. FLP, INS, LPV, ________1. ORY 2. UXZ 3. VXY 4. SVW

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126. DEF, HIJ, MNO, _______1. STU 2. RST 3. RSV 4. SRQ

127. U, O, I, ____, A1. E 2. C 3. S 4. G

128. A, B, D, G, ____1. M 2. L 3. K 4. H

129. Z, U, Q, ____, L1. I 2. K 3. M 4. N

130. A, C, F, H, ____, M1. L 2. K 3. J 4. I

131. AZ, CX, FU, ______1. IR 2. IV 3. JQ 4. KP

132. AZ, GT, MN, _____, YB1. KF 2. RX 3. SH 4. TS

133. BF, CH, _____, HO, LT1. DN 2. EL 3. EK 4. None

134. AD, EH, IL, _____, QT1. LM 2. MN 3. MP 4. OM

135. CAT, FDW, IGZ, _______

1. KJA 2. KTC 3. LHD 4. LJC

Number Analogy:

1.

29 : 31 :: 37 :_______1. 47 2. 43 3. 38 4. 41

2.

26 : 126 :: 37 :_____1. 195 2. 186 3. 217 4. 205

3.

2 : 16 :: 3: _______1. 243 2. 81 3. 27 4. 729

4. If 7 : 2=27, 3 : 4=21 then 5 : 6 = ?1. 33 2. 35 3. 20 4. 15

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5.

48 : 80 ::_______: 5761. 18 2. 24 3. 48 4. 68

6. 52:76::_____:5361. 196 2. 322 3. 488 4. 702

7.

56 : 182 ::______: 9921. 552 2. 600 3. 702 4. 756

8.

3:11::7:_______1. 22 2. 29 3. 18 4. 51

9. 324 : 1621. 64:36 2. 2:1 3. 22:10 4. 134:112

10. 6 : 18 :: 4 :____1. 12 2. 6 3. 8 4. 16

11.

21 : 3 :: 574 :____1. 23 2. 82 3. 97 4. 113

12.

1 : 1 :: 25 :_______1. 26 2. 125 3. 240 4. 625

13. 121 : 12 :: 25 : ?1. 1 2. 2 3. 6 4. 7

14.

42 : 20 :: 64 :______

1. 51 2. 52 3. 53 4. 54

15.

7584 : 5362 :: 4673 :________1. 2367 2. 2451 3. 2531 4. None

16. 25 : 37 :: 49 :______1. 41 2. 56 3. 60 4. 65

17.

25 : 125 :: 36 :_____1. 180 2. 206 3. 216 4. 318

18.

14 :9 :: 26 :______1. 12 2. 13 3. 15 4. 31

19. 8 : 28 :: 27 :______1. 8 2. 28 3. 64 4. 65

20. 583 : 293 :: 488 :_________1. 291 2. 378 3. 487 4. 581

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49.

14 : 9 :: 26 : ?1. 12 2. 13 3. 15 4. 31

50. 27 : 65 :: 1 : ?1. 8 2. 9 3. 10 4. 7

51.

853 : 963 :: 844 : ?1. 921 2. 873 3. 651 4. 861

52.

20 : 8000 :: 30 : ?1. 12000 2. 15000 3. 27000 4. 30000

53. 8 : 72 :: 12 : ?1. 156 2. 200 3. 144 4. 120

54. 9 : 8 :: 16 : ?1. 27 2. 18 3. 17 4. 114

55.

12 : 37 :: 2 : ?1. 6 2. 8 3. 7 4. 10

56.

10 : 99 :: 12 : ?1. 144 2. 143 3. 141 4. 145

57. 81 : 91 :: 100 : ?1. 110 2. 131 3. 111 4. 120

58.

30 : 42 :: 56 : ?

1. 72 2. 68 3. 84 4. 76

59.

7 : 342 :: 9 : ?1. 344 2. 801 3. 999 4. 728

Directions: Each of the following questions consists of a pair of numbers that havea certain relationship to each other, followed by four other pairs of numbers givenas alternatives. Select the pair in which the numbers are similarly related as in thegiven pair.

60. 8 : 15

1. 24 : 36 2.49 : 64 3. 35 : 48 4. 99 : 121

61.

5 : 1001. 4 : 48 2. 4 : 64 3. 3 : 18 4. 9 : 81

62. 3 : 241. 2 : 8 2. 5 : 119 3. 4 : 62 4. 7 : 49

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63.

12 : 211. 18 : 90 2. 28 : 56 3. 41 : 24 4. 17 : 71

64. 8 : 121. 18 : 27 2. 16 : 23 3. 20 : 30 4. 12 : 18

65.

5 : 301. 4 : 20 2. 7 : 21 3. 8 : 72 4. 2 : 4

66.

81 : 91. 12 : 3 2. 18 : 6 3. 62 : 8 4. 56 : 7

67. 72 : 141. 18 : 90 2. 52 : 10 3. 35 : 18 4. 50 : 20

68. 64 : 5121. 7 : 49 2. 9 : 81 3. 6 : 216 4. 25 : 625

69.

8 : 321. 6 : 28 2. 5 : 15 3. 16 : 128 4. 12 : 144

70.

12 : 301. 56 : 89 2. 30 : 56 3. 19 : 29 4. 42 : 58

71. 72 : 831. 51 : 72 2. 23 : 31 3. 42 : 53 4. 20 : 30

Directions Choose the best number which is similar to the numbers given in the

following given set.

72.

539, 278, 4581. 368 2. 549 3. 637 4. 873

73. 126, 168, 1471. 189 2. 104 3. 125 4. 963

74.

284, 362, 1881. 482 2. 354 3. 823 4. 611

Directions (Questions 35-40): Choose the set of numbers from the four

alternatives sets, that is similar to the given set in the question.

75.

(5 8 13)1. (3 4 5) 2. (6 13 22) 3. (7 10 14) 4. (2 5 9)

76. (5 7 9)1. ( 6 6 8) 2. (7 8 9) 3. (8 5 4) 4. (4 7 8)

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77.

(7 24 25)1. (6 35 36) 2. (9 40 42) 3. (5 11 13) 4. (11 60 61)

78. (63 8 3)1. (1 2 1) 2. (80 9 4) 3. (225 15 4) 4. (8 4 2)

79.

(16 9 4)1. (25 36 49) 2. (64 49 36) 3. (25 36 16) 4. (36 9 49)

80.

(2 3 6)1. (5 2 9) 2. (4 2 8) 3. (3 3 8) 4. (4 3 9)

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Letter Analogy

Find out the correct letter pair from the alternative given in answer choices below, todonate the same relationship among the group of letters as established between thesets at the top (question pair).

1. APA : EQE ::_____:________1. BQB: FGF 2. CDC: GHG 3. LML: NON 4. IRI: OSO

2. AP: EQ::_____:______1. AB:CD 2. EF: IK 3. LM:NO 4. IR:OS

3.

JAJ: KEK::_______:_______1. BAB: DED 2. FGI: HIJ 3. KEK: LIL 4. LIL: MOM

4. AZB: CYD::___:______

1. EXF: GWH 2. EFG: HIJ 3. EFG: HIK 4. EZF: CYH

5.

I:V::N:_______1. H 2. X 3. T 4. W

6.

V:N::Z:_____1. X 2. I 3. T 4. M

7. V:X::H:_______1. Y 2. T 3. I 4. Z

8.

PS:DG::_____:_________1. CE:TR 2. KM:OQ 3. EH:TW 4. FH:JL

9.

BC:GH::___:______1. RT:XY 2. ST:UV 3. OP:QR 4. ST:XY

10. JK:QR::_______:______1. ST:UV 2. WX:ZY 3. CF:JL 4. BC:IJ

11. CD:GH::LK:____:________

1. DC 2. EG 3. AB 4. JI

12.

XY: PQ::MN:_______1. TS 2. MO 3. QP 4. BC

13. MN:OP::RS:_______1. BH 2. HI 3. MO 4. UW

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14.

YZ:XY::AB:_______1. ML 2. BD 3. PR 4. PQ

15. DC:HG::ML:_________1. OP 2. NM 3. BA 4. PQ

16.

TS:LK::BA:______1. DE 2. FE 3. GI 4. RP

17.

AB:DE::_____:_______1. GH:JK 2. HI:RS 3. GH:KL 4. ED:BA

18. I:T::___:______1. W:X 2. M:V 3. L:N 4. L:X

19. b:d::p:_______1. a 2. o 3. q 4. d

20.

F:P::E:_______1. F 2. G 3. B 4. W

21.

RAGDE:EDGAR::________:_____1. LUKE:MATTHEWS 2. GANDHI:HDNADI3. EGROEG:GEORGE 4. POLITE:COURTESY

22.

AF:IK::LQ:_____1. MO 2. RS 3. TV 4. TU

23.

FED:MKI::PON:_____1. VUY 2. WUS 3. TVU 4. TVM

24. AYBZ:CWDX::EUFV:______1. GSHT 2. GHST 3. SHGT 4. MVGT

25.

ACEG:IKMO::KMOQ:_________1. SWVY 2. SUWY 3. STVW 4. SWTM

26.

ZWT:ROL::IFC:_______1. AXU 2. AYU 3. ZUT 4. AWT

27. ABD:EFH::IJL:______1. MNP 2. MPN 3. NMP 4. NMT

28.

FHJ:LNP::RTV:________1. ZXB 2. XZT 3. XZB 4. VTM

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29.

DE:45::BC:________1. 23 2. 24 3. 25 4. 26

30. ABE:8::FBD:______1. 14 2. 13 3. 15 4. 12

31.

987:IHG::654:______1. FDE 2. FED 3. EFD 4. DEF

32. K 11 J: :: :

T 20 R ________

1. 7

10 2. 10

18 3. 8

11 4. 10

15

33. Z Y T: :

26 25 20: _______

1. S

19 2. R

17 3. 8

16 4. 19

20

34. LXM:12X13::UXW:_______1. 21X20 2. 21X23 3. 20X23 4. 23X10

35.

ZYB:XWD::UTG:_________1. ISR 2. SRI 3. IRS 4. None

36. ABX:DEU::GHR:_______1. JKO 2. JOK 3. KOJ 4. OKJ

37. ? : DURXQG :: WOULD : TLRIA1. ARMOUR 2. SHROUD 3. SHOULD 4. AROUND

38.

? : YBVLKA :: WOULD : TLRIA1. BEYOND 2. NORMAN 3. BYGONE 4. MATTER

39. LJH : KKI :: CIA : ?1. BJB 2. BBB 3. CBZ 4. BBZ

40. DRIVEN : EIDRVN :: BEGUM : ?1. BGMEU 2. MGBEU 3. UEBGM 4. BGMUE

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Directions: Find out the correct letter pair from the alternative given in answerchoices below, to donate the same relationship among the group of letters asestablished between the sets at the top (question pair).

41.

ZA:YB::XC:______

1. YZ 2. NM 3. BC 4. WD

42. ABCD:WXYZ::EFGH:_____1. STVU 2. STOU 3. STUE 4. STUV

43.

AD:BE::CF:___1. DE 2. BC 3. DG 4. FG

44.

ACDE:OGHI::ESTU:____1. EPQU 2. ABCD 3. OGHK 4. XYZE

45.

BAC:DEF::____:NOP1. GHI 2. JHI 3. GIH 4. HIJ

46. CG:EI::FJ:_____1. JK 2. IJ 3. LM 4. GK

47.

ACF:EDG::IEH:______1. OFI 2. GHI 3. LMN 4. EIJ

48. AEZ:EIY::IOX:_____1. UYZ 2. AEX 3. EIX 4. OUW

49. AZB:BYC::CXD:___1. DWE 2. DEF 3. DFG 4. DMN

50.

BACE:DACE::FACE:_________1. HASE 2. LACE 3. CASE 4. HACE

51. ZYB:XWD::TSH:________1. QFR 2. RFQ 3. RQF 4. None

52. ADG:ZWT::IKN:________

1. RPM 2. PMR 3. MRP 4. PRM

53.

NQS:TWY::KHF:_______1. NLQ 2. QNL 3. LQN 4. None

54. PNR:KMI::XZV:_______1. DAE 2. AED 3. EAD 4. None

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55.

ACEG:DFHJ::_______:ZXVT1. WUSQ 2. SQOM 3. USQO 4. YWUS

56. KcaC:CacK::XgmF: ______1. GmeF 2. FmgX 3. EgmX 4. EmgF

57.

QIOK:MMKO::YAWC:______1. USGA 2. UESG 3. VUES 4. SUEG

58.

ACEG:ZXVT::IKMO:_____1. YACE 2. RPLN 3. SQOM 4. RPNL

59. PNDY:QMEX::JRSF:______1. KQRE 2. KSTE 3. KSRE 4. KQTE

60. POLITE:ETILOP::_____:______1. ELPMIS; SIMPLE 2. DRAOG; BOARD 3. CHART; TRAHC

4. SINGLE; ELGNIS

61. RT:WZ:______:_____1. AC:RU 2. AB:PW 3. PR:LM 4. TU:WX

62. Z:N::____:_______1. H:T 2. X:E 3. M:N 4. T:V

63.

IJ:KL::_____:______1. AB:PQ 2. AD:GH 3. LM:OP 4. MN:OP

64.

AZ:BY::____:______1. CX:BW 2. CW:DY 3. CX:DW 4. CZ:DY

65. LLAMS:SMALL::_____:_________1. CORK:KROC 2. BARK:KRAB 3. TREE:EERT 4. SRENID:DINERS

66.

CBA:FED::______:_______1. IJH:MNL 2. BCA:FGH 3. MCA:JKO 4. IHG:KLJ

67.

FED:IHG::________:______1. ACB:GIJ 2. TSR:WVW 3. IJK:LMO 4. DEF:IGH

68. CEH:IKN::_____:_______1. CDF:IJK 2. OQT:UWZ 3. EFH:KMN 4. BCE:GIJ

69.

CDF:GHJ::____:_____1. BQB:FGF 2. CDC:GHG 3. KLM:OQR 4. PQR:STU

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70. 17

IH:

27

NM:

31

PO :_______

1. GM

16 2. GT

14 3. GV

16 4. GF

13

71. AEI:MQU::XBF:_______1. JNR 2. NJP 3. STV 4. MNO

72. XUR:OLI::FCZ:_______1. WTQ 2. WQT 3. WTM 4. TWC

73.

RPQ:OMN::JIH:_____1. GFE 2. GEF 3. GTB 4. GBT

74. A:Z::B:_____1. X 2. Y 3. W 4. U

75.

ADH:BEI::KTO:______1. LUR 2. LUP 3. MUR 4. MUP

76.

ABY:BCX::GHS:________1. HIR 2. IRH 3. RIH 4. None

77. CXDW:HSIR::KPLO:______1. KPQj 2. KQjP 3. PKQj 4. JKQP

78. BCYX:DEWV::GHTS:_______1. IJRQ 2. JIRQ 3. RIQJ 4. None

79.

ADF:JMO::DGI:_____1. TQO 2. ORT 3. ZXV 4. PON

80.

BYDW:FUHS::AZCX:_____1. EVGT 2. FVGT 3. EGVT 4. FGVT

7. NUMBER RANKING

1.

In a number series given below count each 5 which is not immediately precededby 3 but is immediately followed by 7. How many such 5‟s are there?5 7 3 3 5 7 3 5 7 7 5 3 5 7 5 7 2 3 5 7 5 3 7 5 3 5 7 7 3 5 3 5 5 7

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1. 1 2. 2 3. 3 4. 4

2.

How many numbers are there which are divided by 3 and followed by thenumbers divided by 2 in the given series?3 4 5 9 6 1 5 3 2 4 5 3 4 3 4 9 2 51. 1 2. 2 3. 3 4. 6

3.

How many 5‟s are there in the following number sequence which areimmediately followed by 3, but not immediately preceded by 7?8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 81. 1 2. 2 3. 3 4. 4

4. How many such 7‟s are there in the following number sequence which areimmediately followed by 4 but not immediately preceded by 8?8 7 4 4 7 8 4 7 4 7 8 4 8 8 7 7 4 8 7 4 7 4 8 8 7 7 7 9 4 8 7 7 41. 2 2. 3 3. 4 4. 5

5.

How many 8‟s are there in the following number series which are exactlydivisible by its immediately preceding and immediately succeeding numbers?7 8 3 8 4 8 1 2 8 5 4 8 1 4 8 3 8 8 2 4 8 2 8 5 8 4 8 51. 4 2. 2 3. 5 4. 3

6. How many numbers are there in the given series, which are not preceded by 5but followed by 4?1 5 7 9 6 7 9 5 4 3 2 1 0 91. 1 2. 2 3. 3 4. 4

7.

How many 3‟s are there in the following number sequence which are

immediately preceded by 6 but not immediately followed by 7?2 3 7 4 3 5 6 3 7 4 6 3 8 9 6 3 5 1 8 3 7 2 4 2 8 6 3 91. 1 2. 2 3. 3 4. 4

8.

In the following number series how many 7‟s are there which are immediatelyfollowed by 5 also immediately preceded by 6?7 5 7 6 8 7 5 6 7 5 6 8 6 7 5 7 5 7 71. 1 2. 2 3. 3 4. None

9. How many 3‟s are there in the given series that are exactly followed by 1 and

also immediately preceded by 2? 3 2 3 1 4 3 1 2 3 1 2 4 2 3 1 3 1 3 3

1. 2 2. 3 3. 4 4. 5

10.

How many prime numbers are there which are an odd number and preceded byan even number?3 2 4 2 7 5 4 9 7 8 5 5 6 3 3 5 4 2 3 9 6 2 7 1 2 3 61. 9 2. 7 3. 8 4. 5

11. How many 8‟s are there in the following sequence which are immediatelyfollowed by 6 but not immediately preceded by 9?

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6 8 9 7 6 8 6 9 8 6 2 8 6 9 8 6 8 9 81. 3 2. 1 3. 2 4. None

12. In the following series of numbers, find out how many times 1, 3 and 7 haveappeared together, 7 being in the middle and 1 and 3 on either side of 7.2 9 7 3 1 7 3 7 7 1 3 3 1 7 3 8 5 7 1 3 7 7 1 7 3 9 0 6

1. 3 2. 4 3. 5 4. More than 5

13. How many 4‟s immediately preceded by 5 but not immediately followed by 7 arethere in the following series of numbers?5 4 8 7 4 9 5 4 7 7 4 5 5 4 6 5 4 7 5 4 7 3 2 4 71. 2 2. 3 3. 4 4. 5

14. How many even numbers are there which are not followed by even but precededby even number?

3 2 5 4 4 7 6 5 2 6 7 6 9 8 4 7 5 4 8 5 6 2 1 1 2 4 81. 5 2. 6 3. 4 4. 7

15. Four of the following five are alike in a certain way and so form a group. Whichis the one that does not belonging to the group?1. 81081 2. 18081 3. 18018 4. 80801

16. How many 7‟s are there in the following numbers sequence which areimmediately preceded by 5 but not immediately followed by 3?3 7 5 7 4 5 7 3 9 7 8 5 7 7 8 9 7 1 5 7 6 5 7 4 3 7 5 7 3 81. 1 2. 2 3. 3 4. 4

17. How many 8‟s are there in the following number sequence which are precededby 7 but not immediately followed by 4?2 3 8 2 5 7 8 3 7 8 4 6 9 8 4 3 2 7 8 9 5 7 8 1 5 2 91. One 2. Two 3. Three 4. Four

18.

In a row of children, Hari is eleventh from the left and Manjula is seventeenthfrom the right. When they exchange their places, Hari will be thirteenth fromthe left. Which of the following will be the new position of Manjula from right?1. Eleventh 2. Twenty-ninth 3. Twenty-first 4. Nineteenth

19.

How many numbers are there which are divisible by 3 and are preceded by 3but not followed by 2?3 6 2 2 9 3 6 7 5 3 9 8 7 2 2 3 3 9 3 3 2 3 6 4 3 8 71. 5 2. 4 3. 9 4. 1

20. Which of the following will be the third digit of the number from your right endof the third number after the numbers are arranged in descending order?4 6 9 7 , 6 9 8 9 , 5 3 9 2 , 7 5 1 8 , 6 2 1 5 , 5 9 4 2

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1. 1 2. 5 3. 2 4. 4

21.

Kapil ranked thirteenth from the top and twenty-six from the bottom amongthose who have passed in the annual examination in a class. If six studentshave failed in the annual examination, what was the total number of studentsin that class?

1. 45 2. 38 3. 44 4. 50

22. In a row of boys, Anil is 15th from the left and Vishakh is 7th from the right. Ifthey interchange their positions, Vishakh becomes 15th from the right. Howmany boys are there in the row?1. 21 2. 22 3. 29 4. Can‟t be determined

23. Samir‟s rank is tenth from the top in his class. Prabir, who is 15th from the endis lower in rank than Samir by ten. How students are there in Samir‟s class. 1. 32 2. 31 3. 38 4. 34

24.

How many even numbers are there which are divisible by a prime number andpreceded by an odd number and followed by a prime number?3 4 7 5 8 2 7 9 8 2 6 7 4 5 3 8 2 8 4 5 6 2 7 2 2 3 21. 6 2. 7 3. 9 4. 8

25. In a row of children, Shibu is 5th from the left and Ravi is 6th from right. Whenthey exchange position, Shibu will be 13th from the left. What will be Ravi‟sposition from the right?1. 4th 2. 5th 3. 13th 4. 14th

26.

Madhav ranks thirteenth in a class of thirty-one. What is his rank from the

last?1. 19 2. 17 3. 18 4. 20

27.

In the following series how many such odd numbers are there which aredivisible by 3 or 5, then followed by odd numbers and again followed by evennumbers?12 19 21 3 25 18 35 20 22 21 45 46 47 48 9 50 52 54 55 561. 3 2. 1 3. 2 4. None

28. How many 6‟s present in the following sequence of number which are precededby 1 but not followed by 9? 9 6 1 2 3 1 6 8 3 4 1 6 9 0 5 7 1 6 4 3 2 2 6 51. 1 2. 2 3. 3 4. 4

29. How man y such 5‟s are there in the following number sequence which areimmediately followed by „3‟ but not immediately preceded by „7‟? 8 9 5 3 2 5 3 8 5 5 6 8 7 3 3 5 7 7 5 3 6 5 3 3 5 7 3 8

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1. 1 2. 2 3. 3 4. 4

30.

How many 6‟s are there in the following sequence which are immediatelyfollowed by „3‟ and immediately preceded by „7‟? 6 3 3 7 7 6 6 3 7 3 7 6 7 3 7 6 3 3 6 6 7 7 3 6 7 31. 1 2. 2 3. 3 4. None

31.

How many 8‟s are present in the following sequence of number which arepreceded by 9 but not followed by 6?2 1 9 8 5 4 3 9 8 7 0 9 8 6 8 9 3 9 8 1 2 91. 1 2. 2 3. 3 4. 4

32. In the series given below, how many 8‟s are there which are exactly divisible byits immediately preceding as well succeeding numbers?2 8 3 8 2 4 8 2 4 8 6 8 2 8 2 4 8 3 8 2 8 61. 1 2. 2 3. 3 4. 4

33.

In a row of 16 boys, when Prakash was shifted by two places towards the left,he became 7th from the left end. What was his earlier position.1. 7th 2. 8th 3. 9th 4. 10th

34. How many 5‟s immediately preceded by 9 but not immediately followed by 2 arethere in the following series?5 2 8 5 9 2 1 0 5 6 1 6 5 4 2 1 5 9 5 8 2 7 9 5 2 11. 1 2. 2 3. 4 4. 6

35. How many 6‟s are there in the following number series which are eitherpreceded by 4 or following by 7? 3 1 2 9 6 4 7 6 4 6 7 2 9 7 6 4 4 6 7

1. 1 2. 2 3. 3 4. 4

36.

In the following series of numbers, how many times have the figures 9, 1 and 8appeared together 1 being in the middle and 9 and 8 being on either side of 1?2 1 9 8 1 9 8 3 7 1 9 7 8 1 2 9 1 9 8 1 8 2 1 21. 1 2. 6 3. 3 4. 4

37. How many vowels are there which are followed by prime number and precededby even number?5 i 6 o a t 9 7 e 5 u 4 t n 3 a 6 e 7 i 11 e a 31. 1 2. 2 3. 5 4. None

38. How many consonants are there which are followed by even number andpreceded by vowels?a 1 b 2 c 3 d 4 e f 8 g h i 7 8 9 j k 3 l m 5 k 0 7 a b 1 o n 31. 1 2. 2 3. 7 4. None

39. How many prime numbers are there which are followed by vowels but notpreceded by consonants?5 i 6 o a t 9 7 e 5 u 4 t n 3 a 6 e 7 i 11 e a 3

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1. 1 2. 2 3. 5 4. None

40.

How many composite numbers are there which are not followed by vowels butpreceded by consonants?a 1 b 2 c 3 d 4 e 5 f 6 g 7 h 8 i 9 j 0 k 1 l 2 m 3 n 4 o 5 p 6 q 7 r 8 s 91. 1 2. 2 3. 3 4. 4

“Intellectuals solve problems, geniuses prevent them.”

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1. How many 1‟s are there in the following sequence which are immediatelypreceded by 9 but not immediately followed by 7?7 1 0 1 1 7 1 8 9 1 7 1 2 1 3 1 4 5 7 1 3 9 1 7

1. one 2. two 3. three 4. four

2. How many 9‟s are there in the following sequence which are preceded by 6 butnot immediately followed by 3?6 9 3 7 6 9 6 3 9 6 4 6 9 4 7 6 6 6 9 3 6 7 6 9 2 9 61. 2 2. 3 3. 4 4. 5

3.

Nikhil ranks 15 in the class of 35. What is his rank from the last?1. 20 2. 22 3. 19 4. 21

4. How many 7‟s are there in the following sequence which are immediately

preceded by 5 but not immediately followed by 3?3 7 5 7 4 5 7 3 9 7 5 8 7 7 8 9 7 1 5 7 6 5 7 4 3 7 5 7 3 81. One 2. Two 3. Three 4. Four

5.

Hamilton is 5 months younger to Simon while Bob is 3 months younger toAuden. When Shetty was born Bob was 2 months old. Auden is 5 years old andHamilton is 6 years old. Who among the following is the oldest?1. Simon 2. Bob 3. Auden 4. Shetty

6. How many odd numbers are there in the following series, which are followed by1 and preceded by 2?1 3 2 0 0 4 5 6 8 8 9 1 0 2 3 1 5 0 2 1 3 5 1 6 01. 1 2. 2 3. 4 4. 6

7. If the position of the first and the sixth digits of the sequence of numbers5 3 1 7 6 8 9 2 0 4 are interchanged, the second and seventh and so on,which number would be sixth from the right end?1. 3 2. 1 3. 6 4. 4

8.

How many 7‟s immediately preceded by 6 but not immediately followed by 4 arethere in the following series?7 4 2 7 5 4 3 6 7 5 3 5 7 8 4 3 7 6 7 2 4 1 6 7 4 31. 1 2. 2 3. 4 4. 6

9.

In a row of boys, if Arun who is 12th from left and Ajay 8th from right interchange their positions. Ajay becomes 14th from the right end. How many boysare there in that row?1. 25 2. 24 3. 26 4. 21

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10.

How many 8‟s are in the following number seq uence which are not preceded by7 but immediately followed by 4?8 7 4 7 8 4 7 7 8 4 7 7 8 8 4 7 4 8 4 7 8 8 8 4 4 7 8 4 4 4 8 8 4 7 8 7 41. One 2. Two 3. Three 4. Four

11. How many 7‟s are there in the following sequence which are immediately

preceded by 1‟s and not immediately followed by 3‟ s?9 8 5 1 7 3 1 7 6 5 6 3 7 7 1 4 6 1 7 5 9 3 1 7 4 4 6 1 7 3 3 7 8 1 7 21. 1 2. 2 3. 3 4. 4

12. How many 2‟s are there in the following number sequence which areimmediately preceded by 3 but not immediately followed by 0?3 3 2 2 3 2 2 3 0 3 2 0 2 3 3 2 2 3 0 3 2 0 3 3 2 2 0 3 2 0 3 2 31. One 2. Five 3. Three 4. Four

13. Ravi ranked 13th from the top and 26th from the bottom among those whopassed in the annual examination in a class. If 6 students have failed in the

examination, what was the total number of students in the class?1. 45 2. 44 3. 47 4. 46

14. In the following series of numbers, find out how many times 1, 3 and 7 haveappeared together, 7 being in the middle and 1 and 3 on either side of 7.2 9 7 3 1 7 3 7 7 1 3 3 1 7 3 8 5 7 1 3 7 7 1 7 3 9 0 61. 3 2. 4 3. 5 4. More than 5

15.

How many 5‟s preceded by 6 and not immediately followed by 8 are there in thefollowing series?5 8 2 5 6 8 3 6 5 5 3 5 5 8 8 3 5 6 5 2 8 0 6 5 8 3

1. 1 2. 2 3. 4 4. 6

16. How many 3‟s are there in the following number sequence which areimmediately preceded by 6 but not immediately followed by 7?2 3 7 4 3 2 6 3 7 4 6 3 8 9 6 3 5 1 8 3 7 2 4 2 8 6 3 91. One 2. Two 3. Three 4. Four

17. In the given series how many times it is that the sum of two consecutivenumbers is 8.1 8 3 7 4 7 1 9 4 2 6 4 8 3 71. 2 2. 4 3. 6 4. 7

18. In a row of girls Sunitha is 12th from the left and 9th from the right. How manygirls are there in the row?1. 21 2. 20 3. 22 4. 19

19. How many 6‟s are there in the following sequence which are immediatelypreceded by 8 but not immediately followed by 4? 4, 7, 5, 6, 9, 1, 6, 8, 4, 7, 3,4, 8, 6, 3, 9, 6, 7, 8, 6, 4, 7, 3, 5, 8, 6, 1

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1. 4 2. 5 3. 6 4. None

29.

In a row of boys, Sumit is fifteenth from the left and seventh from the right.How many boys are there in the row?1. 21 2. 27 3. 29 4. 31

30.

In a certain series given below count each 5 which is not immediately precededby 3 but immediately followed by 7. How many such 5‟s are there? 1 5 7 3 5 7 4 7 3 7 2 5 6 5 8 5 7 4 5 6 5 5 7 1 5 7 7 5 51. 1 2. 2 3. 3 4. 4

31.

Ajay‟s position in a row is thirteenth from the front side and sixth from the backside. How many persons are standing in that row?1. 17 2. 18 3. 19 4. 20

32. How many 7‟s immediately preceded by 6 but not immediately followed by 4 arethere in the following series?

7 4 2 7 6 4 3 6 7 5 3 5 7 8 4 3 7 6 7 2 4 0 6 7 4 31. 1 2. 2 3. 4 4. 6

33. How many 2‟s are there in the following series, which are immediately precededby 9 but not followed by 7?7 5 2 4 2 9 2 7 2 9 2 5 4 2 5 7 2 9 1 2 71. 1 2. 2 3. 34 4. 0

34.

Some students are sitting in a single row. John is sitting 14th from the left and Joseph is 7th from the right. What is the total number of the students?1. 21 2. 20 3. 19 4. Can‟t be determined

35. What will be the middle digit of the middle number after the following numbersare arranged in descending order? 268, 197, 678, 129, 2591. 6 2. 9 3. 2 4. 5

36. How many 7‟s are there in the following sequence which are preceded by 4 butnot immediately followed by 2? 4 7 2 7 2 3 5 9 7 4 7 5 2 4 7 9 4 7 8 4 7 11. 1 2. 2 3. 3 4. 4

37. How many 7‟s are there in the following series, which are immediately precededby 5 and followed by 4?

1 5 7 3 4 7 5 7 4 8 5 7 4 3 2 1 7 7 1 5 7 9 1 7 41. 2 2. 4 3. 3 4. None of these

38. Vijay ranks seventh from the top and 28th from the bottom in a class. Howmany students are there in the class?1. 34 2. 35 3. 36 4. 37

39. How many 8‟s are there in the following sequence which are immediatelypreceded by 6 but not immediately followed by 5?

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6 8 5 7 8 5 4 3 6 8 1 9 8 5 4 6 8 2 9 6 8 1 3 6 8 5 3 61. One 2. Two 3. Three 4. Four

40. Rasheed ranked 17th from the top and 36th from the bottom among those whohave passed in the annual examination in a class. If six students have failed inthe annual examination, what was the total number of students in that class?

1. 59 2. 60 3. 61 4. 58

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Letter Ranking

1. How many b‟s between „a‟ and „e‟ are there in the following series?

a b e a e a e a b e a b e a b e a b e b b b e a b e e a b e1. 5 2. 6 3. 7 4. 8

2.

How many 0‟s are followed by a vowel in the following? a e i o u a e i o u a e i o u o a o a o i a e a b c1. 1 2. 3 3. 4 4. 6

3. Find the total number of c s followed by a vowel in the following.a b c a b c a c a c b c b c c c d e e c e a c e a c e a c e1. 4 2. 6 3. 7 4. 8

4. How many n s are there before d in the following.n d n d n d n d n n d d d n d c d n d n d n d n d c d

1. 3 2. 4 3. 5 4. 10

5.

How many p s are there which has „f‟ before in the following? f p f p p c f f f p f p f p f p p f f p p p f f f p f p f p f p p f f p f1. 12 2. 7 3. 6 4. 8

6.

How many c s are there between two consonants in the following.a b c d c d c e c e c f c o c i c j c k c c k1. 3 2. 4 3. 5 4. 6

Directions (Questions 7-11): Study the following letter-number sequence and

answer the questions below.

9 J 7 K Q N P 8 H I X Y 5 C 6 D 4 G 3 F E 2 A B 1

7.

Which of the following element will be the fifth to the left of nineteenth elementfrom your right?1. K 2. 7 3. Y 4. J

8.

Four of the following five are similar on basis of their position in the abovesequence and hence form a group. Which one does not belong to that group?1. 97KP 2. QP8X 3. 7QNH 4. N8HY

9. If every second element is dropped in the above sequence starting from Q (Q isdropped first), which of the following will be eighth element to the left of the 12th element from your left?1. 7 2. 8 3. K 4. N

10.

If every sixth element from left starting from N is replaced by Archana, Rekha,Sima and Neetu (N is replaced by Archana), what will be the position of Rekhafrom your right?

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1. 12th 2. 13th 3. 14th 4. 15th

11.

If the first twelve elements in the above sequence is written in reverse order,then which element will be fifth to the left of twentienth element from your left?1. 8 2. P 3. Q 4. N

12.

In the following colour sequence, R stands for Red, Y for Yellow, G for green, Bfor Blue and W for white. If the sequence is continued, which colour will comenext?B B R B R W B R W G B R W G Y B R B R W B R W1. Yellow 2. White 3. Blue 4. Green

13. In the following series, count those „N‟ which are followed by „X‟ but „X‟ is notfollowed by „T‟. How many such N‟s are there?N X N T Q M N T M X N X C N Q M N N X Q N X T X N A M X N X M1. 2 2. 4 3. 5 4. 7

14.

Five newly born babies were weighed by the doctor. In her resort she pointedout that the child A is lighter than the child B. The child C is lighter than thechild D. The child B is lighter than the child D but heavier than the child E.Which child is the heaviest?1. E 2. D 3. C 4. B

15. How many A‟s are there in the following sequence which are immediatelyfollowed by B as well as immediately preceded by Z?A M B Z A N A A B Z A B A Z B A P Z A B A Z A B1. Three 2. Nil 3. One 4. Two

16.

The result of a class was declared. The boy X stood 5th in the class. The girl Ywas 8th from the last. The position of the boy Z was 6th after X and in the middleof X and Y. Work out total number of the students in the class?1. 23 2. 29 3. 25 4. 26

17. In the following sequence count each N which is immediately followed by X butX is not immediately followed by T. How many such N‟s are there?N X N T Q M N X T M X N X C N Q M N N X Q N X T X N A M N X M1. 2 2. 4 3. 5 4. 7

Directions (Questions 18-37): Each of the following questions is based on the

following alphabet series:A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

18. Which of the following letters will be sixth to the right of the eighteenth letterfrom the left after reversing the second half of the English Alphabet.1. X 2. P 3. O 4. N

19.

If the letters of the English Alphabet interchange positions, so that A takes theplace of Z and Z takes the place of A, B takes place of Y and Y takes the place of

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B and so on, what will be the 4th letter from the right?1. D 2. N 3. O 4. L

20. If the English Alphabet is arranged in reverse order, which letter will be theeighth letter to the left of the seventh letter counting from the right end?1. P 2. O 3. N 4. Q

21.

Which letter should be sixth to the right of the sixteenth letter from the left ifthe second half of the English Alphabet is reversed?1. R 2. V 3. J 4. U

22.

Which letter will be the sixth to the right of the eleventh letter from the rightend of the English Alphabet?1. K 2. V 3. J 4. U

23. Which letter will be the seventh to the left of the fourteenth letter from the rightend of the English Alphabet?

1. E 2. F 3. T 4. S

24. In the English Alphabet which letter is seventh to the right of fifteenth letterfrom the right end?1. S 2. T 3. R 4. H

25.

Which letter will be the tenth to the left of the eighteenth letter from the leftend, of the English Alphabet?1. H 2. Y 3. A 4. There is no such letter

26.

Which letter will be midway between the eighteenth letter from the left end and

tenth letter from the right end of the English Alphabet?1. Q 2. R 3. K 4. No letter

27. If the English Alphabets were written in the reverse order, which will be thesixth letter to the left of the tenth letter from the right?1. W 2. P 3. D 4. K

28. If the English Alphabets were written in the reverse order, which would be thefourth letter to the right of the fifteenth letter from the left?1. G 2. H 3. I 4. S

29.

Which letter will be the tenth to the right of the eighteenth letter from the rightend of the English Alphabets?1. S 2. T 3. P 4. There is no such letter

30.

What will be the seventh letter to the right of the eleventh letter from the right ifthe letters of the English Alphabets were arranged in reverse order?1. D 2. W 3. E 4. V

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31.

Which letter will be the eighth to the right of the seventeenth letter from theright end of the English Alphabets?1. R 2. B 3. K 4. Q

32. What will be the third letter to the left of the fourth letter starting from yourright after every third letter is cancelled?

1. Q 2. J 3. R 4. V

33. Which letter will be midway between the fourteenth letter from the left andnineteenth letter from the right end of the English Alphabet?1. I 2. K 3. M 4. G

34. Which letter is mid-way between the ninth letter from the right and eighth letterfrom the left in the English Alphabets?1. N 2. O 3. L 4. M

35.

If the English Alphabet is written in the reverse order which will be the letter to

the immediate left of M?1. N 2. L 3. O 4. K

36. Which letter is mid-way between eighth letter from the right and the seventhletter from the left in the English Alphabet?1. G 2. L 3. M 4. N

37. Which is the first letter to the right of the letter which is immediately before theninth letter from the left in the English Alphabet?1. I 2. H 3. G 4. J

38.

In the following series, how many times have the alphabets A, M, Z comeconsecutively where in the M is the middle with A and Z being on any of thesides of M?Z N A L M Z A B M Y Z M A Y M A Z A M B N L M A Z Y1. 6 2. 4 3. 1 4. 2

39.

In the following series, count those „N‟ which are followed by X but X is notfollowed by T. How many such N‟s are there?N X N T Q M N T M X N X C N Q M N N X Q N X T X N A M X N X M1. 2 2. 4 3. 5 4. 7

40.

How many Z are there in the following series which are immediately precededby A but not immediately followed by T?A Z T U V T Z A S T A Z O V T U Z A T A Z S T V1. One 2. Two 3. Three 4. Four

41. How many B‟s are there in the following series which are immediately followedby E?C E B E C D P B E B F E B E D F E B C E F C A E

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1. Three 2. One 3. Two 4. None

Directions Study the following letter-number arrangement and answer thequestions given below. A 4 B D 2 C N O T 6 9 V L 3 Q P K 7 J H 5 8 M S E

42.

If the above letter-number arrangement is written in reverse order, which

letter/number will eighth to the right of L?1. R 2. 3 3. 2 4. None

43.

Which of the following will come in place of question mark (?) in the followingsequence with reference to the above arrangement? BCN DNO ___?___CT61. 2OT 2. 2TO 3. TO2 4. None

44.

If it is possible to make a meaningful word with the third, the eighth, the tenthand the twenty sixth letters from your left in above given series, which of thefollowing will be the first letter of that word. If no such word can be made, give

X as the answer. If more than one such word can be made give M as theanswer.1. N 2. B 3. T 4. X

45.

Which of the following be third to the right of the fifteenth letter/number from you right?1. P 2. Q 3. L 4. 3

46.

If every alternate letter/number is dropped I the above arrangement, beginningwith dropped A as first letter, which of the following will be the letter 6th fromleft?

1. L 2. 3 3. V 4. Q

Directions Study the following letter-number sequence and answer the questionsgiven below them. P K 4 M D A 8 S T 3 E J R 6 Q N L H B 7 U G C Z F

47. Which letter/number is the seventh to the right of the fifth letter/number from your left?1. 6 2. J 3. R 4. E

48.

If every fourth letter/number is dropped starting from of the above letter-number sequence, which of the following letter/number will be the eighth from

your right?1. Q 2. 2 3. L 4. E

49. Which letter/number will be midway between the sixth letter/number from your right and twelth letter/number from our left?1. Q 2. 6 3. N 4. J

50.

Which letter/number will be seventh to the left of the sixteenth letter/numberfrom your left?

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1. C 2. T 3. S 4. 2

Directions: Study the following sequence (letters, numbers and symbols) andanswer the questions given below them:N O P 4 + * E M K † 5 $ S L A Z • = @ H T B J 6 F Y

51.

Which letter/number/symbol will be midway between the fifteenth sign from your left and eighteenth letter from your right?1. 5 2. S 3. L 4. $

52.

Which letter/number/symbol is the fifth to the right of the sixteenth sign from your left?1. T 2. 5 3. B 4. Z

53.

Which of the following will be the ninth sign to the right of twenty-fourthposition from your right?1. $ 2. A 3. S 4. L

Directions Answer the following questions based on the series given below.A b C d E 1 f G h i j 2 k l M n O 3 p Q r S t 4 u v W x y 5 z

54.

What is the middle letter/digit in the series given above?1. 3 2. O 3. n 4. Q

55. What would be the answer to the above question, if even numbers were removedfrom the series?1. Same as in above question 2. One letter to the left of the answer of 13. One letter to the right of the answer of 1 4. Can‟t be uniquely

determined

56.

If the second half of the series (excluding n) above was written in reverse order,what would be the 8th letter/digit to the right of the 16th letter from the right?1. U 2. v 3. 4 4. x

57.

If no reversing was done in above question, what would be the answer of abovequestion?1. Same as in above question 2. One letter to the left of the answer ofquestion 33. One letter to the right of the answer of question 3

4. Can‟t be uniquely determined

Directions Study the following letter-number sequence and answer the questiongiven below.A 2 C D 5 F G H 9 K M P 1 3 L E B S U N 8 O I R V T X Z

58. If every alternate starting from your left hand side replaces digits of a clock with1 replaced A, which letter/number will replace 6 of the clock?

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1. F 2. K 3. M 4. I

59.

If the first half of the letter number sequence is written in the reverse order,which letter/number will be fourth to left of eighteenth letter/number from yourright?1. H 2. G 3. E 4. F

60.

If every alternate position is dropped starting from G in the above letter-numbersequence, then how many letters-numbers will be left?1. 18 2. 16 3. 15 4. 17

61.

Which letter will be the sixth to the left of seventh letter from the right end?1. B 2. L 3. E 4. T

Directions Study the following letter-number series and answer the questions givenbelow: H P 9 G A M T 4 B K R 7 N D Y J 3 S C E Q 8

62.

Which letter-number is seventh to right of ninth letter number from your left?1. 9 2. P 3. Y 4. J

63. If every fourth letter/number (starting from A) is dropped from the given lettersequence. Which of the following will be eighth letter/number from your right?1. 4 2. K 3. 7 4. R

64. If the first half of the above sequence is written in the reverse order which of thefollowing will be the ninth letter/number to the right of sixteenth letter/numberfrom your right?1. Q 2. 3 3. Y 4. J

65. If it is possible to make a meaningful word with the first, the second, the fourth,the fifth and the eleventh letters of the above sequence, write the middle letterof that word. If it is not possible to make such a word write M as your answer.1. A 2. H 3. P 4. G

66.

If the alternate letters in the following alphabet starting from A are changed intosmall letter leaving the rest in capitals. Which of the following represents thesecond month after June?A B C D E F G H I J K L M N O P Q R S T U V W X Y Z1. AugusT 2. AUgUsT 3. augusT 4. August

67. If by arranging the letters of the word UTLSO, the name of a flower is formed.Which of the following pairs represents the first and the last letters of the wordso formed?1. TO 2. OS 3. LS 4. TS

68. How many pairs of letters are there in the word PEPURCUSSION which have asmany letters between them in the word as in the alphabet and that too in thesame order?

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1. One 2. Two 3. Three 4. Nil

Directions Study the following letter series and answer the questions given belowthem.A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

69.

Which letter is sixth to the right of fifteenth letter from your left?1. L 2. J 3. K 4. U

70.

If every third letter is dropped starting from C from the given alphabet which ofthe following will be the third letter to the left of ninth letter from your left?1. H 2. Q 3. I 4. U

71. Which letter will be midway between the seventh letter from your left and twelthletter from your right?1. M 2. J 3. K 4. L

Directions Study the following letter-number sequence and answer the questionsgiven below:C Z 4 S R K N H O P X A 9 M J 5 Q T E 6 L U B 3 D V

72.

If every third letter/number is dropped in the above sequence starting from S (Sis dropped first), which of the following will be 5th letter/number to the left of15th position from your left?1. 9 2. M 3. J 4. 5

73. If every 4th position starting from N is replaced by Lata, Nita, Rita, Mili andPriya (N becomes Lata), what will be the position of Priya in the above sequence

counting from your right?1. Third 2. fifth 3. seventh 4. fourth

74. How many p‟s are there in the following letter sequence which are immediatelypreceded by r but not immediately followed by q.q p r p n p r q r p t r p u q r p q r t s p r s r p q s t q r p q1. 9 2. 3 3. 2 4. 5

75.

How many u‟s are there which are immediately followed by v and alsoimmediately preceded by w?u w u v v u w u v u w u v u w u w u v v u w v u u v w u v u w v u v u w

u v u v v u w v u1. 9 2. 7 3. 6 4. 5

76. How many x‟s are there not immediately preceded by y but immediately followedby z in the following series?x y x z x z z y x y y x x z x y x z x y x y z x x z y z z x z y x z1. 9 2. 7 3. 4 4. 5

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77.

How many b‟s are there not immediately preceded by c and not immediatelyfollowed by a in the following series?a b c a c a c b b c a c b b b b c c a a c a b c b a c b a c a b c a b c b a cc a a c b b c b a c b a1. 9 2. 12 3. 8 4. 6

78.

How many m‟s are there immediately preceded by 2 but not immediatelyfollowed by 3 in the following series?m 2 m 2 3 3 2 m 3 m 2 m 2 3 m 2 m 3 3 m 2 2 m 3 m 2 2 m 3 m 3 m m2 m 3 2 m 3 2 m 3 m 2 m 2 m m 2 m 3 2 m 31. 2 2. 3 3. 4 4. 1

79. How many vowels are there which are followed by vowels and preceded byconsonants?o e m u v m n o i k l o o u u v a e m o o e w i o e i e o u o u b i a e i d a i a v vo i1. 9 2. 8 3. 7 4. 6

80.

45D____9____IJ____7F___1. E, 10, 8, G 2. E, 10, 6, G 3. E, 10, 5, G 4. F, 10, 6, G

Odd Man Out (Numbers)

Directions: In each of the following numbers series, one term is wrong which isgiven in one of the four alternatives provided after each series. Find this term.

1. 3, 5, 10, 12, 24, 26, 48, 541. 12 2. 24 3. 26 4. 48

2. 1. 3, 4, 3, 7, 8, 13, 12, 251. 8 2. 13 3. 12 4. 25

3. 2, 5, 11, 20, 30, 47, 651. 20 2. 30 3. 47 4. 65

4.

1, 5, 2, 18, 13, 38, 421. 18 2. 13 3. 38 4. 42

5. 7, 8, 18, 13, 38, 421. 18 2. 13 3. 38 4. 42

6. 1. 7, 8, 18, 57, 228, 1165, 69961. 8 2. 18 3. 57 4. 228

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7. 1. 3, 7, 15, 27, 63, 127, 2551. 7 2. 15 3. 27 4. 63

8. 1. 19, 26, 33, 46, 59, 74, 911. 26 2. 33 3. 46 4. 59

9. 1. 2880, 480, 92, 24, 8, 4, 41. 2880 2. 480 3. 92 4. 24

10. 1. 445, 221, 109, 46, 25, 11, 41. 221 2. 109 3. 46 4. 25

11. 2, 3, 13, 37, 86, 167, 2881. 3 2. 13 3. 37 4. 86

12. 2, 5, 12, 27, 58, 120, 2481. 5 2. 12 3. 27 4. 120

13. 232, 120, 64, 36, 22, 16, 11.51. 120 2. 64 3. 36 4. 16

14. 568, 276, 136, 64, 28, 10, 11. 276 2. 136 3. 64 4. 28

15. 875, 2.75, 8, 18, 40, 85, 1761. 2.75 2. 8 3. 18 4. 40

16. 3, 5, 12, 38, 154, 914, 4634

1. 5 2. 12 3. 38 4. 914

17. 696, 340, 168, 80, 36, 14, 31. 340 2. 168 3. 80 4. 36

18. 634, 314, 164, 74, 34, 14, 41. 314 2. 164 3. 74 4. 34

19. 4, 5, 14, 39, 103, 169, 2901. 5 2. 14 3. 39 4. 103

20. 2, 3, 6, 12, 45, 157.5, 630

1. 3 2. 6 3. 12 4. 45

21. 5, 27, 61, 122, 213, 340, 5091. 27 2. 61 3. 216 3. 340

22. 3, 10, 19, 31, 43, 58, 751. 10 2. 19 3. 31 4. 43

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23. 720, 120, 24, 8, 2, 1, 11. 1 2. 2 3. 24 4. 8

24. 1, 4, 7, 11, 16, 22, 291. 1 2. 4 3. 22 4. 11

25. 58, 57, 54, 50, 42, 33, 221. 57 2. 54 3. 50 4. 42

26. 1, 6, 11, 22, 33, 46, 611. 6 2. 1 3. 46 4. 11

27. 3, 18, 38, 78, 123, 178, 2431. 123 2. 178 3. 3 4. 38

28. 89, 78, 86, 80, 85, 82, 831. 78 2. 86 3. 80 4. 85

29. 3, 10, 29, 60, 127, 18, 3451. 10 2. 29 3. 60 4. 127

30. 1. 17, 19, 23, 29, 33, 37, 411. 17 2. 19 3. 23 4. 33

31. 27, 26, 28, 25, 29, 24, 311. 24 2. 29 3. 31 4. 28

32. 2, 8, 20, 44, 92, 184, 380

1. 380 2. 184 3. 92 4. 44

33. 25, 26, 24, 29, 27, 36, 331. 24 2. 25 3. 29 4. 33

34. 1160, 584, 296, 148, 80, 44, 261. 80 2. 26 3. 44 4. 148

35. 60, 48, 38, 28, 24, 20, 181. 18 2. 20 3. 24 4. 28

36. 144, 132, 125, 113, 105, 93, 84, 72, 61, 50, 39

1. 93 2. 84 3. 50 4. 61

37. 1, 2, 5, 10, 21, 42, 85, 1711. 21 2. 42 3. 85 4. 171

38. 1. 3, 9, 18, 54, 108, 314, 648, 19441. 314 2. 108 3. 54 4. 18

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39. 3, 9, 18, 54, 108, 314, 648, 19441. 314 2. 108 3. 54 4. 18

40. 1, 3, 10, 29, 74, 172, 3821. 10 2. 29 3. 74 4. 172

41. 3, 8, 15, 24, 34, 48, 631. 15 2. 24 3. 34 4. 48

42. 11, 12, 14, 17, 20, 26, 321. 32 2. 26 3. 20 4. 17

43. 2200, 2100, 2000, 1600, 1200, 700, 1001. 2000 2. 2100 3. 100 4. 700

44. 2, 9, 28, 65, 126, 216, 3441. 2 2. 28 3. 65 4. 216

45. 5, 15, 30, 135, 405, 1215, 36451. 3645 2. 1215 3. 405 4. 30

46. 112, 114, 120, 124, 132, 142, 1541. 114 2. 120 3. 124 4. 132

47. 5, 11, 23, 47, 96, 191, 3831. 11 2. 23 3. 47 4. 96

48. 3, 4, 5, 9, 22.5, 67.5, 270, 945

1. 4.5 2. 9 3. 22.5 4. 270

49. 380, 188, 92, 48, 20, 8, 21. 188 2. 92 3. 48 4. 20

50. 7, 9, 17, 42, 91, 172, 2931. 9 2. 17 3. 42 4. 91

Directions : In each of the following numbers series, one term is wrong. Find thisterm.

51. 1. 242 2. 483 3. 362 4. 482

52. 1. 192 2. 141 3. 291 4. 451

53. 1. 1234 2. 1243 3. 4567 4. 3456

54. 1. 972 2. 281 3. 527 4. 549

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55. 1. 8 2. 4 3. 16 4. 17

56. 1. 9 2. 6 3. 15 4. 19

57. 1. 52163 2. 25631 3. 34424 4. 33442

58. 1. 315 2. 207 3. 711 4. 325

59. 1. 3, 7, 5, 11 2. 11, 17, 19, 23 3. 3, 29, 7, 5 4. 2, 4, 3, 5, 7

60. 1. 14 2. 7 3. 28 4. 36

61. 1. 63852 2. 52638 3. 85361 4. 28751

62. 1. 3795 2. 9359 3. 5937 4. 3745

63. 1. 11, 3, 3, 17 2. 14, 5, 3, 47 3. 71, 7, 3, 17 4. 37, 14, 19, 7

64. 1. 936 2. 945 3. 864 4. 954

65. 1. 35, 24 2. 79, 68 3. 57, 46 4. 35, 79

66. 1. 67, 19 2. 71, 11 3. 41, 19 4. 89, 41

67. 1. 5, 13, 17 2. 29, 1, 5 3. 17, 17, 1 4. 15, 5, 5

68. 1. 65, 83 2. 83, 47 3. 34, 79 4. 65, 23

69. 1. 3535 2. 7595 3. 9575 4. 7395

70. 1. 49 2. 140 3. 98 4. 97

71. 1. 98765 2. 98756 3. 987654 4. 9876543

72. 1. 37037x3 2. 37037x6 3. 37037x9 4. 37037x4

73. 1. 121 2. 12321 3. 123321 4. 12345321

74. 1. 876321 2. 387315 3. 349416 4. 372164

75. 1. 6 2. 8 3. 11 4. 15

76. 1. 11 2. 13 3. 15 4. 17

77. 1. 53 2. 63 3. 72 4. 81

78. 1. 6 2. 7 3. 9 4. 12

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79. 1. 27 2. 64 3. 125 4. 343

80. 1. 4 2. 9 3. 16 4. 36

81. 1. 385 2. 572 3. 671 4. 427

82. 1. 121 2. 132 3. 143 4. 152

83. 1. 6 2. 18 3. 12 4. 7

84. 1. 18 2. 6 2. 12 4. 9

85. 1. 7 2. 17 3. 37 4. 9

86. 1. 24 2. 12 3. 36 4. 27

87. 1. 14 2. 28 3. 21 4. 41

88. 1. 4 2. 16 3. 25 4. 55

89. 1. 9 2. 25 3. 36 4. 78

90. 1. 115 2. 98 3. 78 4. 89

91. 1. 189 2. 199 3. 178 4. 235

92. 1. 63 2. 45 3. 81 4. 38

93. 1. 385 2. 572 3. 671 4. 427

94. 1. 35 2. 49 3. 50 4. 63

95. 1. 21 2. 39 3. 51 4. 83

96. 1. 27 2. 125 3. 729 4. 1321

97. 1. 6 2. 12 3. 18 4. 7

98. 1. 15 2. 27 3. 24 4. 28

99. 1. 51 2. 144 3. 64 4. 121

100. 1. 10 2. 26 3. 24 4. 21

101. 1. 43 2. 53 3. 63 4. 73

102. 1. 324 2. 244 3. 136 4. 352

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103. 1. 515 2. 875 3. 380 4. 876

104. 1. 699 2. 789 3. 682 4. 798

105. 1. 688 2. 686 3. 376 4. 867

106. 1. 369 2. 879 3. 789 4. 785

107. 1. 6 2. 18 3. 12 4. 7

108. 1. 579 2. 885 3. 696 4. 398

109. 1. 986 2. 689 3. 995 4. 963

110. 1. 821 2. 731 3. 533 4. 862

111. 1. 724 2. 364 3. 643 4. 736

112. 1. 756 2. 686 3. 843 4. 884

113. 1. 21 2. 69 3. 81 4. 83

114. 1. 37 2. 49 3. 132 4. 154

115. 1. 10 2. 11 3. 15 4. 16

116. 1. 11 2. 13 3. 15 4. 17

117. 1. 372164 2. 376821 3. 318951 4. 319446

118. 1. 7851 2. 6432 3. 5789 4. 1325

119. 1. 1532 2. 8749 3. 4268 4. 5846

120. 1. 7487 2. 5963 3. 8218 4. 6596

121. 1. 263 2. 111 3. 242 4. 383

122. 1. 325 2. 236 3. 178 4. 639

123. 1. 11 2. 13 3. 17 4. 39

124. 1. 7 2. 11 3. 13 4. 14

125. 1. 5 2. 17 3. 23 4. 9

126. 1. 7 2. 5 3. 1 4. 16

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127. 1. 27 2. 19 3. 11 4. 8

128. 1. 539 2. 638 3. 731 4. 751

129. 1. 221 2. 351 3. 691 4. 784

130. 1. 13901 2. 87901 3. 90980 4. 89901

131. 1. 781 2. 258 3. 608 4. 341

132. 1. 5760 2. 6750 3. 7650 4. 8089

133. 1. 2 2. 16 3. 56 4. 128

134. 1. 2468 2. 2648 3. 4826 4. 6482

135. 1. 392 2. 326 3. 414 4. 248

136. 1. 2345 2. 3456 3. 5467 4. 5678

137. 1. 28 2. 65 3. 126 4. 215

138. 1. 150 2. 175 3. 200 4. 250

139. 1. 232 2. 431 3. 612 4. 813

140. 1. 140 2. 240 3. 360 4. 480

141. 1. 49 2. 63 3. 77 4. 81

142. 1. 144 2. 168 2. 196 4. 256

143. 1. 124 2. 235 3. 789 4. 510

144. 1. 369 2. 468 3. 942 4. 279

145. 1. 134 2. 256 3. 679 4. 532

146. 1. 976 2. 843 3. 732 4. 698

147. 1. 8743 2. 7521 3. 8310 4. 1897

148. 1. 2 2. 3 3. 5 4. 7

149. 1. 3 2. 5 3. 7 4. None

150. 1. 11 2. 13 3. 19 4. None

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151. 1. 11 2. 21 3. 31 4. 41

152. 1. 11 2. 31 3. 41 4. None

153. 1. 12 2. 25 3. 37 4. 49

154. 1. 8 2. 64 3. 28 4. 125

155. 1. 751 2. 734 3. 981 4. 853

156. 1. 21 2. 36 3. 49 4. 56

157. 1. 48 2. 12 3. 36 4. 59

158. 1. 8314 2. 2709 3. 1315 4. 2518

159. 1. 381 2. 552 3. 729 4. 903

160. 1. 7 2. 15 3. 31 4. 57

161. 1. 119 2. 136 3. 147 4. 153

162. 1. 9611 2. 7324 3. 2690 4. 1754

163. 1. 99 2. 89 3. 79 4. 59

164. 1. 71 2. 73 3. 79 4. None

165. 1. 73 2. 83 3. 93 4. 103

166. 1. 121 2. 169 3. 225 4. 289

167. 1. 121 2. 529 3. 361 4. None

168. 1. 576 2. 676 3. 900 4. None

169. 1. 729 2. 676 3. 343 4. 216

170. 1. 729 2. 676 3. 625 4. 576

171. 1. 30 2. 56 3. 132 4. 182

172. 1. 30 2. 130 3. 350 4. 1342

173. 1. 21-49 2. 24-64 3. 25-54 4. 81-36

174. 1. 3-4 2. 16-26 3. 26-24 4. 27-22

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175. 1. 48-134 2. 40-110 3. 18-48 4. 30-80

176. 1. 3-4 2. 4-7 3. 5-12 4. 20-21

177. 1. 7-18 2. 9-26 3. 11-36 4. 13-42

178. 1. 22, 4, 5 2. 34, 4, 8 3. 37, 4, 9 4. 54, 4, 13

179. 1. 6-15 2. 21-43 3. 25-51 4. 29-59

180. 1. 56-8 2. 121-17 3. 147-21 4. 168-24

181. 1. 24-21 2. 46-32 3. 62-23 4. 84-24

182. 1. 81-63 2. 24-48 3. 21-15 4. 13-39

183. 1. 252 2. 420 3. 600 4. 702

184. 1. 21 2. 63 3. 39 4. 83

185. 1. 385 2. 427 3. 671 4. 473

186. 1. 47, 59 2. 42, 29 3. 57, 69 4. 73, 61

187. 1. 7 2. 15 3. 31 4. 57

188. 1. 12 2. 16 3. 56 4. 128

189. 1. 3-5 2. 13-17 3. 19-25 4. 23-29

190. 1. 8-27 2. 125-126 3. 343-512 4. 1009-1331

191. 1. 13-156 2. 12-144 3. 15-180 4. 16-176

192. 1. 49-7 2. 36-9 3. 64-8 4. 121-11

193. 1. 13-21 2. 19-27 3. 15-23 4. 16-24

194. 1. 10-20 2. 30-40 3. 40-50 4. 50-60

195. 1. 140-45 2. 110-35 3. 100-30 4. 80-25

196. 1. 13-31 2. 45-54 3. 16-61 4. 71-88

197. 1. 21-6 2. 28-42 3. 42-12 4. 84-24

198. 1. 45-27 2. 30-18 3. 20-10 4. 15-12

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199. 1. 72-45 2. 51-24 3. 46-20 4. 32-13

200. 1. 8-27 2. 125-216 3. 343-512 4. 1009-1331

201. 1. 15-46 2. 12-37 3. 9-28 4. 8-33

202. 1. 9-3 2. 1/2-1/8 3. 1/3-1/12 4. 24/6

203. 1. 32-13 2. 46-20 3. 51-24 4. 72-45

204. 1. 3-11 2. 8-16 3. 5-13 4. 14-24

205. 1. 28-4 2. 56-8 3. 35-5 4. 63-7

206. 1. 2-8 2. 3-27 3. 4-32 4. 5-125

207. 1. 56-8 2. 121-17 3. 147-21 4. 168-24

208. 1. 49-7 2. 36-9 3. 64-8 4. 121-11

209. 1. 8-20 2. 18-45 3. 16-40 4. 14-28

210. 1. 45 2. 126 3. 109 4. 207

211. 1. 324 2. 523 3. 442 4. 343

212. 1. 6589 2. 4323 3. 2341 4. 9673

213. 1. 80-25 2. 140-45 3. 120-35 4. 100-30

214. 1. 10-20 2. 30-40 3. 40-50 4. 50-40

215. 1. 7-3 2. 11-7 3. 13-9 4. 17-8

216. 1. 54-28 2. 34-17 3. 42-21 4. 22-11

217. 1. 49 2. 64 3. 48 4. 100

218. 1. 83-75 2. 58-50 3. 49-42 4. 25-17

219. 1. 70-80 2. 54-62 3. 28-32 4. 21-24

220. 1. 42-4 2. 36-6 3. 32-2 4. 15-5

221. 1. 71, 7, 3, 17 2. 67, 71, 3, 5 3. 41, 5, 3, 47 4. 37, 14, 19, 7

222. 1. 95-82 2. 69-56 3. 55-42 4. 48-34

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223. 1. 80-9 2. 64-8 3. 36-6 4. 49-7

224. 1. 3-5 2. 5-3 3. 6-2 4. 7-3

225. 12-144 2. 13-156 3. 15-180 4. 16-176

226. 1. 23-29 2. 19-25 3. 13-17 4. 3-5

227. 1. 73-61 2. 57-69 3. 42-29 4. 47-59

228. 1. 0 2. 3 3. 8 4. 17

229. 1. 441 2. 163 3. 153 4. 522

230. 1. 240 2. 132 3. 1956 4. 563

231. 1. 30 2. 6 3. 12 4. 18

232. 1. 403 2. 202 3. 431 4. 853

233. 1. 31 2. 41 3. 51 4. 61

234. 1. 11 2. 21 3. 26 4. 31

235. 1. 51 2. 64 2. 121 3. 144

236. 1. 8 2. 64 3. 27 4. 729

237. 1. 62 2. 27 3. 81 4. 54

238. 3, 5, 12, 39, 154, 772, 46341. 5 2. 12 3. 39 4. 154

239. 376, 188, 88, 40, 16, 4, -21. 188 2. 88 3. 40 4. 16

240. 444, 300, 200, 136, 87, 84, 801. 300 2. 200 3. 136 4. 87

241. 2, 3, 12, 37, 86, 166, 2881. 3 2. 12 3. 37 4. 66

242. 4, 9, 19, 43, 90, 185, 3761. 9 2. 19 3. 43 4. 90

243. 49, 48, 45, 42, 33, 24, 131. 48 2. 45 3. 42 4. 33

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244. 3, 3, 6, 16, 72, 360, 21601. 3 2. 6 3. 16 4. 72

245. 3, 7, 15, 27, 63, 127, 2551. 7 2. 15 3. 27 4. 63

246. 3, 4, 8, 16, 33, 58, 941. 4 2. 8 3. 16 4. 33

247. 1, 6, 16, 26, 76, 156, 3161. 6 2. 16 3. 26 4. 76

248. 1, 3, 7, 17, 31, 63, 1271. 1 2. 7 3. 63 4. 17

249. 48, 47, 44, 40, 32, 23, 121. 47 2. 32 3. 40 4. 44

250. 24, 23, 21, 18, 14, 9, 51. 5 2. 9 3. 14 4. 18

251. 12, 20, 32, 42, 56, 72, 901. 20 2. 32 3. 42 4. 56

252. 12, 19, 14, 21, 28, 23, 181. 14 2. 18 3. 21 4. 28

253. 49, 48, 45, 42, 33, 24, 13

1. 48 2. 45 3. 42 4. 33

254. 3, 3, 6, 16, 72, 360, 21601. 3 2. 6 3. 16 4. 72

255. 3, 7, 15, 27, 63, 127, 2551. 63 2. 7 3. 15 4. 27

256. 3, 4, 8, 16, 33, 58, 941. 4 2. 8 3. 16 4. 33

257. 6, 16, 26, 76, 156, 3161. 6 2. 16 3. 26 4. 76

258. 11, 15, 17, 19, 23, 251. 19 2. 11 3. 15 4. 17

259. 1, 4, 3, 9, 5, 361. 9 2. 11 3. 15 4. 17

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260. 2, 5, 11, 22, 32, 471. 11 2. 32 3. 47 4. 22

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Odd Man Out (Letters):

Directions : Four Groups of letters are given; three of them are alike in a certainway while one is different. Choose the odd one.

1. 1. DAG 2. KIN 3. ROU 4. YVB

2. 1. KQW 2. GMS 3. HNS 4. CIO

3. 1. ACEG 2. CEGI 3. GIKM 4. LNOR

4. 1. AFKP 2. BGMQ 3. CHMR 4. DINS

5. 1. ABBC 2. PQQR 2. HIIJ 4. WYYZ

6. 1. YZAB 2. EFGH 3. MNOP 4. VWXZ

7. 1. Bde 2. XPD 3. HQU 4. MKV

8. 1. SIT 2. LIP 3. FAN 4. OUT

9. 1. RUX 2. GJM 3. YBE 4. NPS

10. 1. BDH 2. IKP 3. QSW 4. TVZ

11. 1. NPM 2. IJL 3. QSZ 4. BHK

12. 1. VXZ 2. ACF 3. PRU 4. GIL

13. 1. BAC 2. POQ 3. STV 4. YXZ

14. 1. CDE 2. JKL 3. PQS 4. TUV

15. 1. ZAYB 2. XCWD 3. VEUF 4. TSGH

16. 1. A 2. U 3. Y 4. O

17.

1. IRJQ 2. UFVE 3. SHTG 4. NMOK

18. 1. HKNP 2. KNQT 3. MPSV 4. PSVY

19. 1. OVCI 2. RYFM 3. KRYF 4. MTAH

20. 1. LPVD 2. KOUC 3. BFLV 4. OSYG

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21. 1. SUWYA 2. LJNPR 3. KMOQS 4. BDFHJ

22. 1. VTOJE 2. USNID 3. UPKEA 4. SQLGB

23. 1. WHEAT 2. TRAIN 3. PROUD 4. DRIVER

24. 1. MONDAY 2. TUESDAY 3. FRIDAY 4. HOLIDAY

25. 1. HSRI 2. MVUN 3. OLKP 4. PJQX

26. 1. STUA 2. RQPA 3. MLKA 4. HGFA

27. 1. XGEZ 2. PCAQ 3. LKIN 4. DWUF

28. 1. BDYW 2. CEXZ 3. DFYW 4. EGXV

29. 1. UAZF 2. SCXH 3. RDWJ 4. KBPG

30. 1. ABCD 2. EGIK 3. ACDF 4. CFIL

31. 1. BdEg 2. KmNP 3. PrSu 4. TwXz

32. 1. BCD 2. KMN 3. QRS 4. GHI

33. 1. BDGK 2. JLOS 3. NPSW 4. MORU

34. 1. DkUZ 2. LPuB 3. FoMY 4. UXeN

35. 1. APE 2. EQI 3. IOR 4. OSU

36. 1. XW 2. FG 3. ML 4. PO

37. 1. VT 2. MQ 3. PR 4. FG

38. 1. HGF 2. XWV 3. NML 4. OPQ

39. 1. PRT 2. MOQ 3. GEC 4. TVX

40. 1. VWY 2. QRT 3. LMO 4. JKL

41. 1. BHE 2. DJG 3. SYV 4. PUS

42. 1. JOT 2. OUT 3. FED 4. DIN

43. 1. PUT 2. END 3. OWN 4. ARM

44. 1. FAA 2. OFF 3. ATT 4. IFF

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45. 1. BEJMRU 2. PSXAFI 3. WZEHMP 4. ZCHKQT

46. 1. TSRQ 2. MLKJ 3. YXWV 4. HGFD

47. 1. BAT 2. HAT 3. RAT 4. EAT

48. AZ 2. BY 3. CX 4. None

49. 1. BGL 2. MRV 3. JOT 4. AFK

50. 1. BGO 2. NRP 3. HLJ 4. QUS

Directions: Four Groups of letters are given; three of them are alike in a certainway while one is different. Choose the odd one.

51. 1. GECA 2. NLJH 3. USQP 4. BZXV

52. 1. DHLP 2. CGKO 3. BFJN 4. AEIL

53. 1. AIOV 2. BIPW 3. CJQX 4. DKRY

54. 1. EDCBA 2. JOHGF 3. ONMLK 4. TSRQP

55. 1. BHLR 2. AGKQ 3. DJNT 4. EJOX

56. 1. CHM 2. HMR 3. RWB 4. LPU

57. 1. EWZQ 2. OSLS 3. GFKD 4. VSPM

58. 1. ACEG 2. IKMO 3. TVWY 4. FHJL

59. 1. UTSR 2. IHGE 3. NMLK 4. ZYXW

60. 1. BCDE 2. PQRS 3. WXYZ 4. STUW

61. 1. OFF 2. IFF 3. ATT 4. UXY

62. 1. CEI 2. QSX 3. JLP 4. QSW

63. 1. ZAB 2. IJK 3. YZA 4. STV

64. 1. XUW 2. DAC 3. PMN 4. HEG

65. 1. BIF 2. GMJ 3. DKH 4. PWD

66. 1. ADG 2. PSV 3. SUW 4. CFI

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67. 1. EBA 2. XUT 3. TQP 4. JFE

68. 1. ACE 2. PRT 3. UWY 4. MNO

69. 1. ABD 2. FGI 3. LMO 4. STU

70. 1. DCBA 2. MNOP 3. HGFE 4. LKJI

71. 1. BFIK 2. DHKM 3. PRVX 4. MQTV

72. 1. DCBA 2. MNOP 3. HGFE 4. LKJI

73. 1. PCAQ 2. LKIN 3. XGEZ 4. DWUF

74. 1. MRSN 2. HWXI 3. KQSP 4. ZFGA

75. 1. LPWG 2. XBIS 3. FJQB 4. MQXH

76. 1. ADIP 2. RUZG 3. ORWF 4. PSXE

77. 1. CJTG 2. NUER 3. QXHW 4. PWHT

78. 1. EFGIK 2. CDFIM 3. BCEHL 4. ABDGK

79. 1. USAGE 2. USUAL 3. UKASE 4. URINE

80. 1. AUDIO 2. ARISE 3. AWAKE 4. VIDEO

81. 1. PENAL 2. IDHNI 3. RUUD 4. KRTSINSA

82. 1. ALMZ 2. BTUY 3. CPQX 4. DEFY

83. 1. EDKL 2. LMST 3. NMUV 4. QPRS

84. 1. PRVX 2. MQTV 3. DHKM 4. BFIK

85. 1. XZCG 2. OQTX 3. IMNQ 4. EGJN

86. 1. XYVZ 2. QPMR 3. KJHL 4. DCAE

87. 1. RSXY 2. NOUV 3. MNST 4. DEJK

88. 1. BD 2. IK 3. PN 4. SU

89. 1. POCG 2. KLIZ 3. BUDX 4. FQMV

90. 1. CFIL 2. PSVX 3. JMPS 4. ORUX

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91. 1. FCGDE 2. TRQPS 3. KJHMF 4. KHGJI

92. 1. DE 2. PQ 3. TU 4. MO

93. 1. BD 2. MP 3. NQ 4. HK

94. 1. BCD 2. NPR 3. KLM 4. RQP

95. 1. RTW 2. QOM 3. IKG 4. IKM

96. 1. BEH 2. CFI 3. DGJ 4. EHL

97. 1. EBA 2. XUT 3. TQP 4. JFE

98. 1. BYX 2. LPO 3. EVU 4. FUT

99. 1. RJN 2. XTP 3. MIE 4. ZWR

100. 1. EBD 2. IFH 3. QNO 4. YVX

101. 1. RVCNZ 2. LPWGT 3. GTHSYB 44. FUJQOL

102. 1. aBC 2. BaC 3. abC 4. BCa

103. 1. BD 2. CE 3. DF 4. FG

104. 1. ZW 2. YV 3. XV 4. WT

105. 1. ABC 2. BCd 3. CDe 4. Efh

106. 1. bacd 2. figh 3. lomn 4. qrst

107. 1. T 2. H 3. K 4. S

108. 1. HEARS 2. DEARS 3. ERROR 4. FEARS

109. 1. BATU 2. ZYSU 3. SRPN 4. IJSU

110. 1. RNJ 2. XTP 3. MIE 4. ZWR

111. 1. DAL 2. TQS 3. LIK 4. XTW

112. 1. GTSH 2. BYXC 3. ETUF 4. LONM

113. 1. BEFJ 2. DFGJ 3. KNQS 4. QTUY

114. 1. KOM 2. SWV 3. BFD 4. GKI

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115. 1. LKHG 2. VUQP 3. XWTS 4. FEBA

116. 1. DEJK 2. MNST 3. RSXY 4. NOUV

117. 1. YXVU 2. QPNM 3. LKHG 4. FECB

118. 1. QPTS 2. AZDC 3. KJNM 4. SRWV

119. 1. PLHD 2. QMIE 3. VRNJ 4. VQNI

120. 1. ACE 2. FHI 3. KMO 4. PRT

121. 1. AKEW 2. PNTO 3. LCUF 4. HJMX

122. 1. AJKL 2. IXYZ 3. OFGH 4. VCBA

123. 1. AOT 2. CPA 3. REB 4. TIW

124. 1. ECA 2. JHF 3. OMK 4. UXY

125. 1. WVU 2. NML 3. HGF 4. DBA

126. 1. CDE 2. JKL 3. PQS 4. TUV

127. 1. AD 2. BE 3. CF 4. EF

128. 1. AZ 2. BY 3. CX 4. DU

129. 1. AN 2. BO 3. CP 4. ES

130. 1. OpRs 2. TuWx 3. FgHi 4. LNOp

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Odd Man Out (Words):

Directions: Four of the following five are alike in a certain way and so form a group.Which is the one that does not belong to the group.

1.

1. Rupee 2. Lira 3. Coin 4. Dinar

2.

1. Jovial 2. Sad 3. Lively 4. Cheerful

3. 1. Helicopter 2. Aircraft 3. Steamer 4. Chariot

4. 1. Rain 2. Mist 3. Fog 4. Cloud

5. 1. Algebra 2. Geometry 3. Mathematics 4. Trigonometry

6. 1. Niece 2. Mother 3. Aunt 4. Son

7.

1. Tooth 2. Chin 3. Nose 4. Ear

8.

1. Lame 2. Dwarf 3. Fat 4. Tail

9.

1. Ostrich 2. Crow 3. Eagle 4. Vulture

10.

1. Carnatic 2. Kuchipudi 3. Kathak 4. Manipuri

11. 1. Ditch 2. Canal 3. Channel 4. Drive

12. 1. Auroville 2. Wembly 3. Cenotaph 4. Pentagon

13. 1. President 2. Prime Minister 3. Governor 4. Chief Justice

14.

1. Dictionary 2. Magazine 3. Newspaper 4. Library

15. 1. City 2. Town 3. Village 4. Home

16.

1. Pond 2. River 3. Canal 4. Stream

17.

1. Blacksmith 2. Goldsmith 3. Tailor 4. Sailor

18.

1. Large 2. Big 3. Sizable 4. Light

19. 1. Passenger 2. Driver 3. Captain 4. Pilot

20. 1. Diamond 2. Topaz 3. Ruby 4. Pearl

21. 1. Calf 2. Cub 3. Piglet 4. Hireling

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22.

1. Different 2. Separate 3. Distinct 4. Similar

23.

1. Cripple 2. Help 3. Disable 4. Weaken

24. 1. Horse 2. Goat 3. Bullock 4. Cat

25.

1. Where 2. Near 3. Beside 4. Above

26. 1. Ears 2. Hands 3. Fingers 4. Eyes

27.

1. Eagle 2. Vulture 3. Ostrich 4. Swan

28. 1. Sofa 2. Bed 3. Divan 4. Chair

29.

1. Snake 2. Lizard 3. Turtle 4. Whale

30.

1. Mercury 2. Venus 3. Moon 4. Jupiter

31.

1. April 2. May 3. July 4. September

32. 1. Half 2. Should 3. Could 4. Gold

Directions In this type of questions, 4 or 5 pairs of words have been given. Exceptone pair, others bear a common relationship. Find the pair which is different.

33.

1. Broom : Sweep 2. Soap : Clean 3. Spoon : Feed 4. Knife : Sword

34.

1. Newspaper : Editor 2. Film : Director 3. Stamps : Philatelist

4. Book : Author

35.

1. Mother : Daughter 2. Father : Son 3. Uncle : Aunt 4.Uncle : Nephew

36. 1. Soft : Wool 2. Hard : Stone 3. Smooth : Glass 4. Gentle : Tender

37. 1. Bank : Manager 2. College : Principal 3. Navy :Commander 4. Post office : Post man

38. 1. Paper : Pen 2. Garden : Flower 3. Wood : Saw 4.

Nail : Hammer

39.

1. Twigs : Nest 2. Wood : Furniture 3. Pitcher : Pottery4. Gold : Ornaments

40. 1. Tailor : Clothes 2. Chef : Food 3. Author : Book 4. Scale : Length

41.

1. Indigo 2. Orange 3. Pink 4. Green

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42.

1. Eagle 2. Kiwi 3. Emu 4. Penguin

43.

1. Arrow 2. Spear 3. Bullet 4. Sword

44. 1. Brick 2. Heart 3. Club 4. Spade

45.

1. Uttar Pradesh 2. Delhi 3. Maharashtra 4. Sikkim

46. 1. Jockey 2. Rook 3. Bishop 4. Pawn

47.

1. Wise 2. Arrogance 3. Rude 4. Honest

48. 1. Agra 2. Manali 3. Kulu 4. Darjeeling

49.

1. Table-tennis 2. Foot-ball 3. Badminton 4. Cricket

50.

1. Afghanistan 2. Mongolia 3. China 4. Bangladesh

51.

1. Khajuraho 2. Dilwara 3. Madurai 4. Ellora

52. 1. Goblin 2. Imp 3. Goblet 4. Gnome

53. 1. Goldsmith 2. Carpenter 3. Tailor 4. Teacher

54. 1. Economics 2. Physics 3. Chemistry 4. Botany

55. 1. Sesame 2. Mustard 3. Rapeseed 4. Cashewnut

56.

1. Assassinate 2. Murder 3. Kills 4. Kidnap

57.

1. Hanger 2. Platform 3. Dock 4. Park

58.

1. Shoulder 2. Foot 3. Elbow 4. Arm

59.

1. Laos 2. India 3. Bolivia 4. Afghanistan

60.

1. Cap 2. Veil 3. Turban 4. Helmet

61. 1. Ass 2. Cow 3. Rhinoceros 4. Lion

62. 1. Wheat 2. Mustard 3. Rice 4. Gram

63. 1. Biscuits 2. Bread 3. Chocolate 4. Pastry

Directions In this type of questions, 4 or 5 pairs of words have been given. Exceptone pair, others bear a common relationship. Find the pair which is different.

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64.

1. Husband : Wife 2. Dog : Cat 3. Chief Minister : M.L.A.4. Crow : Cuckoo

65.

1. Spain : Madrid 2. Japan : Singapur 3. India : Delhi 4.U.S.A : Washington

66.

1. Error : Blunder 2. Crime : Sin 3. Famous : Renowned 4. Lion : Lioness

67.

1. Snake : Hiss 2. Lion : Roar 3. Birds : Chirp 4. Frog : Bleat

68.

1. Farmer : Plough 2. Butcher : Chopper 3. Author : Book 4. Jockey : Tack

69. 1. Sheep : Lamb 2. Horse : Pony 3. Man : Woman 4. Dog : Puppy

70.

1. Steel : Utensil 2. Bronze : Statue 3. Duralumin : Aircraft 4. Iron : Rails

71.

1. Pituitary 2. Pancreas 3. Thalamus 4. Adernal

72.

1. Pellagra 2. Goitre 3. Scurvy 4. Anaemia

73. 1. Arrow 2. Axe 3. Knife 4. Dagger

74. 1. Metre 2. Furlong 3. Acre 4. Mile

75. 1. Pupil 2. Iris 3. Cornea 4. Medulla

76. 1. Sucrose 2. Ptyalin 3. Analyse 4. Pepsin

77.

1. Potassium 2. Silicon 3. Zirconium 4. Gallium

78.

1. Almond 2. Turmeric 3. Pepper 4. Cuminseed

79.

1. Hepatitis 2. Tetanus 3. Cancer 4. Conjectivitis

80.

1. Autocracy 2. Bereaucracy 3. Democracy 4. Diplomacy

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Analytical Reasoning

Arrangements:

1. In a row of girls of sheetal who is 10th from the left and Lina who is 9th from theright change their seats. Sheetal becomes 15th from the left. How many girls arethere in a row?1. 16 2. 23 3. 32 4. 25

2. Five boys are so standing that they from a circle. Ajay is between Ramesh andDominic, Soloman is to the left of Babu. Ramesh is to the left of Soloman. Whois the right of Ajay?1. Dominic 2. Soloman 3. Babu 4. Ramesh

3. In a row of 16 boys when Prakash was shifted by two places towards the left, he

became 7th

from the left end. What was his earlier position from the right end ofthe row?1. 12th 2. 10th 3. 14th 4. 8th

4. Five boys are sitting in a row. A is on the right of B, E is on the left of B, but tothe right of C. If A is on the left of D. Who is sitting in the middle.1. E 2. B 3. A 4. C

5. Some boys are sitting in row. P is sitting 14th from the left and Q is 7th from theright. If there are four boys between P and Q, how many boys are there in therow?

1. 19 2. 21 3. 25 4. 23

6. If (i) six persons, A, B, C, D, E and F are standing in a circle, not necessarily inthe same order. (ii) B is between F and C. (iii) A is between E and D and (iv) F isto the left of D, which of the following is between A and F?1. B 2. C 3. D 4. E

7. In a row of boys, Anil is 15th from the left and Vishakh is 7th from the right. Ifthey interchange their positions. Vishakh becomes 15th from the right. Howmany boys are there in the row?1. 21 2. 25 3. 29 4. Can‟t be determined

8. Five persons were playing card game sitting in a circle all facing the center.Mukund was to the left of Rajesh, Vijay was to the right of Anil and betweenAnil and Nagesh. Who was to the right of Nagesh?1. Rajesh 2. Vijay 3. Anil 4. Mukund

9. In front of a camera, Mr. X is sitting to the left of that man, who is at the centerof the row, but Mr. X is to right of Mr. Y . Mr. P is to the right of Mr. Z and Mr. Ris the right of Mr. P. Mr. R is second from the man, sitting at the center. Who is

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sitting at the center of the row?1. Mr. X 2. Mr. Y 3. Mr. Z 4. Mr. R

10. A ranks fifth in a class. B is eighth from the last. If C is sixth after A and just inmiddle of A and B, how many students are there in the class?1. 25 2. 26 3. 23 4. 24

11. Suresh is 7 ranks ahead of Ashok in the class of 39. If Ashok‟s rank is 17th fromthe last, what is Suresh‟s rank from the start? 1. 15 2. 14 3. 24 4. 16

12. In a row of children Munni is nirth from the left of Tunni is thirteenth from theright. When they exchange places, Munni will be seventeenth from the left.Which of the following will be the new position of Tunni from the right?1. 20th 2. 7th 3. 21st 4. 9th

13. Some boys are sitting in a row, P is sitting 14th from the left and Q is seventh

from the right. If there are four boys between P and Q, how many boys are therein the row?1. 19 2. 21 3. 25 4. 23

14. In a row of trees, one tree is the 9th from either end of the row. How many treesare there in the row?1. 17 2. 19 3. 16 4. 18

15. In a certain class, Rakesh is 29th from the top and mohan is 16th from thebottom in the alphabetical arrangements of names. If they have 7 boys betweenthem what is the number of students in the class?

1. 52 2. 45 3. 36 4. 35

16. Rakesh ranks seventh in a class of twenty. What is his rank from the last?1. 15th 2. 13th 3. 14th 4. 8th

17. Of the five villages: 1) Phulwade is smaller than Dhanwade 2) Ambawade isbigger than Khelwade 3) Sonewade is bigger than Dhanwade but is not as big asKelwade. Which is biggest village?1. Ambawade 2. Phulwade 3. Dhanwade 4. Kelwade

18. It (A) Ashok is taller than Suresh (B) Raju is taller than Ashok (C) Chandu is

shorter than Suresh, then chandu is __________1. taller than ashok 2. As tall as suresh 3. taller than suresh 4. shorter than Ashok

19. Five boys Rakesh, Anil, Mahesh, Suresh and Manjit are sitting in a circle.A) Anil is sitting between Rakesh and Suresh B) To Manjit‟s right suresh isseated.Who is seated to Mahesh‟s left?

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1. Anil 2. Suresh 3. Manjit 4. Rakesh

20. Four girls are swimming in a stream. 1) Harjeet is further ahead of Manjula 2)Neena is behind Manjula 3) Ruchi is between Manjula and Neena.Who is second from the last?1. Neena 2. Manjula 3. Ruchi 4. Harjeet

21. Five poles are standing in a row. M is on the left of N, O is on the right of P,which is on the right of N. If L is on the left of M, which pole is in center?1. L 2. M 3. N 4. O

22. Five boys are sitting in a row. Sanjay is just on the one side of Pradeep but not just on any side of Timur. Kailash is just on one side of Ramesh who is sittingleft of all and Timur is not sitting just on any side of Kailash who are sitting oneither side of Sanjay?1. Kailash & Pradeep 2. Ramesh & Pradeep 3. Only Pradeep 4. Pradeep & Timur

23. Six families A, B, C, D, E and F are living in houses in a row. B has F and D asneighbours, E has A and C as neighbours. A does not live next to D. Who areF‟s next door neighbours? 1. B and E 2. B and D 3. B and C 4. Data Insufficient

24. Sudha is taller than Pushpa but shorter than Malati. Geeta is shorter than Vinuand Vinu is not as tall as Pushpa. Who should be in the middle if they stand ina row according to height?1. Pushpa 2. Malati 3. Sudha 4. Geeta

25. Among five friends, Manish is taller than Harish, but not as tall as Jayesh. Jayesh is taller than Vijay and Sharad. Vijay is shorter than Harish but tallerthan one who is shortest among them. Who is the fourth in the descendingorder of their heights?1. Manish 2. Harish 3. Sharad 4. Can‟t be determined

26. If Shirish is taller than Charu but shorter than Raju and Charu is just as tall asDilip but taller than Ashok, then Dilip is _______1. Just as tall as Shirish 2. Shorter than Charu3. Taller than Raju 4. Taller than Ashok

27. While going to the school, Anil was behind Sunil and Rohit was ahead of

Madan. Ramesh was in between Anil and Rohit. Who was leading?1. Anil 2. Sunil 3. Rohit 4. Madan

28. Priti scored more than Rahul. Yamuna scored as much as Divya. Lotika scoredless than Manju. Rahul scored more than Yamuna. Manju scored less thanDivya. Who scored the lowest?1. Yamuna 2. Manju 3. Lotika 4. Rahul

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35. Which course is taught by S?1. C 2. E 3. Either C or D 4. D

36. Which lecture‟s course immediately follows after course B? 1. Q 2. P 3. S 4. T

37. Which course is taught in the month of January?1. C 2. D 3. E 4. Data inadequate

Directions (Questions 38-40): Six persons A, B, C, D, E and F sitting forming acircle and one is facing other front to front B is between A and C, E is between Fand D. F is sitting straight opposite to A and right to E.

38. D is between which of the following pairs?1. EF 2. AE 3. AB 4. CF

39. If the position of B and E are interchanged and also that of C and D, A will be in

between which of the following pairs?1. CB 2. ED 3. FD 4. CE

40. Who is at the immediate left of D?1. E 2. F 3. B 4. A

41. Six friends A, B, C, D, E and F are sitting in a closed circle facing the center. Eis to the left of D. C is between A and B. F is between E and A. Who is to the leftof B?1. D 2. C 3. A 4. F

42. In a row of children, Shibu is fifth from the left and Lakhya is sixth from theright. When they exchange position, Shibu will be thirteenth from the left. Whatwill be Lakhya‟s position from the right? 1. 14th 2. 7th 3. 11th 4. 18th

43. In a march past seven persons are standing in a row. Q is standing in a row. Qis standing left to R but right to P. O is standing right to N and left to P.Similarly, S is standing right to R and left to T. Find out who is standing in themiddle?1. P 2. R 3. Q 4. O

44. Five boys took part in a race. Ram finished before Mohan but behind Gopal.Abbas finished before sailesh but behind Mohan. Who won the race?1. Ram 2. Gopal 3. Mohan 4. Abbas

45. Six persons playing a game sitting in a circle facing the center. Vijay was to theleft to Sudhir. Amar was between Rakesh and Saurav. Neerav was second to theleft of Amar. Who is second to the right of Vijay?

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1. Neerav 2. Rakesh 3. Saurav 4. Data Insufficient

46. In a row of girls, if Seeta who is 10th from the left and Lalitha who is 7th fromthe right, interchange their seats, Seeta becomes 15th from the left. How manygirls are there in the row?1. 17 2. 20 3. 22 4. 21

47. In a row of boys, Anand is eleventh from the left and Deepak is fifteenth fromthe right. When Anand and Deepak interchange their positions, Anand will befifth from the left. Which of the following will be Deepak‟s position from theright?1. 7th 2. 17th 3. 11th 4. 9th

48. In a photograph Shyam is to the left of Madan. Mary is to the right of George,Karim is in between Shyam and Mary. Who is at the corner?1. Shyam 2. Mary 3. George 4. Karim

49. Six students A, B, C, D, E and F are standing in a row. B is between F and D, E

is between A and C. A does not stand next to either F or D. C does not standnext to D. F is between which of the following pairs of students?1. B and D 2. B and A 3. B and E 4. B and C

50. Madhav ranks seventeenth in a class of thirty one. What is his rank from thelast?1. 13 2. 14 3. 15 4. 16

51. In a row of children, shibu is fifth from the left and Lakhya is sixth from theright. When they exchange positions, shibu will be thirteenth from the left.

What will be Lakhya‟s position from the right? 1. 4th 2. 5th 3. 13th 4. 14th

52. Four girls A, B, C and D are sitting in a circle. B and C are facing each other.Which of the following is definitely true?1. A is to the left of C 2. D is to the left of C 3. A & D are facing each other 4. A is not between B & C

53. Raju and Manoj are ranked 14 and 15 respectively from the top in a class of 30students. What will be their respective ranks from the bottom.

1. 15th & 16th 2. 16th & 15th 3. 17th & 16th 4. 18th & 17th

54. Mahesh ranked 13th from the top and 26th from the bottom among those whohave passed the annual examination in a class. If six students have failed in theannual examination, what was the total number of students in that class?1. 44 2. 20 3. 21 4. 38

55. There are five books A, B, C, D, E. C lies above D, E is below A. D is above A, Bis below E. Which is the bottom most book?

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1. A 2. B 3. E 4. C

56. If (A) Suresh is taller than Ashutosh (B) Raju is taller than Charu but shorterthan Bala (C) Ashutosh is shorter than Charu (D) Charu is taller than Suresh,then who is the tallest?1. Suresh 2. Ashutosh 3. Raju 4. Bala

57. If (A) Mahesh is taller than suresh (B) Anil is taller than Mahesh (C) Ramesh istaller than Anil (D) Puneet is tallest of all. If they stand according to theirheight, who will be exactly in the middle?1. Mahesh 2. Suresh 3. Ramesh 4. Anil

58. Sunita is standing on a stairs below Sulekha, Rani is below Sulekha andMadhu is between Rani and Sulekha who is second from bottom?1. Rani 2. Sulekha 3. Madhu 4. Sunita

59. Five boys are up on the ladder. A) A is further up the ladder than B B) B is

between A and C C) D is further up than A.Who is the third from the bottom.1. B 2. C 3. A 4. D

60. Five books are lying in a pile. E is lying on A and D is under B. A is lying aboveB and C is lying under D. Which book is lying at the bottom?1. A 2. B 3. C 4. D

61. Four boys are sitting in a row. Bipin is sitting just on one side to Gopal, but not just on any side to Raju. If raju is not just on any side of Farukh then who aresitting just both side of Farukh?

1. Only gopal 2. Only bipin 3. nobody 4. Bipin and Gopal

62. Five students are sitting in a row. Tapesh is on the right of Zahir. Manoj is onthe left of Zahir but is on the right of Love. Tapesh is on the left of Qeer. Who issitting 1st from the left?1. Zahir 2. Tapesh 3. Qeer 4. Love

63. Five bags are lying in a pile one above the other. If A is above B, C is above Dbut below E and D is above A, which bag is in the middle?1. A 2. D 3. C 4. B

64. Prakash is taller than Geetha. Amar is taller than Prabhat but not as tall as

Geetha. Prabodh is taller than Prakash. Who among them is the shortest?1. Prabhat 2. Geetha 3. Amar 4. Prabodh

65. Of the six towns, Dhulia is bigger than Amalner, Shrirampur is bigger thanNasik, Jalgaon is not as big as Shrirampur but bigger than Amalner, Amalner issmaller than Nasik but bigger than Manmad. Which is the smallest?

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1. Amalner 2. Nasik 3. Jalgaon 4. Manmad

66. Ashok is taller than Kavitha but not as tall as Jayesh. Jayesh is shorter thanSubodh who is not as tall as Prabodh. Who is tallest in the group?1. Prabodh 2. Subodh 3. Kavitha 4. Ashok

67. Ravi is taller than Jyoti who is shorter than Raju. Mohan is taller than Ravi butshorter than Suresh. Raju is shorter than Ravi. Who is the tallest?

1. Ravi 2. Raju 3. Suresh 4. Data Insufficient68. Amar is taller than Samir, Pravath is taller than Umesh but not as tall as

Samir; Ashok is shorter than Umesh. Who is shortest?1. Amar 2. Samir 3. Pravath 4. Ashok

69. Shyam is older than Pradeep. Praveen is as old as Anjan. Amrut is youngerthan Suresh who is as old as Anjan. Pradeep is older than Praveen. Which boyis oldest of all?1. Pradeep 2. Praveen 3. Suresh 4. Shyam

70. Roshan is taller than Hardik who is shorter than Susheel, Mirza is taller thanHarry but shorter than Hardik, Susheel is shorter than Roshan. Who is thetallest?1. Roshan 2. Susheel 3. Hardik 4. Harry

Directions Read the following statements and answer the questions given below.

a) Six friends A, B, C, D, E and F are sitting in a closed circle facing the center, b) Eis to the left of D, c) C is between A and B, d) F is between E and A.

71. Who is to the left of E?

1. A 2. C 3. D 4. F

72. Who is to the right of C?1. A 2. B 3. D 4. E

Directions Read the following information to answer questions below.

Six persons were playing game sitting in a circle facing the center. Vijay was to theleft of Sudhir, Amar was between Rakesh and Saurav. Neeru was second to the leftof Amar.

73. Who is second to the right of Vijay?

1. Neeru 2. Rakesh 3. Saurav 4. Can‟t be determined

74. Who is/are between Amar and Vijay?1. Saurav and Sudhir 2. Rakesh & Saurav 3. Sudhir & Rakesh 4. Data Insufficient

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75. Which of the following is the position of Vijay from Neeru?1. 2nd from the left 2. 3rd from left 3. 3rd from right 4.Can‟t be determined

Directions: Read the following information carefully and answer the questions givenbelow:i.

Seven members of World Forest Conservation Committee – A, B, C, D, E, F and

G planted seven saplings on seven days of the week which was celebrated as“Plantation Week”. ii. A planted the sapling on Monday, the first day of the Plantation Weekiii.

B planted the sapling a day before when C planted the sapling and the very nextday of E.

iv.

D planted the sapling on some day after that of B but that day was not themiddle day of the week.

v. F planted the sapling on the last day of the plantation week and it was the thirdday after C planted the sapling.

76. Which of the following pairs of members planted the saplings on Wednesday

and Thursday respectively?1. D and G 2. B and G 3. B and C 4. Can‟t be determined

77. On which day did B plant the sapling?1. Tuesday 2. Wednesday 3. Thursday 4. Can‟t be determined

78. Who among the following planted sapling on Saturday?1. Either B or C 2. Either D or G 3. Only C 4. Only E

79. Who planted the sapling on the middle day of the plantation week?1. B 2. D 3. E 4. C

80. On which day did D plant the sapling?1. Monday 2. Wednesday 3. Tuesday 4. Can‟t be determined

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Problem Solving:

Directions (Questions 1-5): Read the following information and answer thequestions given below it.

1.

Seven students P, Q, R, S, T, U and V take a series of tests.2. No two students get similar marks.3.

V always scores more than P.4. P always scores more than Q.5. Each time either R scores the highest and T gets the least, or alternatively S

scores the highest and U or Q scores the least.

1.

If S is ranked sixth and Q is ranked fifth, which of the following can be true?1. V is ranked first of fourth 2. R is ranked second and third3. P is ranked second or fifth 4. U is ranked third or fourth

2.

If R gets most, V should be ranked not lower than ___________1. Second 2. Third 3. Fourth 4. Fifth

3.

If R is ranked second and Q is ranked fifth which of the following must be true?1. S is ranked third 2. T is ranked sixth 3. P is ranked sixth 4. V is ranked fourth

4.

If S is ranked second, which of the following can be true?1. U gets more than V 2. V gets more than S 3. P gets morethan R 4. P gets more than V

5.

If V is ranked fifth, which of the following must be true?1. S scores the highest 2. R is ranked second 3. T is rankedthird 4. Q is ranked fourth”

Directions (Questions 6-10): Study the following information carefully and answerthe questions given below it:

Five friends A, B, C, D and E are sitting on a bench.

1.

A is sitting next to B2.

C is sitting next to D3.

D is not sitting with E4. E is on the left end of the bench5.

C is on second position from the right6. A is on the right side of B and to the right side of E7.

A and C are sitting together

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6.

Where is A sitting?1. Between B and C 2. Between D and C 3. Between E and D 4. Between C and E

7. Who is sitting in the centre?1. A 2. B 3. C 4. D

8.

C is sitting between ________1. B and D 2. A and E 3. D and E 4. A and D

9.

What is the position of D?1. Extreme left 2. Extreme right 3. Third from left 4. Second from left

10. What is the position of B?1. Second from right 2. Centre 3. Extreme left 4.Second from left

Directions (Questions 11-15): Study the following information carefully andanswer the questions given below it.

A sales representative plans to visit each of six companies K, N, P, Q, R and Sexactly once during the course of one day. She is setting up her schedule for the dayaccording to the following conditions.She must visit M before N and R.She must visit N before Q The third company she visits must be P

11.

Which of the following must be true of the sales representative‟s schedule?

1. She visits M before Q 2. She visits N before R3. She visits P before M 4. She visits P before S

12. If the sales representatives visits S first, which company must she visit second?1. M 2. N 3. P 3. Q

13.

The sales representative could visit any of the following companies immediatelyafter P except ____1. S 2. R 3. Q 4. M

14. If the sales representative visits Q immediately before r and immediately after S,

she must visit Q.1. First 2. Second 3. Fourth 4. Fifth

15. Which of the following could be the order in which the sales representative visitthe six companies?1. M, S, P, N, R, Q 2. Q, N, P, R, S, M 3. M, R, N, Q, P, S 4. P, S, M, R, Q, N

Directions (Questions 16-20): Read the following information carefully and answerthe questions given below it.

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On a shelf are placed six volumes side by side labeled A, B, C, D, E and F. Threevolumes B, C and E have green covers while the other volumes have yellow covers.A, D and B are new volumes while the rest are old volumes. A, C and B are lawreports, while the rest are Gazetteers.

16.

Which volume is new, yellow covered and a Gazetteer?1. B 2. D 3. E 4. F

17.

Which two volumes are old Gazetteers and have green covers?1. B, C 2. B, E 3. B, F 4. Only E

18. Which is green covered, old and a law report volume?1. A 2. B 3. C 4. D

19. Which is the yellow covered new law report volume?1. A 2. D 3. B 4. C

20.

Which of the following is the old volume of a Gazetteer?1. C 2. D 3. E 4. B

Directions (Questions 21-25): Study the following information carefully andanswer the questions given below it:

From amongst six boys A, B, C, D, E and F and five girls P, Q, R, S and T, a term ofsix is to be selected under the following conditions:A and D have to be together. C cannot go with S. S and T have to be together. Bcannot be teamed with E. D cannot go with P. B and R have to be together. C and Q

have to be together.

21.

If there be five boys in the team, the long girls member is _____________1. P 2. Q 3. R 4. S

22. If including P, the team has three girls, the members other than P are ___________1. BCFQR 2. ADEST 3. ADBST 4. BFRST

23. If the team including C consist of four boys, the members of the team otherthan C are _________1. ADEPQ 2. ABDQR 3. DEFAQ 4. BEFRQ

24. If four members including E have to be boys, the members other than E are ___________1. ABCQR 2. ADFST 3. BCFQR 4. ACDFQ

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25.

If four members have to be girls, the members of the team are ____________1. BCPQRS 2. BFPRST 3. BCQRST 4. BCPQRT

Directions (Questions 26-30): Study the following information carefully andanswer the questions given below it:

There are six teachers A, B, C, D, E and F in a school. Each

of the teachers teaches two subjects, one compulsory subject and other optionalsubject. D‟s optional subject was History while three others have it as compulsorysubject. E and F have Physics as one of their subjects. F‟s compulsory subject isMathematics which is an optional subject of both C and E. History and English areA‟s subjects but in terms of compulsory and optional subjects, they are just reverseof those of D‟s. Chemistry is an optional subject of only one of them. The only femaleteacher in the school has English as her compulsory subject.

26. What is C‟s compulsory subject?1. History 2. Physics 3. Chemistry 4. English

27.

Who is a female member in the group?1. A 2. B 3. D 4. None

28. Which of the following has same compulsory and optional subjects as those ofF‟s? 1. D 2. B 3. A 4. None

29. Disregarding which is the compulsory which is the optional subject who hassame two subject combination as F?1. A 2. B 3. E 4. D

30.

Which of the following groups has History the compulsory subject?1. A, C and D 2. B, C and D 3. C and D 4. A, B and C

Directions (31 – 36) : A family has 6 children viz., Savitha, Sadguna, Swathi,Srinivas, Suvidha and Susheel not born in the same order. Any two consecutivechildren has 2 years age difference.

(i)

Swathi is older than Srinivas and Susheel.(ii) Suvidha born as 2nd child in the family and she is 4 years elder than

Sadguna.(iii)

Susheel born last and he is 6 years younger to Srinivas.

31.

Who had born first?1. Swathi 2. Suvidha 3. Srinivas 4. Sadguna

32. Who had born as a 5th child in the family?1. Srinivas 2. Swathi 3. Sadguna 4. Savitha

33. What is the age difference between Suvidha and Susheel?1. 10 years 2. 8 years 3. 6 years 4. 2 years

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34.

If Swathi‟s age is 23 years then what is the age of Savitha? 1. 11 years 2. 13 years 3. 15 years 4. 17 years

35. Who is the eldest child of the family?1. Swathi 2. Suvidha 3. Srinivas 4. Susheel

36.

Who is the eldest child of the family?1. Swathi 2. Suvidha 3. Srinivas 4. Susheel

Directions (37 – 40) : Four friends are playing cards game. Anil is facing North andSunil sat to his left. Vikrant is opposite to Sunil and Vikranth‟s right is Vinod.

37. Who is opposite to Vinod?1. Anil 2. Sunil 3. Vikranth 4. Can‟t be determined

38.

Who is facing west?

1. Anil 2. Sunil 3. Vikranth 4. Vinod

39. Who is to the right of Vinod?1. Vikranth 2. Anil 3. Sunil 4. Can‟t be determined

40. Who is facing South?1. Anil 2. Sunil 3. Vikranth 4. Vinod

Directions Study the following information carefully and answer the questions

given below it:

There are five persons P, Q, R, S and T. One is football player, one is chess playerand one is hockey player. P and S are unmarried ladies and do not participate inany game. None of the ladies plays chess or football. There is a married couple inwhich T is the husband. Q is the brother of R and is neither a chess player nor ahockey player.

41.

Who is the football player?1. P 2. Q 3. R 4. S

42.

Who is the hockey player?1. T 2. S 3. R 4. Q

43. Who is the chess player?1. S 2. P 3. T 4. R

44. Who is the wife of T?1. P 2. Q 3. R 4. S

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45.

The three ladies are _____________1. P, Q and R 2. Q, R and S 3. P, Q and S 4. P, R and S

Directions Study the following information carefully and answer the questionsgiven below it:

P, Q, R, S, T and X are members of a family. There are two married couple. Q is anEngineer and is father of T. X is grandfather of R and is a lawyer. S is grandmotherof T and is a housewife. There is one Engineer, one Lawyer, one Teacher, oneHousewife and two students in the family.

46.

Who is the husband of P?1. R 2. X 3. Q 4. S

47.

Which of the following are two married couples?1. XS, QP 2. XS, QT 3. XS, RP 4. TS, RX

48.

Which of the following is definitely a group of male members?1. Q, X, T 2. X, T 3. Q, X, P 4. Q, X

49. Who is the sister of T?1. R 2. S 3. P 4. Data inadequate

50. Which of the following can be P‟s profession? 1. Housewife 2. Engineer 3. Teacher 4. Engineer or Teacher


Prashant Arora has three children – Sangeeta, Vimal and Ashish. Ashish marriedMonika, the eldest daughter of Mr. and Mrs. Roy. The Roys married their youngestdaughter to the eldest son of Mr. and Mrs. Sharma, and they had two children nameAmit and Shashi. The Roys have two more children, Roshan and Vandana, bothelder to Veena. Sameer and Ajay are sons of Ashish and Monika. Rashmi is thedaughter of Amit.

51.

What is the surname of Rashmi?1. Sharma 2. Roy 3. Arora 4. Can‟t be determined

52.

How is Sameer related to the father of Monika?1. Grandson 2. Son 3. Cousin 4. Son-in-law

53. What is the surname of Sameer?1. Roy 2. Sharma 3. Arora 4. Can‟t be determined

54. How is Mrs. Roy related to Ashish?1. Aunt 2. Mother-in-law 3. Mother 4. Sister-in-law

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A training college has to conduct a refresher course for teaches of seven differentsubjects Mechanics, Psychology, Philosophy, Sociology, Economics, Science andEngineering from 22nd July to 29th July.

Course should start with Psychology.23rd July, being Sunday, should be holiday.Science subject should be on the previous day of the Engineering subject.Course should end with Mechanics subject.Philosophy should be immediately after the holiday. There should be a gap of one day between Economics and Engineering.

55. The refresher course will start with which one of the following subjects?1. Psychology 2. Mechanics 3. Philosophy 4. Economics

56.

Which subject will be on Tuesday?

1. Mechanics 2. Engineering 3. Economics 4. Psychology

57. Which subject precedes Mechanics?1. Sociology 2. Engineering 3. Philosophy 4. Psychology

58. How many day‟s gap is there between Science and Philosophy? 1. One 2. Two 3. Three 4. Four

59.

Which subject is following by Science?1. Engineering 2. Psychology 3. Philosophy 4. Economics

60.

Which subject will be on Saturday?1. Engineering 2. Mechanics 3. Philosophy 4. Data Inadequate

Directions There are six students in a class A, B, C, D, E and F. D is taller than Eand F. There is only one person between B and C. A is between E and F. There arefour persons between C and F.

61. Who is the tallest in the group?1. D 2. A 3. C 4. E

62. Who is between D and E?

1. B 2. A 3. F 4. C

63.

Who is shortest in that group?1. C 2. F 3. E 4. A

64. Who are shorter than E?1. F and E 2. F and B 3. A and F 4. C and E

65. Who are taller than A but shorter than D?

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1. F and E 2. E and B 3. F and B 4. C and E

Directions Five persons P, Q, R, S and T belongs to five different cities Chennai,Bangalore, Hyderabad, Pune and Delhi. They are invited to deliver a seminar ondifferent subject Viz., Chemistry, Physics, Mathematics, History and Economics butnot necessarily in the same order.

(i)

P who belongs to Bangalore gives seminar on Economics.(ii)

The person who gives seminar on Physics belongs to Chennai.(iii) T does not give seminar on Chemistry or History but belongs to Hyderabad.(iv)

S does not belongs to Pune but gives seminar on Chemistry and History is theoption of R.

66. Who belongs to Pune?1. R 2. Q 3. S 4. T

67. Physics seminar will be given by?1. Q 2. R 3. S 4. T

68.

T gives seminar on?1. Physics 2. Chemistry 3. History 4. Mathematics

69.

S belongs to which city?1. Chennai 2. Hyderabad 3. Pune 4. Delhi

70. Who belongs to Chennai?1. R 2. S 3. Q 4. T

Directions In a family of six persons P, Q, R, S, T and U, there are 3 males and 3

females. There are 2 married couples and 2 persons who are unmarried. Each oneof them reads different News Papers Viz., Eenadu, Vaartha, Vijetha, AndhraJyothi,AndhraBhumi and Saakshi. T, who reads Vaartha is mother-in-law of P, who is the wife of R. S is the father of Rand he does not read Eenadu or Saakshi. Q reads AndhraBhumi and is the sister ofU who reads Vijetha. R does not read Saakshi.

71. Who among the following reads Eenadu?1. R 2. S 3. P 4. Data inadequate

72. How is U related to T?

1. Brother 2. Son 3. Grandson 4. Can‟t say

73.

Which of the following is one of the married couples?1. P – S 2. T – R 3. T – P 4. R – P

74. Who reads Saakshi?1. T 2. S 3. Q 4. P

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75.

How is T related to R?1. Son 2. Father 3. Mother 4. Mother-in-law

Directions 6 persons L, M, N, O, P and Q are standing in a row. They wear 6different coloured dresses viz., Red, Green, Blue, Black, Violet and White.

(i)

M is 4th

from the right end and wears Blue colour dress. And Q is secondleft to him.(ii) Person wears Black dress stands 4th from the left end and N is immediate

right to him.(iii)

P is at one end and wears Red dress.(iv)

O does not wear violet or white and person stands immediate left to Pwears violet dress.

76.

Who wears green dress?1. L 2. M 3. N 4. O

77.

Who stands in the middle?1. L and N 2. O and M 3. M and L 4. O and N

78.

Who stands at the both ends?1. M and L 2. P and Q 3. N and O 4. Q and N

79.

If white dressed person is called Manager who is the Manager?1. P 2. N 3. O 4. Q

80. O wears which colour dress?1. Red 2. Green 3. Black 4. Violet

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Critical Reasoning

Exercise 1:

1. Recent studies have highlighted the harmful effects of additives in food (colors,preservatives, flavor enhancers etc.). There are no synthetic substances in the foodswe produce at Munchon Foods – we use only natural ingredients. Hence you can besure you are safeguarding your family‟s health when you buy our products.

Which of the following, if true, would most weaken the contention of MunchonFoods?

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A. Some synthetic substances are not harmfulB. Some natural substances found in foods can be harmfulC. Food without additives is unlikely to taste goodD. Munchon Foods produces only breakfast cereals

E. Without preservatives some foods could cause harm

2. A fruit known as amla in certain parts of Asia is an excellent source of vitamin C.A small quantity of the fruit grated and added to salads provides almost all the dailyrequirement of this vitamin. However, the fruit is very sour. A new process designedto remove most of the sour taste will make the fruit acceptable to American tastes.We are therefore starting to grow this fruit for sale in the United States.

The argument above assumes all of the following except

A. Americans generally won‟t eat very sour foodsB. The new process does not remove a significant part of the vitamin contentC. That a market exists for a new source of vitamin CD. The fruit can be used only in saladsE. Apart from being sour there are no other objections to eating this fruit

3. Most scientists agree that new lines of interdisciplinary research are the needof the hour. Even government committees on science have stressed the need formore interdisciplinary projects. Yet, of ten proposals for new interdisciplinaryprojects last year, only one was successfully funded. Some have suggested that thismeans that as yet researchers are not coming up with sufficiently persuasive

projects, or that their proposals are not of high enough quality, or even that thereputations of these researchers is not high enough. However, the real reasonprobably lies in the way funding is organized. Funding is still allocated accordingto the old categories and there are no funds specifically for research thatoverlaps different subject areas.

The two parts in bold-face are related to each other in which of the following ways?

A. The first is a finding that the author finds unacceptable; the second is theauthor‟s own positionB. The first is a finding that the author attempts to account for; the second is afinding that contradicts the author‟s main conclusion.C. The first is a fact that the author attempts to account for. The second is data thatexplicitly supports the author‟s main conclusion.D. The first is a position that the author opposes; the second is the author‟s mainposition.E. The first is a situation that the author finds paradoxical; the second is anassumption that the author uses to reinforce the paradox.

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4. Anton: I sold my house on an internet site last year and was happy with theprice. I got a speedy sale and the cost of advertising was insignificant. I wouldadvise you to avoid real estate agents.

Barbie: It is in the interest of the real estate agent to get me the best price for myproperty because he gets a commission based on the selling price. Therefore, when

selling my house I will certainly use an agent rather than trying to sell the house byword of mouth, or by advertising in newspapers or on the internet.

Barbie‟s could strengthen her position by pointing out all of the following except

A. Houses of comparable value often obtain a lower price when sold on the internetB. Very few houses are sold on the internet at the moment an so a valid comparisonis difficultC. The agent‟s service includes many add-on benefits in terms of legal fees,surveyor‟s reports and advice that are not available on internet sites

D. Some buyers pay the agent to find them a cheap houseE. The agent‟s commission is usually less than the difference between the internetprice and the higher price the agent obtains for you

5. Early data on seat-belt use showed that seat-belt wearers were less likely to bekilled in road accidents. Hence, it was initially believed that wearing a seat-beltincreased survival chances in an accident. But what the early analysts had failed tosee was that cautious drivers were more likely to wear the belts and were also lesslikely to cause „big accidents‟, while reckless drivers were more likely to be involvedin „big‟ accidents and were less likely to wear the belts.

Which of the following, if true, could an opponent of the view presented above bestcite as a reason for recommending continued use of seat-belts?

A. Careful drivers who are involved in accidents caused by reckless drivers, wouldbe more likely to survive if wearing a beltB. All drivers should be required by law to wear a beltC. The ratio of „big‟ to „small‟ road accidents is very smallD. In fatal accidents seat-belt wearers in the front seat are less likely to survive thanthose wearing seat belts in the back seatE. On average, careful drivers pay lower insurance premiums than do drivers who

have been involved in accidents.

6. French cuisine is highly regarded all over the world. Yet in Paris there are moreAmerican restaurants selling burgers and fries (which many people now class as„junk food‟) than there are in any other European capital city. Obviously the Frenchare very fond of „junk food‟, and are not too proud to eat it.

Which of the following, if true, would most weaken the author‟s contention?

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A. There are also a larger number of Lebanese restaurants in Paris than there are inother European capital citiesB. French Cordon Bleu cuisine is very expensiveC. The number of French tourists eating in New York burger restaurants is very lowD. Junk food is actually has high nutritional value when eaten in moderation

E. There are an unusually large number of American tourists in Paris who eat atburger joints

7. Scientists investigating a rare metabolic disorder hypothesized that obesity was apredisposing factor in the development of the disease. A study of twenty patientsfound that, on average, the patients were close to the normal weight for their height.

Before concluding that obesity is not a predisposing factor, the researchers wouldfind the answer to which of the following questions most useful?

A. Are the patients above or below normal height?B. Were any of the patients underweight when the disorder was diagnosed?C. Does weight loss reduce the severity of the symptoms?D. Have the patients always been close to the normal weight for their heights?E. How many of the patients had obese parents?

8. In research designed to investigate the possibility of animals developingfriendship with other, unrelated, members of their species, a group of 29chimpanzees were reared together for 15 years. At the end of that time the chimpswere presented with two options for obtaining food: press a lever and feedthemselves, or press another identical lever and feed themselves, and at the same

time deliver food to the chimp next door. (The chimps were able to see each other).The researchers found that the chimps were no more likely to choose the leverthat fed a neighbor. The researchers concluded that the chimps had no concept offriendship. However, one critic has suggested that the animals were in anartificial environment from which little can be concluded, and that, at the least,the test ought to have involved the animals being able to touch.

What role do the parts in boldface play in the argument above?

A. The first is a position that the critic opposes. The second is a position that the

critic supports.B. The first is an observation that supports the researchers‟ position. The second isan observation that opposes the researchers‟ position.C. The first is a finding on which the researchers base their conclusion. The secondis a suggestion that might cast doubt on that finding.D. The first is an observation that supports the critic‟s conclusion. The second is thecritic‟s conclusion.E. The first is part of the evidence that the critic disputes. The second is asuggestion that the researchers do not accept.

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12. Thousands of people have tonsillectomies every year and all live normal livesafter the operation. We can conclude, from this observation, that the tonsils have nofunction in the body.

The argument would be most weakened by which of the following, if it were true?

A. People live normal lives after appendectomies but the appendix is known to bepart of the digestive system.B. Another part of the body can take over the function of the tonsils if they areremoved.C. The tonsils have been shown to have a vital role to play in the physiology oflaboratory rabbits and guinea pigs.D. The human tonsil develops as part of the immune system, a system of vitalimportance in defense against disease.E. Tonsillectomies are performed only when the tonsils become seriously infected.

13. Photography is no longer an art form. Nowadays everyone has access to digitalcameras that only need to be pointed at the subject in order to generate a perfectimage.

The writer of the argument apparently assumes that

A. the selection of the subject is not an important artistic factor in photographyB. digital cameras will continue to improve in qualityC. digital cameras can never go wrongD. photography with all other types of camera is an art form

E. art is not perfect

14. The enormous distances between stars are not spaces entirely devoid of matter.The interstellar spaces are filled with ‘dust’: very low density matter. Thisminiscule amount of matter, spread over almost infinite distances, acts like acurtain obscuring the stars that lie behind. If it were not for this material we wouldsee no dark patches in the sky at night: the sky would be entirely covered withstars.

The two parts in boldface play what roles in the argument above?

A. The first is a suggestion that the author wishes to dispute. The second ishypothesis that the author wishes to explain.B. The first is the main point the author wishes to make. The second is ahypothetical result of accepting that point.C. The first is a fact that the author thinks is important in explaining a certainphenomenon. The second is a result that the author would expect if that fact werenot true.

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Which is the following is an assumption that the researchers apparently made inthis study?

A. The women who participated in the study were sufficiently representative ofmodern women in general.

B. Male faces are, in general, attractive to women.C. Visual images are important to women.D. It is impossible to predict what features an ideal face would have.E. Women in previous ages would have preferred more masculine men.

18. Red is a color which has powerful effects on human beings as well as animals. Agroup of psychologists carried out an experiment which confirms the subconsciouseffects of this color on human behavior. They provided selected sports teams atschool and college level with either red or blue shorts and recorded the outcome ofthe games. The teams wearing red won in a disproportionate number of matches. The psychologists suggested that either the teams wearing red subconsciously felt

themselves more powerful, or that the non-red teams were subconsciouslyintimidated by the red color.

Which of the following, if true, would most weaken the psychologists‟ suggestion?

A. Each team wore red in some matches and blue in others.B. The color blue has the subconscious effect of making human beings lesscompetitive.C. The effect was only observed if all the team members wore white shirts.D. Red signifies danger in some cultures whereas it signifies happiness in others.

E. In a subsequent study, teams with all-red outfits were more likely to report thatthey thought they would win no matter what color the opponents wore.

19. It is often thought that our own modern age is unique in having a large numberof people who live into old age. It has frequently been assumed that plagues, wars,and harsh working conditions killed off most people in previous ages before theycould reach old age. However, recent research shows that in 17th centuryEurope, for example, people over sixty comprised 10 percent of thepopulation. The studies also revealed that although infant mortality remained highuntil the 20th century in Europe, people who survived to adulthood could expectto live to be old.

The portions in boldface play which of the following roles in the argument above?

A. The first is a conclusion that the author supports. The second is data thatcontradicts that conclusion.B. The first is a finding that the author contests. The second is a finding that theauthor accepts.

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C. The first is an assumption that the author thinks is invalid. The second is datathat validates that assumption.D. The first is a position that the author opposes. The second is a finding thatsupports the author‟s position.E. The first is a position that the author opposes. The second is an assumptionwhich, if valid, negates the author‟s view.

20. A marriage counselor noted that couples who have occasional violent argumentsare less likely to divorce within the next six months than those who have frequentbut less violent arguments. He concluded that frequent arguing is a major factor inthe causation of severe marital disharmony.

The counselor‟s conclusion is most weakened by which of the followingobservations?

A. Couples who have already come to the point of divorce argue continuously over

small matters.B. People who have recently divorced are more likely to argue violently when theymeet.C. Many people in happy marriages have occasional violent arguments.D. Recently divorced people rarely cite frequent arguments as a cause of maritaldisharmonyE. A significant fraction of couples close to divorce do not talk to each other.

21. The Dean claimed that, as a result of continued cutbacks in the budget for purescience research, fewer students are choosing a career in physics, and therefore thenumber of postgraduate students studying physics is likely to decline.

Which of the following, if true, casts most doubt on the Dean‟s conclusion?

A. The number of students majoring in physics at the undergraduate level has beenincreasing steadily over the years, a trend that is expected to continue.B. The number of students studying chemistry declined even before cutbacks inresearch funding were noted.C. Most postgraduate students of physics move to careers in computer science andengineering.D. The Dean‟s own university has recently increased the number of staff membersteaching physics.E. The budget cutbacks are less severe for the pure sciences than for appliedsciences.

22. A nature conservancy expert found little support for his campaign to protecttoads. He suggested that, even thought the campaign highlighted the vital role thetoads played in the ecology of the region, people were unenthusiastic about savingtoads as these animals are perceived as unpleasant creatures, and people seldomfeel passionate about animals with which they have no positive feelings.

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The expert‟s opinion would be most strengthened by which of the followingobservations?

A. Ecological conservation is an increasingly important concern in the region.

B. A recent campaign to save bats achieved a measure of success only after acartoon bat was adopted as the mascot of the local football team.C. Snakes and lizards also need protection in this region as a result of humanactivity.D. The campaign to protect toads has been in existence for over five years and yetthe toad population continues to decline.E. The children in the local schools were found to have a greater aversion to toadsthan to snakes.

23. Many people report that exposure to certain foods such as cheese, red wine, andchocolate, are associated with the onset of migraine headaches. Other people report

that exposure to certain smells (especially strong perfumes) seems to trigger amigraine headache, and some note that exposure to bright and flickering lights canbe followed by a migraine. It would seem that a person with a tendency to getmigraines should try to find which of these situations is associated with the onset ofthe headache and then avoid this stimulus.

All of the following, if true, would indicate potential problems with therecommendation above except

A. the time delay between the trigger and the onset of the headache can make it

exceptionally difficult to identify the triggerB. the presence of a known trigger doesn‟t always cause a migraineC. in many cases an internal hormonal change triggers a migraineD. in a high proportion of cases the patients report multiple triggers for theirheadachesE. most of the known triggers are common and almost unavoidable features ofmodern life

24. It is strange that in Sentacity there are so many corner shops selling food items.After all there are many supermarkets in the city which sell food at cheaper prices,and many of these supermarkets are open 24-hours.

Which of the following, if true, would be of least help in explaining the paradoxicalobservation?

A. The corner shops are selling specialist food items not available in thesupermarkets.B. The supermarkets are mostly located on the outskirts of the city and requireresidents to use cars or public transport to reach them.

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C. The main business of the local shops is newspaper distribution and food itemsrepresent a small part of their turnover.D. The corner shops are mainly family-owned businesses and have been there formuch longer than the supermarkets and are perceived as an important feature ofthe community.E. The corner shops are willing to make home deliveries.

Exercise 2:

1. Fact 1: Television advertising is becoming less effective: the promotion of brandnames promoted on television that viewers of the advertising can recall is slowlydecreasing.

Fact 2: Television viewers recall commercials aired first or last in a cluster ofconsecutive commercials far better than they recall commercials aired somewhere inthe middle.

Fact 2 would be most likely to contribute to an explanation of fact 1 if which of thefollowing were also true?

a. The total time allotted to the average cluster of consecutive televisioncommercials is decreasing.b. The average number of clusters of consecutive commercials per hour of television

is increasing.c. The average number of hours per day that people spend watching television isdecreasing.d. The average number of television commercials in a cluster of consecutivecommercials is increasing.e. The average television viewer currently recalls fewer than half the brand namespromoted in commercials he or she saw.

2. The average normal infant born in the United States weighs between twelve andfourteen pounds at the age of three months. Therefore, if a three-month-old childweighs only ten pounds, its weight gain has been below the United States average.

Which of the following indicates a flaw in the reasoning above?

a. The phrase "below average" does not necessarily mean insufficient.b. Average weight gain is not the same as average weight.c. Some three-month old children weigh as much as seventeen pounds.d. It is possible for a normal child to weigh ten pounds at birth.e. Weight is only one measure of normal infant development.

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3. Which of the following best completes the passage below?

People buy prestige when they buy a premium product. They want to be associatedwith something special. Mass-marketing techniques and price-reduction strategiesshould not be used because ___________ .

a. continued sales depend directly on the maintenance of an aura of exclusivityb. expansion of the market niche to include a broader spectrum of consumers willincrease profitsc. manufacturing a premium brand is not necessarily more costly thanmanufacturing a standard brand of the same productd. affluent purchasers currently represent a shrinking portion of the population ofall purchaserse. purchasers of premium products are concerned with the quality as well as withthe price of the products

4. Which of the following best completes the passage below?

In a survey of job applicants, two-fifths admitted to being at least a little dishonest.However, the survey may underestimate the proportion of job applicants who aredishonest, because _____.

a. some generally honest people taking the survey might have claimed on thesurvey to be dishonestb. some people who claimed on the survey to be dishonest may have beenanswering honestlyc. some people who claimed on the survey to be at least a little dishonest may bevery dishonest

d. some dishonest people taking the survey might have claimed on the survey to behoneste. some people who are not job applicants are probably at least a little dishonest

5. A program instituted in a particular state allows parents to prepay theirchildren's future college tuition at current rates. The program then pays the tuitionannually for the child at any of the state's public colleges in which the child enrolls.Parents should participate in the program as a means of decreasing the cost of their

children's college education.

Which of the following, if true, is the most appropriate reason for parents not toparticipate in the program?

a. The prepayment plan would not cover the cost of room and board at any of thestate's public colleges.

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b. The amount of money accumulated by putting the prepayment funds in aninterest-bearing account today will be greater than the total cost of tuition for any ofthe public colleges when the child enrolls.c. Some of the state's public colleges are contemplating large increases in tuitionnext year.d. The annual cost of tuition at the state's public colleges is expected to increase at

a faster rate than the annual increase in the cost of living.e. The parents are unsure about which public college in the state the child willattend.

6. Most consumers do not get much use out of the sports equipment they purchase.For example, seventeen percent of adults in the United States own jogging shoes,but only forty-five percent of the owners jog more than once a year, and onlyseventeen percent jog more than once a week.

Which of the following, if true casts most doubt on the claim that most consumersget little use out of the sports equipment they purchase?

a. Many consumers purchase jogging shoes for use in activities other than jogging.b. Joggers who jog more than once a week are often active participants in othersports as well.c. Consumers who take up jogging often purchase an athletic shoe that can beused in other sports.d. Joggers are most susceptible to sports injuries during the first six months inwhich they jog.e. Joggers often exaggerate the frequency with which they jog in surveys designedto elicit such information.

7. It is true that it is against international law to sell plutonium to countries that donot yet have nuclear weapons. But if United States companies do not do so,companies in other countries will.

Which of the following is most like the argument above in its logical structure?

a. It is true that it is illegal for a government official to participate in a transactionin which there is an apparent conflict of interest. But if the facts are examinedcarefully, it will clearly be seen that there was no actual conflict of interest in thedefendant's case.b. It is true that it is against the police department's policy to negotiate with

kidnappers. But if the police want to prevent loss of life, they must negotiate insome cases.c. It is true that it is against the law to burglarize people's homes. But someone elsecertainly would have burglarized the house if the defendant had not done so first.d. It is true that company policy forbids supervisors to fire employees without twowritten warnings. But there have been many supervisors who have disobeyed thispolicy.

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e. It is true that it is illegal to refuse to register for military service. But there is along tradition in the United States of conscientious objection to serving in the armedforces.

8. Neither a rising standard of living nor balanced trade, by itself, establishes acountry's ability to compete in the international marketplace. Both are required

simultaneously since standards of living can rise because of growing trade deficitsand trade can be balanced by means of a decline in a country's standard of living.

If the facts stated in the passage above are true, a proper test of a country's abilityto be competitive is its ability to

a. keep its standard of living constant while trade deficits rise.b. balance its trade while its standard of living rises.c. balance its trade while its standard of living falls.d. increase trade deficits while its standard of living rises.e. decrease trade deficits while its standard of living falls.

9. The program to control the entry of illegal drugs into the country was failure in1987. If the program had been successful, the wholesale price of most illegal drugswould not have dropped substantially in 1987.

The argument in the passage depends on which of the following assumptions?

a. The price paid for most illegal drugs by the average consumer did not dropsubstantially in 1987.b. The supply of illegal drugs dropped substantially in 1987.c. The wholesale price of a few illegal drugs increased substantially in 1987.

d. Domestic production of illegal drugs increased at a higher rate than did the entryof such drugs into the country.e. A drop in demand for most illegal drugs in 1987 was not the sole cause of thedrop in their wholesale price.

10. The program to control the entry of illegal drugs into the country was failure in1987. If the program had been successful, the wholesale price of most illegal drugswould not have dropped substantially in 1987.

The argument in the passage would be most seriously weakened if it were true that

a. in 1987 smugglers of illegal drugs, as a group, had significantly more funds attheir disposal than did the country's customs agents.b.domestic production of illegal drugs increased substantially in 1987.c. in 1987 illegal drugs entered the country by a different set of routes than theydid in 1986.d. the author's statements were made in order to embarrass the officialsresponsible for the drug-control program.e. the country's citizens spent substantially more money on illegal drugs in 1987than they did in 1986.

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11. Hardin argued that grazing land held in common (that is, open to any user)would always be used less carefully than private grazing land. Each rancher wouldbe tempted to overuse common land because the benefits would accrue to theindividual, while the costs of reduced land quality that results from overuse wouldbe spread among all users. But a study comparing 217 million acres of common

grazing land with 433 million acres of private grazing land showed that the commonland was in better condition.

The answer to which of the following questions would be most useful in evaluatingthe significance, in relation to Hardin's claim, of the study described above?

a. Was the private land that was studied of comparable quality to the common landbefore either was used for grazing?b. Did any of the ranchers whose land was studied use both common and privateland?c. Were the users of the common land that was studied at least as prosperous as

the users of the private land?d. Did the ranchers whose land was studied tend to prefer using common landbefore either was used for grazing?e. Were there any owners of herds who used only common land, and no privateland for grazing.

12. Hardin argued that grazing land held in common (that is, open to any user)would always be used less carefully than private grazing land. Each rancher wouldbe tempted to overuse common land because the benefits would accrue to theindividual, while the costs of reduced land quality that results from overuse wouldbe spread among all users. But a study comparing 217 million acres of common

grazing land with 433 million acres of private grazing land showed that the commonland was in better condition.

Which of the following, if true and known by the ranchers, would best help explainthe results of the study?

a. With private grazing land, both the costs and the benefits of overuse fall to theindividual user.b. An individual who overuses common grazing land might be able to achieve higherreturns than other users can, with the result that he or she would obtain acompetitive advantage.

c. The cost in reduced land quality that is attributable to any individual user is lesseasily measured with common land than it is with private land.d. If one user of common land overuses it even sightly, the other users are likely todo so even more, with the consequence that the costs to each user outweigh thebenefits.e. there are more acres of grazing held privately than there are held in common.

13.

In Los Angeles, a political candidate who buys saturation radioadvertising will get maximum name recognition.

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The statement above logically conveys which of the following?

A. Radio advertising is the most important factor in political campaigns inLos Angeles.

B.

Maximum name recognition in Los Angeles will help a candidate to wina higher percentage of votes cast in the city.

C.

Saturation radio advertising reaches every demographically distinctsector of the voting population of Los Angeles.D. For maximum name recognition a candidate need not spend on media

channels other than radio advertising.E. A candidate's record of achievement in the Los Angeles area will do little

to affect his or her name recognition there.

14.

The rate of violent crime in this state is up 30 percent from last year. The fault lies entirely in our court system: Recently our judges' sentenceshave been so lenient that criminals can now do almost anything without fearof a long prison term.

The argument above would be weakened if it were true that

a. 85 percent of the other states in the nation have lower crime rates thandoes this state.

b. white collar crime in this state has also increased by over 25 percent inthe last year.

c. 35 percent of the police in this state have been laid off in the last yeardue to budget cuts.

d.

polls show that 65 percent of the population in this state oppose capitalpunishment.

e.

the state has hired 25 new judges in the last year to compensate fordeaths and retirements.15.

The increase in the number of newspaper articles exposed asfabrications serves to bolster the contention that publishers are moreinterested in boosting circulation than in printing the truth. Even minorpublications have staffs to check such obvious fraud.

The argument above assumes that

a. newspaper stories exposed as fabrications are a recent phenomenon.b.

everything a newspaper prints must be factually verifiable.

c.

fact checking is more comprehensive for minor publications than formajor ones.d.

only recently have newspapers admitted to publishing intentionallyfraudulent stories.

e.

the publishers of newspapers are the people who decide what to print intheir newspapers.

16.

Bill earns more commission than does Sandra. But since Andrew earnsmore commission than does Lisa, it follows that Bill earns more commissionthan does Lisa.

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Any of the following, if introduced into the argument as an additional premise, makes theargument above logically correct EXCEPT:

a.

Andrew earns more commission than Billb. Sandra earns more commission than Lisac.

Sandra earns more commission than Andrewd.

Sandra and Andrew earn the same amount of commissione.

Bill and Andrew earn the same amount of commission17.

During the SARS days, about 23,500 doctors who had treated SARSsufferers died and about 23,670 doctors who had not engaged in treatment forSARS sufferers died. On the basis of those figures, it can be concluded that itwas not much more dangerous to participate in SARS treatment during theSARS day than it was not to participate in SARS treatment.

Which of the following would reveal most clearly the absurdity of the conclusion drawnabove?

a. Counting deaths among doctors who had participated in SARS

treatment in addition to deaths among doctors who had not participatedin SARS treatment

b.

Expressing the difference between the numbers of deaths amongdoctors who had treated SARS sufferers and doctors who had nottreated SARS suffers as a percentage of the total number of deaths

c. Separating deaths caused by accidents during the treatment to SARSsuffers from deaths caused by infect of SARS suffers.

d.

Comparing death rates per thousand members of each group ratherthan comparing total numbers of deaths

e.

Comparing deaths caused by accidents in the United States to deathscaused by infect in treating SARS suffers.

18.

In 2003 an airline in United State lost more than half, on average, of theforeign passengers they had previously served each year. Researchers havealleged that this extreme drop resulted from a rise in price of tickets forinternational lines from $60 to $90 per 1,000 miles.

Which of the following, if feasible, offers the best prospects for alleviating the problem of thedrop in passengers as the researchers assessed it?

a.

Cooperating with other airlines to provide more international lines.b. Allowing foreign passengers to pay the same as the previous

international line

c.

Reemphasizing the goals and mission of the airline as serving bothdomestic passengers and foreign passengers

d. Increasing the financial resources of the airline by raising the ticketprice for domestic passengers

e. Offering superior VIP service for foreign passengers.

Answers:

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Exercise 1:

1. B2. D

3. C4. D5. A6. E7. D8. C9. C10. B11. D12. B13. A

14. C15. E16. E17. A18. B19. D20. A21. C22. B23. B24. E

Exercise 2:

1. d 2. b 3. a 4. d 5. b 6. a7. c 8. b 9. e 10. b 11. a 12. d13. d 14. c 15. e 16. a 17. d 18. b

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Cubes

Examples

Directions: A cube is coloured red on all faces. It is cut into 64 smaller cubes of equal size. Now,answer the following questions based on this statement.

Example 1. How many cubes have no face coloured?(a) 24(b) 8(c) 0(d) 16

Example 2. How many cubes are there which have only one face coloured?(a) 4(b) 16(c) 24(d) 8

Example 3. How many cubes have two red opposite face?(a) 8(b) 16(c) 24(d) 0

Example 4. How many cubes have three faces coloured(a) 16(b) 24(c) 4(d) 8

Solution. The given figure shows the cube coloured real on all faces, and divide into 64 smallercubes.

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Here n = Side of big cube/Side of small cube= 4/1 = 4

1. Number of smaller cubes with no surface painted= (n – 2)3 = (4 – 2)3 = 23 = 8

2. Number of smaller cubes with one surface painted(n – 2)2 × 6 = (4 – 2)2 × 6

= 22 × 6 = 24

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3. Number of smaller cubes with two surface painted= (n – 2) × 12 = (4 – 2) × 12

2 × 12 = 24

4. Number of smaller cubes with three surfaces painted = 8

Exercise 20

Directions: A wooden cube is painted blue on all the four adjoining sides and green on two oppositesides, i.e., top and bottom. It is then cut at equal distances at right angles four times vertically (top tobottom) and two times horizontally (along the sides) as shown in the figure, where the dotted linesrepresents the cuts made. Study diagram and answer the following questions:

1. How many cubes will have one face painted only in Blue?(a) 2(b) 1(c) 4(d) 3

2. How many cubes will have one face painted only in Green?

(a)

1(b) 2(c) 3(d) 4

3. How many cubes arte formed in all ?(a) 24(b) 27(c) 32(d) 16

4. How many cubes will have at least three sides painted.(a) 6

(b)

2(c) 3(d) 8

5. How many cubes will have no face painted at all ?(a) 5(b) 4(c) 3(d) 2

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Directions: A cube is coloured red on two opposite faces. Blue on two adjacent faces and yellow onthe two remaining faces. It is then cut into two halves along the plane parallel to the red faces. Onepiece is then cut into four equal cubes and the other one into 32 equal cubes.

6. How man cubes do not have any coloured face?(a) 2(b) 4(c) 8(d)

0

7. How many cubes do not have any red face?(a) 16(b) 8(c) 24(d) 20

8. How many cubes have at least two coloured faces?(a) 20(b) 24(c) 28(d) 32

9. How many cubes have each a yellow face with other faces blank?(a) 16(b) 14(c) 17(d) 4

10. How many cubes have at least one blue face?(a) 14(b) 16(c) 20(d) 4

Directions: A cube is painted red on two adjacent faces and black on the faces opposite to the redfaces and green on the remaining faces is cut into sixty-four smaller cubes of equal size.

11. How many cubes are there which have no face painted?(a) 0(b) 4(c) 8(d) 16

12. How many cubes have only one face painted?(a) 8(b) 16(c) 24(d)

32

13. How many cubes have less then three faces painted?(a) 8(b) 24(c) 28(d) 48

14. How many cubes are there with three faces painted ?

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(a) 8(b) 16(c) 4(d) 24

15. How many cubes have one face green and one of the adjacent faces black or red ?(a) 8(b) 16(c)

24(d) 28

Direction: A cube is painted red on two adjacent faces and on one opposite face, yellow on twoopposite faces and green on the remaining face. It is then cut into 64 equal cubes.

16. How many cubes have only one red coloured face?(a) 8(b) 4(c) 16(d) 12

Directions: A solid cube has been painted yellow, blue and black on pairs of opposite face. The cubeis the cut into 36 smaller cubes such that 32 cubes are of the same size while 4 others are of biggersize. Also no face of any of the bigger cubes is painted blue.

17. How many cubes have at least one face painted blue.(a) 0(b) 8(c) 16(d) 32

18. How many cubes have only one face painted.(a) 12(b) 8(c) 4(d) 0

19.

How many cubes have at least two faces painted.(a) 8(b) 16(c) 20(d) 24

20. How many cubes have two or more faces painted.(a) 36

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(b) 34(c) 28(d) 24

21. How many cubes only three faces painted?(a) 8(b) 4(c) 2(d)

0

22. How many cubes do not have any of their faces painted yellow?(a) 0(b) 8(c) 16(d) 20

23. How many cubes have at least one of their faces painted black ?(a) 0(b) 8(c) 16(d) 20

24. How many cubes have at least one of their faces painted yellow or blue?(a) 36(b) 32(c) 16(d) 0

25. How many cubes have no face painted?(a) 0(b) 8(c) 12(d) 16

26.

How many cubes have two faces painted yellow and black respectively?(a) 0(b) 8(c) 12(d) 16

Directions: A cube is painted blue on all faces is cut into 125 cubes of equal size. Now, answer thefollowing questions

27. How many cubes are not painted on any face?(a) 8(b) 16(c) 18(d)

27

28. How many cubes are painted on one face only?(a) 8(b) 16(c) 36(d) 54

Directions :A cuboid of dimensions (4 cm x 3 cm x 3 cm). The block is painted yellow on the pair ofopposite surfaces of dimensions (4 cm x 3 cm). Remaining two opposite surfaces of dimensions (4 cm

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x 3 cm) are painted red. And two surfaces of dimensions (3 cm x 3 cm) are painted with greencolours. Now the block is divided among cubes of dimensions (1 cm x 1 cm 1 cm)?

29. How many smaller cubes will have one surface painted?(a) 16(b) 12(c) 14(d) 18

30. How many cubes will have no surfaces painted?(a) 1(b) 4(c) 2(d) 8

31. In how many cubes all the three colours appear?(a) 24(b) 20(c) 8(d) 16

32.

How many cubes will have only two surfaces painted ?(a) 12(b) 16(c) 20(d) 32

33. How many cubes will have at least one surface painted?(a) 32(b) 18(c) 24(d) None of these

Directions: A solid cube each side 8 cm has been painted red, blue and black on pairs of oppositefaces. It is then cut into cubical block of each side 2 cm.

34.

How many cubes have no face painted?(a) 0(b) 4(c) 8(d) 12

35. How many cubes have only one face painted?(a) 8(b) 16

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(c) 24(d) 28

36. How many cubes have only two faces?(a) 8(b) 16(c) 20(d) 24

37. How many cubes have three faces painted?(a) 0(b) 4(c) 6(d) 8

38. How many cubes have three faces painted with different colours?(a) 0(b) 4(c) 8(d) 12

39.

How many cubes have two faces painted red and black and all other faces unpainted?(a) 4(b) 8(c) 16(d) 32

40. How many cubes have only one face painted red and all other faces unpainted ?(a) 4(b) 8(c) 12(d) 16

41. How many cubes have two faces painted black?(a)

2(b) 4(c) 8(d) None

42. How many cubes have one face painted blue and one face painted red?(the other faces may be painted or unpainted):

(a) 16(b) 12(c) 8(d) 0

43. How many cubes are there in all?(a)

64(b) 56(c) 40(d) 32

Directions: The six faces of a cube are coloured black brown, green, red ,white and blue, such that:(i) Red is opposite black(ii) Green is between red and black(iii) Blue is adjacent to White

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(iv) Brown is adjacent to blue(v) Red is at the bottom.

Answer the following questions based on this information.

44. Which colour is opposite brown?(a) White(b) Red(c)

Green(d) Blue

45. The four adjacent colours are(a) Black, Blue, Brown, Red(b) Black, Blue, Brown, White(c) Black, Blue, Red, White(d) Black, Brown, Red, White

46. Which of the following can be deduced from (i) and (iv)(a) Black in on the top(b) Blue is on the top(c) Brown is on the top(d)

Brown is opposite Black

Logical Deductions

Types of statements:

The statements can be divided into four categories depending on their sense. They are

1. General

2. Particular3.

Negative and

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4. Particular Negative

A general statement starts with a word “all” or “every” or “each”

Eg: All x are y.Every x is y.

A particular statement focuses on a particular group or sector. It normally starts with “some”,“many”, “most” or a name.

Eg: Some x are y.Many x are y.Sachin is good.

A negative statement contains a negative word like “no” or “not”.

Eg: No x is y.All y are not x.

A particular negative statement combine both the features of particular and negative statement.

Eg: Some x are not y.Many y are not z.Sachin is not good.

Distribution:

When “All x are y” is given we can say that all the points of set x belong to y but we cant define sucha property common to all the points of y. In other words we can say a property common to all pointsof x but not y. Then it is said that “x” is distributed but “y” is not.

In “All x are y”, x becomes the subject and y becomes the object.

So, a general statement distributes only the subject but not the object.

Similarly, a particular statement distributes neither subject nor the object.

A negative statement distributes both the subject and the object.

A particular statement distributes the object but not the subject.

In short, the distribution can be said as follows:

General statement: Subject – Yes Object – NoParticular Statement: Subject – No Object – NoNegative Statement: Subject – Yes Object – YesParticular Negative: Subject – No Object – Yes

Deriving a deduction:

When two statements are given to you, your duty is to derive a deduction that logically follows boththe statements logically. For this we will make use of the distribution. The process of deriving aconclusion is as follows:

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Step 1: Identify the common term for both the statements. If no common term is present the nodeduction can be derived.

Step 2: Apply the distribution properties to subjects and objects depending on the type of thestatement.

Rule: If and only if the common term is having the distribution only once, then the deduction can bederived. Else there can be no deduction.

Eg: All x are y. All x are z.

Soln: Common term : xIn first statement and the second statement, x is distributed (since x is subject in both).

So the common term has 2 distributions => no deduction follows.

Step 3: When you decide that there is a deduction possible then read out all the words present inthe two statements excluding the common term and repeated words, from left to right.

Eg:

All x are y. All y are z.

Soln:

Common term: y. It is distributed only once (in second statement).

So a deduction can follow. It is All x are z. (Excluding y and repeated words).

Rule: Particularity and negation are called special properties and if any statement contains a specialproperty the same should be followed by the conclusion also.

Eg:

Some x are y. All y are z.

Soln:

Common term: y. It is distributed only once (in second statement).

So a deduction follows. It is Some x are z. (Here some is a special property and so conclusion alsofollows the same. Common term is excluded.)Rule: For two particular or negative statements there can be no conclusion.

Examples:

1. All x are y. All z are y.

Soln:

No conclusion follows. (since common term y is not distributed at all)

2. All x are y. Some y are z.

Soln:

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No conclusion since common term y is not distributed at all.

3. All x are y. No y is z.

Soln:

No x is z (or) No z is x. (Since No is a special property)

4. Some x are y. No y is z.

Soln:

Some x are not z. (Since some and not are special properties and so should be present in conclusion).

Exercise:

1.

All books are hooks.All hooks are crooks.

a) All hooks are books.b) All crooks are hooks.c) All crooks are books.d) All books are crooks.

2. Some crooks are hooks.No hook is a book.

a) Some hooks are not books.b) Some hooks are crooks.c) Some crooks are books.d) Some crooks are not books.

3. Some goods are expensive.Some expensive things are qualitative.

a) Some goods are qualitative.b) Some goods are not qualitative.c) Some qualitative are goods.d) No conclusion

4. All posters are good looking.Some posters are expensive.

a) Some good looking are not expensive.b) Some good looking are expensive.c) Some expensive are not good looking.d) Some expensive are good looking.

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5. All expensive are posters.Some good looking are posters.

a) Some posters are good looking.b) Some good looking are expensive.c) Some expensive are good looking.d) None of these

6. All boxes are dolls.No baskets are boxes.

a) Some dolls are baskets.b) Some dolls are not baskets.c) Some baskets are not dolls.d) None of these

7. All dolls are boxes.No baskets are boxes.

a) Some dolls are not baskets.b) Some dolls are baskets.c) No dolls are baskets.d) None of these

8. No tables are watches.Some watches are lamps.

a) Some lamps are tables.b) No lamp is a table.c) Some lamps are not tables.d) None of these

9. All my girl friends are beautiful.Sudha is very beautiful.

a) Sudha is my friend.b) Sudha is not my friend.c) (a) or (b)

d) None of these

10. No cow is a cat.All cats are rats.

a) Some rats are cats.b) Some rats are not cats.c) Some rats are not cows.d) None of these

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11. All women are men.All men are crazy.

a) All men are women.b) No men is crazy.c) All women are crazy.d) All crazy are women.

12. Some shirts are benches.No bench is a table.

a) Some shirts are tables.b) Some shirts are not tables.c) No table is a shirt.d) None of these

13. All roads are poles.No pole is a house.

a) Some roads are houses.b) Some roads are not houses.c) No road is house.d) None of these

14. No man is monkey. John is a man.

a) John is not a monkey.b) John may or may not be a monkey.c) (a) or (b)d) None of these

15. All businessmen except Ramji are dishonest.All dishonest people smoke.

a) All businessmen except Ramji smoke.b) Ramji does not smoke.c) (a) or (b)d) None of these

16. Few takers are givers.No givers are almighty.

a) Some givers are not takers.b) Some takers are not almighty.c) Some almighty are takers.d) None of these

17. Some crows are jackals.No fox is a crow.

a) Some jackals are not foxes.

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b) Some jackals are foxes.c) No jackal is a fox.d) No fox is a jackal.

18. Only cats are animals.No historian is an animal.

a) Some cats are historians.b) Some historians are cats.c) Some cats are not historians.d) Some historians are not cats.

19. Some girls are cute.Some Americans are cute.

a) Some Americans are not cute.b) Some girls are Americans.c) Some girls are not Americans.d) None of these

20. No kindhearted is bandit.All bandits are blackmailers.

a) Some blackmailers are kindhearted.b) Some kindhearted are blackmailers.c) Some kindhearted are not blackmailers.d) Some blackmailers are not kindhearted.

21. No fruit is a flower.No flower is a stem.

a) No fruit is a stem.b) Some fruits are not stems.c) No stem is a fruit.d) None of these

22. Some bowls are dishes.No dish is a glass.

a) Some bowls are not glasses.b) Some glasses are not bowls.c) No bowl is a glass.

d) No glass is a bowl.

23. Some bowls are plates.All plates are glasses.

a) Some bowls are not glasses.b) Some glasses are bowls.c) Some bowls are glasses.d) None of these

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24. Some huts are not buildings.No building is a hotel.

a) Some huts are not hotels.b) No hotel is a hut.c) Some hotels are not huts.d) None of these

25. All cups are pens.Some pens are tables.

a) Some cups are tables.b) Some tables are cups.c) Some cups are not tables.d) None of these

26. All colleges are schools.No theatre is a school.

a) No school is a theatre.b) Some colleges are not schools.c) Some colleges are not theatres.d) No college is a theatre.

27. Some computers are CPUs.All CPUs are mouses.

a) Some computers are not mouses.b) Some mouses are computers.c) Some computers are mouses.d) None of these

28. Some horses are dogs.No rabbit is a dog.

a) Some horses are not rabbits.b) Some horses are rabbits.c) No horse is a rabbit.d) None of these

29. Some pearls are beads.All rings are beads.

a) Some pearls are rings.b) All rings are pearls.c) Some rings are pearls.d) None of these

30. Some biscuits are chocolates.No brinks are biscuits.

a) No biscuits are fruits.

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b) Some chocolates are drinks.c) Some drinks are not chocolates.d) None of these

Data Interpretation

It deals with careful reading, understanding, organizing and interpreting the data

provided so as to derive meaningful conclusions. Mostly used tools for interpretation of a data are

o Ratioo

Percentageo Rateo Average

Types of Data Interpretation: The numerical data pertaining to any event can bepresented by any one or more of the following methods.

1. Tables2. Line Graphs3. Bar Graphs or Bar Charts

4.

Pie Charts or Circle Graphs

1. Tables: It is the systematic presentation of data in tabular form to understand the giveninformation and to make clear the problem in a certain field of study. It has six elementsnamely:

o Title: It is the heading of the table.o Stule: It is the section of the table containing row headingso Column Captions: It is the heading of each columno Body: It consists the numerical figures

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o

Footnotes: It is for further explanation of the tableo Source: It is the authority of the data

Eg: Study the following table and answer the questions given below it.

Annual Income of Five Schools

Figures in ‟00 rupees Sources of Income School A School B School C School D School E

Tuition Fee 120 60 210 90 120 Term Fee 24 12 45 24 30Donations 54 21 60 51 60

Funds 60 54 120 42 55Miscellaneous 12 3 15 3 15

Total 270 150 450 210 280

1. The income by way of donation to school D is what per-cent of its miscellaneous?

Sol: Required percentage = %27

300

5100

2. Line Graph: A line graph indicates the variation of a quantity w.r.t two parameterscalibrated on X and Y-axis respectively.Note:

1. Any part of the line graph parallel to X-axis represents no change in the value of Yparameter w.r.t the value of X parameter.

2. The steepest or maximum part of the line graph indicates maximum percentagechange of the value during the two consecutive period in which the related part lies.

3. If the steepest part is a rise slope, then it is the highest percentage growth.

4.

If the steepest part is a decline slope, it will represent a maximum percentage fall ofthe value calibrated in the other axis.

3. Bar Graph: Bar graphs are diagrammatic representation of a discrete data.

Types of Bar Graphs:

o Simple Bar Graphs: A simple bar graph relates to only one variable. The values ofthe variables may relate to different years or different terms.

o

Sub-divided Bar Graph: It is used to represent various parts of sub-classes of totalmagnitude of the given variable.

o Multiple Bar Graphs: In this type, two or more bars are constructed adjoining eachother, to represent either different components of a total or to show multiplevariables.

4. Pie Chart: In this method of representation, the total quantity is distributed over a total

angle of o360 which is one complete circle or pie.

Note: Here, the data can be plotted w.r.t only one parameter.

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Exercise

Directions (Questions 1 to 5): In the graph given below, the sales in Rs. Thousand areshown. Answer the questions based on it.

1. By

how much the amount of sales in 1991 was less than those in 1993?

a) Rs.100 b) Rs.1 lakhc) Rs. One thousand d) None of these

2. What were the approximate average sales (in thousands) for period 1990 to 1995?a) 300 b) 400c) 450 d) None of these

3. The sales in 1991 are what percent of those in 1992?a) 80 b) 70c) 15 d) 45

S a l e s i n

t h o u s a n d s

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4. In which year the sales showed the least percentage increase to those in preceding year?

a) 1990 b) 1992c) 1993 d) 1994

5. The sales in 1994 are how many times to those in 1992?

a) 1.4 b) 1.1c) 0.60 d) 0.75Directions (Questions 6 to 10): Study the table carefully and answer the questionsgiven below it.

Factories 1990 1991 1992 1993 1994

A 15 18 25 15 18B 12 23 40 20 15C 20 20 50 25 20D 25 18 38 14 18E 30 32 32 30 30

6. In which year, the production of cars of all factories was the closest to the averageno. of cars produced during 1990-1994?a) 1990 b) 1991c) 1994 d) None of these

7. Which factory showed a decrease of 20% in the production of cars in 1994 ascompared to 1993?a) A & C b) Bc) C d) D & E

8.

In which of the given years was there maximum production of cars?a) 1994 b) 1993c) 1990 d) None of these

9. What is the ratio of production of cars of factory A to that of factory E in 1994?a) 5 : 3 b) 3 : 5c) 2 : 7 d) None of these

10. In which year was the total production of cars of factories about 30% of the totalproduction of cars during 1990-1994?a) 1991 b) 1993

c) 1994 d) 1992

Production of Cars in different factories during the period 1990-1994

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Directions (Questions 11 to 15): India‟s total trade with foreign countries for a year isgiven in the pie charts as shown below. Analyze the charts carefully and answer thequestions based on them.

11. India‟s exports to which of thefollowing countries are more than theimports from that country?a) U.S.A. b) U.S.S.R.

c) JAPAN d) Both

U.S.A. & U.S.S.R.

12. The ratio of the angle subtended bythe arcs corresponding to U.S.A. forthe exports to imports is nearly?

a)1659

11315

x

x b)

1139

16515

x

x

c) 1.67 d) 1.33

13. The ratio of the total imports fromFrance and U.K. to the total exportsto these countries is nearly?

a) 1.25 b) 1.33c) 1.22 d) 1.46

14. Which of the following statement is not true?a) The exports to Japan are less than the imports from Japan.b) The imports from U.K. are more than the exports to U.K. by 6% of Rs.51,959 million.c) The total exports of U.S.A., U.S.S.R., Japan, U.K., West Germany and France are morethan the total imports from these countries.

d) Two of the above statements are true.

15. If the area of the sector corresponding to U.S.S.R. in exports pie chart is A, the areaof the sector corresponding to Japan in the imports pie chart is? (the radii of both thecircles being same)

a)2

A b)

8

3 A

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c)8

5 A d)

8

7 A

Directions (Questions 16 to 20): Study the following table carefully & answer thequestions given below.

Sugar cane production in million tons by six major states during 1986 to1990.

Year/States P Q R S T X TOTAL1986 140 65 48 38 39 22 3521987 132 63 62 56 40 23 3761988 150 55 72 49 36 27 389

1989 168 60 45 65 43 25 4061990 170 45 70 62 42 23 412

16. In the year 1990, how many of the given states have a share of 15% or more in thetotal sugarcane production?

a) 3 b) 4c) 5 d) All

17. Which of the following states shows constant fall in sugarcane production every year?

a) P b) Qc) R d) None

18. What was the approximate % increase in sugarcane production in S from 1987 to1990?

a) 5 b) 7c) 20 d) 11

19. In which year does P has a share about 35% in the total sugarcane production?a)1986 b) 1987c) 1988 d) 1989

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20. In which year during the given period was the % of Q‟s share the highest in the totalproduction?

a) 1986 b) 1987c)1988 d) 1989

Directions (Questions 21 to 25): The questions given below are based on the followingtable.

Railway Time Table Geetanjali Express

CityArrival

Time (hrs)Departure Time (hrs)

CumulativeMileage

BOMBAY --- 0900 0IGATPURI 1100 1102 80NASIK 1450 1455 281BHUSAWAL 1710 1712 391AKOLA 2240 2245 730NAGPUR 0005 0015 800

DURG 0100 0102 845 JAMSHEDPUR 0415 0428 995CALCUTTA 0625 --- 1100

21. The largest run for the train between two successive halts is?a) Jamshedpur-Calcutta b) Bombay-Calcuttac) Bhusawal-Akola d) Akola-Nagpur

22. The average speed the train maintained between two successive stations was thehighest between?

a) Bhusawal-Akola b) Jamshedpur-Calcutta

c) Nagpur-Durg d) Bombay-Igatpuri

23. The average speed that the train maintained between Bombay and Calcutta wasnearly equal to?

a) 42 miles/hr b) 52 miles/hrc) 61 miles/hr d) 74 miles/hr

24. If we consider the journey that begins at Bombay and ends at Calcutta, the train hasthe longest halt at?

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a) Bombay b) Calcuttac) Jamshedpur d) Nagpur

25. The train begins its journey from Calcutta to Bombay eight hours after it has arrivedCalcutta. If the train left Bombay on Monday, on what day will it have returned toBombay? (Assume that on the return journey the train maintains the same averagespeed as on onward journey)

a) Monday b) Tuesdayc) Wednesday d) None of these

Directions (Questions 26 to 30): Study the following graph and answer the questionsgiven below it.

26. In which of the following year was it likely that the quantity of rubber imported tobridge the gap between demand and supply was maximum?

a) 1991 b) 1993

c) 1995 d) None

27. In 1991, the production of rubber was what percent of the requirement?a) 150 b) 67c) 45 d) 300

28. During which year was the percentage drop in the requirement of rubber over theprevious year, the maximum?

a) 1994 b) 1993c) 1991 d) None of these

Requirement and production of Rubber over the yearsProduction

Requirement

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29. For which of the two years was the average yearly production of rubber equal to theaverage yearly requirement?

a) 1992 & 1995 b) 1992 & 1993c) 1994 & 1995 d) 1993 & 1995

30. In 1992, the quantity of requirement of rubber was what percent of the quantity of

production?a) 25 b) 72c) 65 d) 70

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Data Sufficiency

Data sufficiency questions appear in the ANALYTICAL section of the exam.. Thesequestions require knowledge of the following topics:

Arithmetic Elementary algebra

Commonly know concepts of geometry

Data sufficiency questions are designed to measure your ability to analyze aquantities problem, recognize which given information is relevant, and determine atwhat point there is sufficient information to solve a problem. In these questions, youare to classify each problem according to the five or four fixed answer choice, ratherthan find a solution to the problem.

Each Data sufficiency question consists of a question, often accompanied by someinitial information, and two statements, labeled (1) and (2), which containadditional information. You must decide whether the information in each statement

is sufficient to answer the question or- if neither statement provides enoughinformation – whether the information in the two statements together is sufficient. Itis also possible that the statements in combination do not give enough informationanswer the question.

Begin by reading the initial information and the question carefully. Next, considerthe first statement. Does the information provided by the first statement is sufficientto answer the question? Go on the statement. Try to ignore the information given inthe first statement when you consider the second statement. Now you should beable to say, for each statement, whether it is sufficient to determine the answer.

Next, consider the two statements in tandem. Do they, together, enable you toanswer the question?

Give our answers as per the following statements

A statement (1) alone is sufficient butstatement (2) alone is not sufficient

B statement (2) alone is sufficient but

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statement (1) alone is not sufficient

C Both statements together are sufficientbut neither statement alone is sufficient

D Each statement alone is sufficient

E Both statement together are still not sufficient

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EXERCISE-1

1.

How much is 20 percent of a certain number?1) 10 percent of the number is 5.2) 40 percent of twice the number is 40.

2.

A thoroughly blended biscuit mix includes only flour and baking powder. What isthe ratio of the number of grams of baking powder to the number of grams offlour in the mix?1)

Exactly 9.9 grams of flour is contained in 10 grams of the mix.2)

Exactly 0.3 gram of baking powder is continued in 30 grams of the mix.

3. What is the value of x ?1)

x = - x2)

x2 = 4

4.

Is r greater than 0.27?

1)

r is grater than ¼.2)

r is equal to 3/10.

5. What is the value of the sum of a list of n odd integers?1)

n = 82) The square of the number of integers on the list is 64.

6. In the figure above, if lines k and m are parallel, what is value of x ?1)

y = 1202) z =60

7. What percent of a group of people are women with red hair?1)

Of the women in the group, 5 percent have red hair.2) Of the men in the group, 10 percent have red hair.

8.

If r and s are positive integers, r is what percent of s ?

1)

r =3/4 s 2) r s =75/100

9.

Is it true that a > b?1)

2a > 2b2)

a + c> b + c

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10.

In a certain class, one student is to be selected at random to read. What is theprobability that a boy will read?1)

Two-third of the students in the class are boys.2) Ten of the students in the class are girls.

11.

If 5x + 3y = 17, what is the value of x?

1)

x is a positive integer.2)

y = 4x

12.

Does the product jkmn equal 1?1)

jk / mn =12)

j = 1/k and m = 1/n

13. A certain expressway has exits J, K, L, and M, in that order. What is the roaddistance from exit k to exit L?1) The road distance from exit J to exit L is 21 kilometers2)

The road distance from exit M is 26 kilometers.

14.

Is the integer k a prime number?1)

2k = 62) 1 < k < 6

15.

If ab ≠ 0, in what quadrant of the coordinate system above does point (a, b)lie?1)

(b, a)lies in quadrant IV.2) (a, -b) lies in quadrant III.

EXERCISE- 2

1.

Is x greater than 1.8?1) x > 1. 7

2)

x > 1. 9

2.

If n is an integer, is n + 1 odd?1) n + 2 is an even integer.2)

n -1 is an odd integer.

3. Is 1< x < 2?1)

0 < x2) x < 3

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4.

Water is pumped into a partially filled tank at a constant rate through an inletpipe. At the same time, water is pumped out of the tank at a constant ratethough an outlet pipe. At what rate, in gallons per minute, is the amount ofwater in the tank increasing?1) The amount of water initially in the tank is 200gallons.2)

What is pumped into the tank at a rate of 10 gallons per minute and out of

the tank at rate of 10 gallons every 2 ½ minutes.

5. Is x a negative number?1)

9x > 10x 2)

x + 3 is positive.

6. Does 2m – 3n = 0?1) m ≠ 02)

6m = 9n

7.

What is the value of the integer x

1)

X is a prime number.2)

31 ≤ x ≤ 37

8. If P , Q , and R are three distinct points, do line segments PQ and PR have thesame length?1) P is the midpoint of line segment QR .2)

Q and R lie on the same circle with center P

9.

Is the number x between 0.2 and 0.7?1)

560x < 2802) 700x > 280

10. If i and j are integers, is i + j an even integer?1)

i < 102) i = j

11. If n + k = m , what is the value of k ?1)

n = 102)

m + 10 = n

12.

Is the triangle above equilateral?1) x = y2)

z = 60

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13.

Is x an integer?1) x/2 is an integer.2) 2x is an integer.

14.

What is the value of x?1)

2x + 1 = 02) (x +1)2 = x2

15.

What is the value of 1/k + 1/r? 1)

k + r = 202) kr = 64

EXERCISE-3

1.

If x is equal to one of the numbers ¼, 3/8, or 2/5, what is the value of x?

1)

¼ < x < ½2)

1/3 < x < 3/5

2. In Δ PQR, if PQ = x, QR = x+2, and PR = y, which of the three angles of Δ PRQ hasthe greatest degree measure?1) y = x + 32)

x = 2

3.

What distance did Jane travel?1) Bill traveled 40 miles in 40 minutes.2) Jane traveled at the same average rate as Bill.

4. What number is 15 percent of x?1)

18 is 6 percent of x.2) 2/3 of x is 200.

3.2☐ Δ 6

5. If ☐ and each represent single digits in the decimal above, what digit does ☐ represent?1)

When the decimal does is rounded to the nearest tenth, 3.2 is the result.2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.

6.

The profit from the sale of a certain appliance increases, though notproportionally, with number of units sold. Did the profit exceed $4 million onsales of 380,000units?1) The profit exceeded $2 million on sales of 200, 000 units.2)

The profit exceeded $5 million on sales of 350, 000 units.

7.

What is the value of xy – yz?1)

y = 2

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2)

x – z =5

8.

Will the first 10 volumes of a 20- volume encyclopedia fit upright in the bookrack shown above?1) x= 50 centimeters2) The height of the tub is 1 meter.

9.

A circular tub has a band painted around its circumference, as shown above.What is the surface area of this painted band?1)

x = 0.52)

The height of the tub is 1 meter.

10.

What is the value of integer n ?1) n (n +1) = 62)

22n = 16

11. The inside of a rectangular carton is 48 centimeters long, 32 centimeterswide, and 15 centimeters high. The carton is filled to capacity with k identicalcylindrical cans of fruit that stand upright in rows and columns, as indicated inthe figure above. If the can are 15 centimeters high, what is the value of k?1)

Each of the cans has a radius of 4 centimeters.2) Six of the cans fit exactly along the length of the carton

x – 4 = z y – x = 8

8 – z =t12. For the system of equation given, what is the value of z ?

1)

x = 72)

t = 5

13.

Is x equal to 5?1) x≥ 5 2)

x ≤ 5

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14. The table above shows the distance, in kilometers, by the most direct route,

between any two of the four cities, R, S, T, and U. For example, the distancebetween City R and City U is 62 kilometers. What is the value of x?1) By the most direct route, the distance between S and T is twice the distance betweenS and R.2) By the most direct route, the distance between T and U is 1.5 times the distancebetween R and T.

15. What is the value of the two-digit integer x ?1)

The sum of the two digits is 3.2) x is divisible by 3

EXERCISE -4

1.

What is the tenths digit in the decimal representation of a certain number?1) The number is less than 1/32)

The number is greater than1/4

2.

If the two floors in a certain building are 9 feet apart, how many steps are therein a set of stairs that extends from the first floor to the second floor of thebuilding?1)

Each step is ¾ foot high2) Each step is 1 foot wide.

3. If xy ≠ 0, is x/y < 0? 1)

x = - y2) -x = -(-y)

4. How many people are directors of both Company k and Company R?1) There were 17 directors present at a joint meeting of the directors of Company

K and Company R, and no directors were absent.2) Company K has 12 directors and Company R has 8 directors.

5. If x and y are positive, is x/y greater than 1?

1)

xy > 12)

x – y > 0

6.

What is the value of z in the triangle above?1) x + y = 1392)

y + z = 108

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7.

If x, y, and z are nonzero numbers, is xz = 12?1) x2 yz = 12 xy2) z/4 = 3/x

8.

A certain company currently has how many employees?1)

If 3 additional employees are hired by the company and all of the presentemployees remain, there will be at least 20 employees in the company.

2)

If no additional employees are hired by the company and 3 of the presentemployees resign, there will be fewer than 15 employees in the company.

9. What is the value of n in the equation -25 + 19 +n = s ?1) s = 22)

n/s = 4

10.

At a certain picnic, each of the guests was served either a single scoop or a

double scoop of ice cream. How many of the guests were served a double scoopof ice cream?1) At the picnic, 60 percent of the guests were served a double scoop of ice

cream.2)

A total of 120 scoops of ice cream were saved to all the guests at the picnic.

11.

What is the value of xy?1) y = x + 12)

y = x2 +1

12.

What is the value of 1/x + 1/y?

1)

x + y = 142) xy = 24

13. If d denotes a decimal, is d ≥ 0.5? 1)

When d is rounded to the nearest tenth, the result is 0.5.2) When d is rounded to the nearest integer, the result is 1.

14. If a real estate agent received a commission of 6 percent of the selling price ofa certain house, what was the selling price of the house?1)

The selling price minus the real estate agent‟s commission was $84,600. 2) The selling price was 250 percent of the original purchase price of $36,000.

15. If √x = n, what is the value of x? y

1) yn =102)

y = 40 and n = ¼

EXERCISE- 5

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1.

How many integers are there between, but not including, integers r and s?1) s – r = 102)

There are 9 integers between, but not including, r+1 and s+1.

2. What is the number of members of Club X who are at least 35 years of age?1)

Exactly ¾ of the members of Club X are under 35 years of age?

2)

The 64 women in Club X constitute 40 percent of the club‟s membership.

3. Carlotta can drive from her home to her office by one of two possible roués. If shemust also return by the longer route, what is the distance of the shorter route?1)

When she drive from her home to her office by the shorter route and returnsby the longer route, she drives a total of 42 kilometers.

2) When she drive both ways, from her home to her office and back, by thelonger route, she drives a total of 46 kilometers.

4. Is x > y?1)

x = y+2

2)

x/2 = y -1

5. If m is an integer, is m odd?1) m/2 is NOT an even integer.2)

m – 3 is an even integer.

6.

What is the area of triangular region ABC above?1) The product of BD and AC is 20.2) x = 45

7. What is the value of b + c?1)

ab + cd + ac + cd = 62) a +d = 4

8. What is the average (arithmetic mean)of j and k ?1)

The average (arithmetic mean) of j +2 and k + 4 is 11.2)

The average (arithmetic mean) of j, k, and 14 is 10.

9.

Paula and Sandy were among those people who sold raffle tickets to raise moneyfor Club X. If Paula and Sandy sold a total of 100 if the tickets, how many of thetickets did Paula sell?1) Sandy sold 2/3 as many of the raffle tickets as Paula did.

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2)

Sandy sold 8 percent of all the raffle tickets sold for Club X.

10.

Is ax = 3 – bx?1) x( a + b) =32) a =b = 1. 5 and x =1.

11.

A number of people each wrote down one of the first 30 positive integers. Wereany of the integers written down by more than one of the people?1) The number of people who wrote down an integer was greater than 402)

The number of people who wrote down an integer was less then 70.

12. In the figure above, is CD > BC?1)

AD = 202) AB = CD

13.

How much did a certain telephone call cost?1) The call lasted 53 minutes.2) The cost for the first 3 minutes was 5 times the cost for each additionalminute.

14. In a certain office, 50 percent of the employees are college graduates and 60percent of the employees are over forty years old. If 30 percent of those over fortyhave master‟s degrees how many of the employees over forty have master‟sdegrees?1) Exactly 100 of the employees are college graduates.2)

Of the employees 40 years old or less, 25 percent have master‟s degrees.

15. Is rst = 1?1)

rs =12) st=1

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EXERCISE- 6

1. The figure above represents a circle graph of Company H‟s total expenses brokendown by the expenses for each of its five divisions. If O is the center of the circleand if Company H‟s total expenses are $5, 400, 000, what are the expenses fordivision R?1)

x= 942) The total expenses for division S and T are twice as much as the expenses for

division R.

2. If Ms. Smith‟s income was 20 percent more for 1991 than it was for 1990, howmuch was her income for 1991?

1)

Ms. Smith‟s income for the fist 6 months of 1990 was $17,500 and herincome for the last 6 months of 1990 was $20,000.

2) Ms. Smith‟s income for 1991 was $7,500 great than her income for 1990.

3. In the figure above, segments PR and QR are each parallel to one of therectangular coordinate axes. Is the ratio of the length of QR to the length of QR tothe length of PR equal to 1?1) c = 3 and d = 4.2) a= -2 and b = -1

4.

While on a straight road, car X and car Y are traveling at different rates. If car Xis now 1 mile ahead of car Y, how many minutes from now will car X be 2 milesahead of car Y?1) Car X is traveling at 50 miles per hour and car Y is traveling at 40 miles per

hour.2) Three minutes age car X was ½ mile ahead of car Y.

5.

If a, b and c are integers, is a – b + c greater than a + b – c?1) b is negative.2)

c is positive.

6.

If a certain animated cartoon consists of total of 17,280 frames on film, howmany minutes will it take to run the cartoon?

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1)

The cartoon runs without interruption at the rate of 24 frames per second.2) It takes 6 times as long to run the cartoon as it takes to rewind the film, and

it takes a total of 14 minutes to do both.

7. A box contains only red chips, white chips, and blue chips. If a chip is randomlyselected from the box, what is the probability that the chip will be either white or

blue?1)

The probability that the chip will be blue is 1/52) The probability that the chip will be red is 1/3

8. If the successive tick marks shown on the number line above are equally spacedand if x and y are the numbers designating the end points of intervals as shown,what is the value of y?1) x = ½

2)

y – x = 2/3

9.

On a company- sponsored cruise, 2/3 of the passengers were companyemployees and the remaining passengers were their guests. If 3/4 of thecompany-employee passengers were managers, what was the number ofcompany-employee passengers who were NOT mangers?1) There were 690 passengers in the cruise.2)

There were 230 passengers who were guests of the company employees.

10.

In the xy-plane, does the point (4, 12) lie on line k?1) point (1, 7) lies on line k.

2)

point (-2, 2) lies on line k.

11. The length of the edging that surrounds circular garden K is ½ the length ofthe edging that surrounds circular garden G. What is the area of garden K? (Assume that the edging has negligible width.)1)

The area of G is 25π square meters 2) The edging around G is 10 π meters long.

12. An employee is paid 1.5 times the regular hourly rate for each hour worked inexcess of 40 hours per week, excluding Sunday, and 2 times the regular hourlyrate for each hour worked on Sunday. How much was the employee paid lastweek?1)

The employee‟s regular hourly rate is $10. 2) Last week the employee worked a total of 54 hours but did not work more

than 8 hours on any day.

13.

What was the revenue that a theater received from the sale of 400 tickets,some of which were sold at the full price and the remainder of which were sold ata reduced price?

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1)

The number of tickets sold at the full price was ¼ of the total number oftickets sold.

2)

The full price of a ticket was $25

14.

If o represents one of the operations +, -, and , is k o ( l +m ) = (k o l ) + (k o m )forall numbers k, l, and m ?

1)

k o1 is not equal to 1ok for some numbers k.2) 0 represents subtraction.

15.

How many of the 60 cars sold last month by a certain dealer had neitherpower widows nor a stereo?1)

Of the 60 cars sold, 20 had a stereo but not power windows.2) Of the 60 cars sold, 30 had both power windows and a stereo.

EXERCISE-7

1.

By what percent did the median household income in County Y decrease from

1970 to 1980?1)

In 1970 the median household income in Country Y was 2/3 of the medianhousehold income in Country X

2)

In 1980 the median household income in Country Y was ½ of the medianhousehold income in Country X

2. A certain group of car dealerships agreed to donate x dollars to a Red Crosschapter for each car sold during a 30- day period. What was the total amountthat was expected to be donated?1) A total of 500 cars were expected to be sold.2)

Sixty more cars were sold than expected, so that the total amount actually

donated was $28,000.

3. While driving on the expressway, did Robin ever exceed the 55-mile-per-hourspeed limit?1) Robin drove 100 miles on the expressway.2)

Robin drove for 2hours on the expressway.

4. In Jefferson School, 300 students study French or Spanish or both. If 100 ofthese students do not study French, how many of these students study bothFrench and Spanish?1)

Of the 300 students, 60 do not study Spanish.

2)

A total of 240 of the students study Spanish.

5. A certain salesperson‟s weekly salary is equal to a fixed base salary plus acommission that is directly proportional to the number of items sold during theweek. If 50 items are sold this week, what will be the salesperson‟s salary for thisweek?1)

Last week 45 items were sold.2) Last week‟s salary was $ 405.

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6. If Juan had a doctor‟s appointment on a certain day, was the appointment on aWednesday?1) Exactly 60 hours before the appointment, it was Monday.2) The appointment was between 1: 00 p.m and 9: 00 p.m

7.

What is the value of 5x2

+ 4x -1?1)

x(x + 2) = 02) x = 0

8. At Larry‟s Auto supply Store, Brand X antifreeze is sold by the gallon and BrandY motor oil is sold by the quart. Excluding sales tax, what is the total cost for 1gallon of brand X antifreeze and 1 quart of Brand Y motor oil?1) Excluding sales tax, the total cost for 6 gallons of Brand X antifreeze and 10

quarts of Brand Y motor oil is $58. (There is no quantity discount.)2) Excluding sales tax, the total cost for 4 gallons of Brand X antifreeze and 12

quarts of Brand Y motor oil is $44. (There is not quantity discount.)

9.

Is m n ?1) m + n < 02)

mn < 0

10.

When a player in a certain game tossed a coin a number of times, 4 moreheads than tails resulted. Heads or tails resulted each time the player tossed thecoin. How many times did heads result?1)

The player tossed the coin 24 time.2) The player received 3 points each time heads resulted and 1 point each time

tails resulted for a total of 52 points.

11.

If S is the infinite sequence S 1 = 9, S 2 = 99, S 3 = 999, …. S k = 10k – 1,….is every term in S divisible by the prime number p ?1)

P is greater than 2.2) At least one term in sequence S is divisible by p.

12. Quadrilateral RSTU shown above is a site plan for a parking lot in which sideRU is parallel to side ST and RU is longer than ST. what is the area of theparking lot?1)

RU = 80 meters2)

TU = 2010 meters

13. If n and k are greater than zero, is n/k an integer?1)

n and k are both integers.

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2)

n2 and k2 are both integers.

14.

If the average (arithmetic mean) of six numbers is 75, how many of thenumbers are equal to 75?1) None of the six numbers is less than 75.2)

None of the six numbers is grater than 75.

15. Is x = y – z?1) x + y =z2)

x < 0

EXERCISE -8

1. What was the total amount of revenue that a theater received from the sale of400 tickets, some of which were sold at x percent of full price and the rest ofwhich were sold at full price?

1)

x = 502)

Full-price tickets sold for $20 each.

2.

Any decimal that has only a finite number of nonzero digits is terminatingdecimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If rand s are positive integers and the ratio r/s is expressed as a decimal, is r/s aterminating decimal.1)

90 < r < 1002)

s = 4

3. In the figure above, what is the value of x + y?1)

x = 702) ABC and ADC are both isosceles triangles.

4. Are positive integers p and q both greater than n?1)

p – q is greater than n.

2)

q > p

5.

Whenever Martin has a restaurant bill with an amount between $10 and $99, hecalculates the dollar amount of the tip as 2 times the tens digit of the amount ofhis bill. If the amount of Martins most recent bill was between $10 and $99, wasthe tip calculated by Martin on this bill greater than 15 percent of the amount ofthe bill?1) The amount of the bill was between $15 and $50.2) The tip calculated by Martin was $8.

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6. The price per share of stock X increased by 10 percent over the same period thatthe price per share of stock Y decreased by 10 percent. The reduced price pershare of stock Y was what percent of the original price per share of stock X?1) The increased price per share of stock X was equal to the original price per

share of stock.

2)

The increased price per share of stock X was 10/11 the decrease in the price pershare of stock Y.

7.

Is k greater than t ?1) kt = 242)

k 2 > t 2

8.

In the figure above, if the area of triangular region D is 4, what is the length of aside of square region A?1)

The area of square region B is 9.2)

The area of square region C is 64/9

9.

If x is to be selected at random from set T, what is the probability that ¼ x -5 0?1)

T is a set of 8 integers2) T is contained in the set of integers from 1 to 25, inclusive.

10. If Sara‟s age is exactly twice Bill‟s age, what is Sara‟s age? 1)

Four years ago, Sara‟s age was exactly 3 times Bill‟s age. 2) Eight years now, Sara‟s age will be exactly 1.5 times Bill‟s age.

11. What is the value of ( a + b)2 1) ab =0

2)

(a – b)2

= 36

12.

In the figure above, what is the ratio KN / MN?1) The perimeter of rectangle KLMN is 30 metes.

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2)

The three small rectangles have the same dimensions.

13.

If n is a positive integer, is 150/n an intriguer?1) n < 72) n is a prime number.

14.

Is 2x – 3y < x2

?1)

2x – 3y = -22) x > 2 and y > 0.

15.

A report consisting of 2,600 words is divided into 23 paragraphs. A 2-paragraph preface is then added to the report. Is the average (arithmetic mean )number of words per paragraph for all 25 paragraphs less than 120?1) Each paragraph of the preface has more than 100 words.2)

Each paragraph of the preface has fewer than 150 words.

EXERCISE-9

1.

If x/2 = 3/y, is x less than y?1) y 32)

y 4

2.

If v and w are different integers, does v = 0?1) vw = v2 2)

w = 2

3.

What is the value of 36,500(1.05)n?1) n2 – 5n + 6 = 0

2)

n – 2 0

4.

In the rectangular coordinate system above, if OP < PQ, is the area of region OPQgreater than 48?1)

The coordinates of point P are (6,8).2) The coordinates of point Q are (13, 0).

5.

If r and s are positive integers, is r/s an integer?1) Every factor of s is also a factor of r .2)

Every prime factor of s is also a prime factor of r.

6.

If zn = 1, what is the value of z?

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1)

n is a nonzero integer.2) z > 0

7. In the expression above, if xn 0, what is the value of S1)

x =2n2) n = ½

8. If x is an integer, is x x< 2x?1)

x < 02) x = -10

9. If n is a positive integer, is the value of b – a at least twice the value of 3n – 2n?1)

a =2n + 1 and b = 3n + 1 2) n = 3

10.

The inflation index for the year1989 relative to the year 1970 was 3.56,indicating that, on the average, for each dollar spent in 1970 for goods, $3.56

had to be spent for the same goods in 1989. If the price of a Model K mixerincreased precisely according to the inflation index, what was the price of the ofthe mixer in 1970?1)

The price of the Model K mixer was $102. 40 more in 1989 than in 1970.2) The price of the Model K mixer was $142. 40 in 1989.

11. Is 5k less than 1,000?1)

5k +1 > 3,0002) 5k-1 = 5k - 500

12. If the integer n is greater than 1, is n equal to 2?

1) n has exactly two positive factors.2) The difference of any two distinct positive factors of n is odd.

13.

Every member of a certain club volunteers to contribute equally to thepurchase of a $60 gift certificate. How many members does the club have?1)

Each member‟s contribution is to be $4.2) If 5 club members fail to contribute, the share of each contributing member

will increase by $2.

14.

If m and n are positive integers, is n – m an integer?1) n > m + 152)

n = m (m +1)

15. If x < 0, is y > 0?1)

x/y < 02) y – x> 0

EXERCISE-10

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1.

What is the circumference of the circle above with center O?1)

The perimeter of OXZ is 20 + 102.2) The length of arc XYZ is 5.

2.

What is the value of a4 – b4?1) a2 – b2 = 162)

a + b = 8

3.

In a certain business, production index p is directly proportional to efficiencyindex e , which is in turn directly proportional to investment index i . What is p if I= 70?1)

e = 0 .5 whenever i = 60.

2)

p = 2.0 whenever i = 50.4.

If x -y, is x-y/ x + y > 11) x >02)

y < 05. In the rectangular coordinate system, are the points (r, s) and (u, v) equidistant

from the origin?1) r + s =12)

u = 1- r and v = 1 – s.6. On Jane‟s credit card account, the average dally balance for a 30-day billing

cycle is the average (arithmetic mean) of the daily balances at the end of each ofthe 30days. At the beginning of a certain 30-day billing cycle, Jane‟s credit card

account had a balance of $600. Jane made a payment of $300 on the accountduring the billing cycle. If no other amounts were added to or subtracted fromthe account during billing cycle, what was the average daily balance on Jane‟saccount for the billing cycle?1) Jane‟s payment was credited on the 21st day of the billing cycle.2)

The average daily balance through the 25th day of the billing cycle was $540.

7.

If x is an integer, is 9 x+ 9 -x = b?1) 3 x +3 -x = b + 22)

x > 08. If m > 0 and n >0, is m +x/ n + x > m/n?

1)

m < n2)

x > 09. If n is a positive integer, is (1/10)n < 0.01?

1)

n > 22) (1/10) n-1 <0.1

10.

Is 1/p > r/ (r2 +2)?1) p = r2)

r > 011. Is n an integer?

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1)

n2 is an integer.2)

n is an integer.12.

If n is a positive integer, is n3 – n divisible by 4?1) n = 2k +1, where k is an integer.2)

n2 + n is divisible by 6.13. What is the tens digit of positive integer x?

1)

x divided by 100 has a remainder of 30.2) x divided by 110 has a remainder of 30.14. If x, z and positive integers, is x-y odd?

1)

x = z2 2) y = (z -1)2

15. Henry purchased 3 items during a sale. He received a 20 percent discount offthe regular price of the most expensive items and a 10 percent discount off theregular price of each of the other 2 items. Was the total amount of the 3discounts greater than 15 percent of the sum of the regular prices of the 3 items?1) The regular price of the most expensive item was $50, and the regular price of

the next most expensive item was $20.2)

The regular price of the least expensive item was $15.

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Venn Diagrams

The term venn Diagram relates to the different type of figures drawn to represent relationship betweentwo or more objects. These figures represent by a circle, triangle, square and rectangle. The concept ofvenn diagram originates from set theory. A basis concept of set, subset, disjoint set can help tounderstand the concept of venn diagram. To understand these terms, we are given following pointswith examples.

Example 1. An object is said to have an intersection with the other object, when two objects sharesomething in common.For Examples:

(a) Dogs, Pets(b) Fathers, Brothers(c) Clerks, Government Employees

Example 2. An object is said to be a subset of another object, if former is a part of latter.For examples:

(a) Minutes, Hours(b) Females, Mothers(c) Engineers, Human Beings

Example 3. An object is said to be disjoint with other, when two objects share nothing in common.For examples:

(a) Table, Chair(b) Doctors, Engineers(c) Human Beings, Rates

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Directions (Qs. 1-4) : Each of the se questions below contains three group of things. You are tochoose from the following fine numbered diagrams, a diagram that depicts the correct relationshipamong the three groups of things in each questions.

5. Tables, Chairs, Furniture6. Tie, Shirts, Pantaloon7.

Dogs, Pets, Cats8.

Brinjal, Meat, Vegetables

SOLUTIONS1. (d) Tables and chairs are unrelated items, but both are the items of furniture.

2. (c) Tie, shirt and pantaloon are separated items.

3. (d) Dogs and cats are entirely different from each other. But both are pet animals.

4. (e) Brinjal is a vegetable. But meat is entirely different.

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Example 5. Which one of the following diagrams correctly represents the relationship among theclasses: Judge, Thief, Criminal.

Solution (b) All thieves are criminal. But judge is entirely different.

Example 6. Which one of the following sets is best represented in the adjoining diagram?

(a) Animals, Insects, Cockroaches(b) Country, States, Districts(c) Animals, Mates, Females and Hermaphrodities(d) States Districts, Union Territory

Solution (d). Districts from the part of the state but, union territory is entirely different.

Example 7. In the following diagram, the square represents girls, the circle represents tall persons,the triangle is for tennis players and the rectangle stands for the swimmers. On the basis of theabove diagram, answer the following questions.

1. Which letter represents tall girl, who do not play tennis and are not swimmers?(a) E(b) G(c) D(d) C

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2. Which letter represents girls who are swimmers, play tennis but are not tall?(a) F(b) B(c) E(d) None of these

3. Which letter represents tall persons who are gents and swimmers but do not play tennis?(a) J(b) K(c)

L(d) I

4. Which letter represents tall girls who are swimmers but don‟t play tennis? (a) H(b) G(c) D(d) C

SOLUTION

1. (c). Tall girls are represented by the region common to the square and the circle i.e., D, C, G, andH. But according to the given conditions, the girls are neither a part of rectangle nor the triangle.So, Answer is D.

2. (d). Girls, who are swimmers and play tennis are represented by the region i.e., H. But accordingto the given condition girls should not be tall. So, required region should not be a part of thecircle. Since, it is a part of the circle, hence the answer is none of these.

3. (b). Tall persons are represented by regions inside the circle i.e., C, D, G, H, I, J and K. Sincepersons are not girls and do not play tennis, so the region should not be a part of either thesquare or the triangle. So, C, D, G, H should be excluded. Also according to the given conditions,the persons should be swimmers. So, the required region should be a part of the rectangle.Hence, the answer is K.

4. (b). Tall girls who are swimmers are represented by the region common to the square, circle andthe rectangle i.e., G and H. But according to the given conditions, girls should not be tennisplayers. So, the required region should not be apart of the triangle, so H should be excluded.Hence, the answer is G.

Example 8. Read the figure and find the region representing persons who are educated andemployed but not confirmed.(a) b, d(b) a, b, c(c) a, c(d) a, d, c

Solution (a). The required region is the one which is common to the circles but lies outside thetriangle. So the answer is b and d .

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Exercise:

Direction for Questions 1 to 3:

In a class of 150 students 55 speak English; 85 speak Telugu and 30 speak neither English nor Telugu.1. How many speak both English and Telugu?

(a)

10(b) 120(c) 20(d) 45

2. How many speak only Telugu?(a) 85(b) 55(c) 95(d) 65

3. How many speak at least one of the two languages from English & Telugu?(a) 110

(b)

120(c) 130(d) 100

Directions for Questions 4 and 5:

A class of 30 students comprises boys who can play Cricket, Hockey and Football. 3 boys play onlycricket, 3 bys play only Hockey and 2 play only football. 4 boys could play all three games, while 11could play Football and Cricket, and 10 boys could play Football and Hockey.

4. How may boys played Cricket and Hockey but not Football?(a) 1(b) 2

(c)

3(d) 5

5. How many boys can play atleast two games?(a) 16(b) 18(c) 10(d) 22

Directions for Questions 6 to 9:

In a class, 70 students passed in Mathematics, 50% of the students passed in English, 25% of thestudents passed in both and 5% of the students passed in neither Mathematics nor English.

6. How many students are there in the class?(a) 93(b) 145(c) 100(d) 140

7. How many students passed in only one subject?(a) 75(b) 53(c) 80

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(d) 70

8. How many students failed in atleast one subject?(a) 5(b) 25(c) 50(d) 75

9.

What is the ratio of the number of students who passed in English to that in Mathematics?(a) 1 : 1(b) 2 : 3(c) 5 : 7(d) 10 : 9


In a survey of 150 readers it has been found that 75 read newspaper A, 90 read newspaper B ad 70read newspaper C. 40 read A and B; 35 read B and C; 30 read A and C and 10 read all the three.

10. How many respondents read none of the newspapers?(a) 30(b) 20(c)

10(d) 40

11. How many read exactly two newspapers?(a) 75(b) 105(c) 95(d) 85

12. How many read exactly one newspaper?(a) 35(b) 55(c) 235

(d)

12013. How many read neither A nor B?

(a) 45(b) 70(c) 110(d) 15


Scholars colony has a population of 2800 members.Number of members reading only English newspaper = 650Number of members reading only Hindi newspaper = 550

Number of members reading only Marathi newspaper = 450Number of members reading all three newspaper = 100Number of members reading Hindi as well as English newspaper = 200Number of members reading Hindi as well as Marathi newspaper = 400Number of members reading English as well as Marathi newspaper = 300

14. Find number of members reading Hindi newspaper?(a) 950(b) 1050(c) 650(d) 550

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15. Find number of members reading none of the newspapers?(a) 450(b) 550(c) 2550(d) 2650

16. Find number of members reading only one newspaper?

(a)

450(b) 1100(c) 1600(d) 1650

17. Find number of members reading atleast two newspapers?(a) 400(b) 500(c) 600(d) 700


The following table gives the statistics of a class in which each student opted for

Maths or Statistics or both. Unfortunately most of the figures have been erased but Iremember some information.

Mat hs

Stati stics

Bo th

Tot al

Male 50

Female

Total 70 15

0 The information is as follows:

1. 13 1/3% of the students took both Maths and Statistics2.

40% of the students were females.3. None of the females took both Mathematics and Statistics.

Fill the table and answer the following Questions.

18. How many males took both Mathematics and Statistics?(a) 40

(b)

10(c) 20(d) 60

19. How many students took only Mathematics?(a) 50(b) 80(c) 60(d) 10

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20. How many males took only Statistics?(a) 0(b) 40(c) 20(d) 30

21. How many females took only Mathematics?(a) 10(b)

50(c) 70(d) 40

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In a class of 160 students, it was found that 65 play Cricket 70 play Hockey and 90 play Football, 30play Cricket and Hockey, 40 Cricket and Football, 35 play Hockey and Football and 15 play none ofthese three games.

22. How many play all three games?(a) 745

(b)

105(c) 25(d) 55

23. If 10 students who play only Hockey now start playing Cricket also; and 10 students who playonly football stop playing Football and start playing Cricket how many will play both Cricket andHockey?(a) 30(b) 40(c) 20(d) 55

24. How many students play exactly one game?(a) 90

(b)

75(c) 105(d) 145

25. If 5 students stop playing Hockey and start playing Cricket, what is the least number of studentsplaying only Football and Hockey but not Cricket?(a) 15(b) 30(c) 10(d) 5

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VERBAL

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Reading Comprehension

Exercise 1:

In the sixteenth century, an age of great marine and terrestrial exploration,

Ferdinand Magellan led the first expedition to sail around the world. As a youngPortuguese noble, he served the king of Portugal, but he became involved in thequagmire of political intrigue at court and lost the king's favor. After he wasdismissed from service to the king of Portugal, he offered to serve the futureEmperor Charles V of Spain.A papal decree of 1493 had assigned all land in the New World west of 50 degrees Wlongitude to Spain and all the land east of that line to Portugal. Magellan offered toprove that the East Indies fell under Spanish authority. On September 20, 1519,Magellan set sail from Spain with five ships. More than a year later, one of theseships was exploring the topography of South America in search of a water routeacross the continent. This ship sank, but the remaining four ships searched along

the southern peninsula of South America. Finally they found the passage theysought near a latitude of 50 degrees S. Magellan named this passage the Strait of AllSaints, but today we know it as the Strait of Magellan.One ship deserted while in this passage and returned to Spain, so fewer sailors wereprivileged to gaze at that first panorama of the Pacific Ocean. Those who remainedcrossed the meridian we now call the International Date Line in the early spring of1521 after ninety-eight days on the Pacific Ocean. During those long days at sea,many of Magellan's men died of starvation and disease.Later Magellan became involved in an insular conflict in the Philippines and waskilled in a tribal battle. Only one ship and seventeen sailors under the command ofthe Basque navigator Elcano survived to complete the westward journey to Spainand thus prove once and for all that the world is round, with no precipice at theedge.1. The sixteenth century was an age of great ___exploration.A. cosmicB. landC. mentalD. common manE. none of the above2. Magellan lost the favor of the king of Portugal when he became involved in apolitical ___.

A. entanglementB. discussionC. negotiationD. problemsE. none of the above3. The Pope divided New World lands between Spain and Portugal according to theirlocation on one side or the other of an imaginary geographical line 50 degrees westof Greenwich that extends in a ___ direction.

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A. north and southB. crosswiseC. easterlyD. south eastE. north and west4. One of Magellan's ships explored the ___ of South America for a passage across

the continent.A. coastlineB. mountain rangeC. physical featuresD. islandsE. none of the above5. Four of the ships sought a passage along a southern ___.A. coastB. inlandC. body of land with water on three sidesD. border

E. answer not available6. The passage was found near 50 degrees S of ___.A. GreenwichB. The equatorC. SpainD. PortugalE. Madrid7. In the spring of 1521, the ships crossed the ___ now called the International DateLine.A. imaginary circle passing through the polesB. Imaginary line parallel to the equator

C. areaD. land massE. answer not found in article

Marie Curie was one of the most accomplished scientists in history. Together withher husband, Pierre, she discovered radium, an element widely used for treatingcancer, and studied uranium and other radioactive substances. Pierre and Marie'samicable collaboration later helped to unlock the secrets of the atom.Marie was born in 1867 in Warsaw, Poland, where her father was a professor ofphysics. At the early age, she displayed a brilliant mind and a blithe personality.

Her great exuberance for learning prompted her to continue with her studies afterhigh school. She became disgruntled, however, when she learned that the universityin Warsaw was closed to women. Determined to receive a higher education, shedefiantly left Poland and in 1891 entered the Sorbonne, a French university, whereshe earned her master's degree and doctorate in physics.Marie was fortunate to have studied at the Sorbonne with some of the greatestscientists of her day, one of whom was Pierre Curie. Marie and Pierre were marriedin 1895 and spent many productive years working together in the physicslaboratory. A short time after they discovered radium, Pierre was killed by a horse-

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drawn wagon in 1906. Marie was stunned by this horrible misfortune and enduredheartbreaking anguish. Despondently she recalled their close relationship and the joy that they had shared in scientific research. The fact that she had two youngdaughters to raise by herself greatly increased her distress.Curie's feeling of desolation finally began to fade when she was asked to succeed herhusband as a physics professor at the Sorbonne. She was the first woman to be

given a professorship at the world-famous university. In 1911 she received the NobelPrize in chemistry for isolating radium. Although Marie Curie eventually suffered afatal illness from her long exposure to radium, she never became disillusioned abouther work. Regardless of the consequences, she had dedicated herself to science andto revealing the mysteries of the physical world.8. The Curies' ____ collaboration helped to unlock the secrets of the atom.A. friendlyB. competitiveC. courteousD. industriousE. chemistry

9. Marie had a bright mind and a __personality.A. strongB. lightheartedC. humorousD. strangeE. envious10. When she learned that she could not attend the university in Warsaw, shefelt___.A. hopelessB. annoyedC. depressed

D. worriedE. none of the above11. Marie ___ by leaving Poland and traveling to France to enter the Sorbonne.A. challenged authorityB. showed intelligenceC. behavedD. was distressedE. answer not available in article12. _____she remembered their joy together.A. DejectedlyB. Worried

C. TearfullyD. HappilyE. Sorrowfully13. Her ____ began to fade when she returned to the Sorbonne to succeed herhusband.A. misfortuneB. angerC. wretchedness

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D. disappointmentE. ambition14. Even though she became fatally ill from working with radium, Marie Curie wasnever ____.A. troubledB. worried

C. disappointedD. sorrowfulE. disturbed

Mount Vesuvius, a volcano located between the ancient Italian cities of Pompeii andHerculaneum, has received much attention because of its frequent and destructiveeruptions. The most famous of these eruptions occurred in A. D. 79. The volcano had been inactive for centuries. There was little warning of the comingeruption, although one account unearthed by archaeologists says that a hard rainand a strong wind had disturbed the celestial calm during the preceding night.

Early the next morning, the volcano poured a huge river of molten rock down uponHerculaneum, completely burying the city and filling in the harbor with coagulatedlava.Meanwhile, on the other side of the mountain, cinders, stone and ash rained downon Pompeii. Sparks from the burning ash ignited the combustible rooftops quickly.Large portions of the city were destroyed in the conflagration. Fire, however, was notthe only cause of destruction. Poisonous sulphuric gases saturated the air. Theseheavy gases were not buoyant in the atmosphere and therefore sank toward theearth and suffocated people.Over the years, excavations of Pompeii and Herculaneum have revealed a great dealabout the behavior of the volcano. By analyzing data, much as a zoologist dissects a

specimen animal, scientist have concluded that the eruption changed large portionsof the area's geography. For instance, it turned the Sarno River from its course andraised the level of the beach along the Bay of Naples. Meteorologists studying theseevents have also concluded that Vesuvius caused a huge tidal wave that affected theworld's climate.In addition to making these investigations, archaeologists have been able to studythe skeletons of victims by using distilled water to wash away the volcanic ash. Bystrengthening the brittle bones with acrylic paint, scientists have been able toexamine the skeletons and draw conclusions about the diet and habits of theresidents. Finally, the excavations at both Pompeii and Herculaneum have yieldedmany examples of classical art, such as jewelry made of bronze, which is an alloy of

copper and tin. The eruption of Mount Vesuvius and its tragic consequences have provided us witha wealth of data about the effects that volcanoes can have on the surrounding area. Today volcanologists can locate and predict eruptions, saving lives and preventingthe destruction of cities and cultures.15. Herculaneum and its harbor were buried under ___lava.A. liquidB. solidC. flowing

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D. gasE. answer not available16. The poisonous gases were not ___ in the air.A. able to floatB. visibleC. able to evaporate

D. invisibleE. able to condense17. Scientists analyzed data about Vesuvius in the same way that a zoologist ___ aspecimen.A. describes in detailB. studies by cutting apartC. photographsD. chartE. answer not available18. ____have concluded that the volcanic eruption caused a tidal wave.A. Scientist who study oceans

B. Scientist who study atmospheric conditionsC. Scientist who study ashD. Scientist who study animal behaviorE. Answer not available in article19. Scientist have used ___water to wash away volcanic ash from the skeletons ofvictims.A. bottledB. volcanicC. purifiedD. seaE. fountain

Conflict had existed between Spain and England since the 1570s. England wanted ashare of the wealth that Spain had been taking from the lands it had claimed in theAmericas.Elizabeth I, Queen of England, encouraged her staunch admiral of the navy, SirFrancis Drake, to raid Spanish ships and towns. Though these raids were on asmall scale, Drake achieved dramatic success, adding gold and silver to England'streasury and diminishing Spain's omnipotence.Religious differences also caused conflict between the two countries. Whereas Spainwas Roman Catholic, most of England had become Protestant. King Philip II of

Spain wanted to claim the throne and make England a Catholic country again. Tosatisfy his ambition and also to retaliate against England's theft of his gold andsilver, King Philip began to build his fleet of warships, the Armada, in January1586.Philip intended his fleet to be indestructible. In addition to building new warships,he marshaled one hundred and thirty sailing vessels of all types and recruited morethan nineteen thousand robust soldiers and eight thousand sailors. Although someof his ships lacked guns and others lacked ammunition, Philip was convinced thathis Armada could withstand any battle with England.

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The martial Armada set sail from Lisbon, Portugal, on May 9,1588, but bad weatherforced it back to port. The voyage resumed on July 22 after the weather becamemore stable. The Spanish fleet met the smaller, faster, and more maneuverable English ships inbattle off the coast of Plymouth, England, first on July 31 and again on August 2. The two battles left Spain vulnerable, having lost several ships and with its

ammunition depleted. On August 7, while the Armada lay at anchor on the Frenchside of the Strait of Dover, England sent eight burning ships into the midst of theSpanish fleet to set it on fire. Blocked on one side, the Spanish ships could onlydrift away, their crews in panic and disorder. Before the Armada could regroup, theEnglish attacked again on August 8.Although the Spaniards made a valiant effort to fight back, the fleet sufferedextensive damage. During the eight hours of battle, the Armada drifted perilouslyclose to the rocky coastline. At the moment when it seemed that the Spanish shipswould be driven onto the English shore, the wind shifted, and the Armada driftedout into the North Sea. The Spaniards recognized the superiority of the English fleetand returned home, defeated.

20. Sir Francis Drake added wealth to the treasury and diminished Spain's ____.A. unlimited powerB. unrestricted growthC. territoryD. treatiesE. answer not available in article21. Philip recruited many ___soldiers and sailors.A. warlikeB. strongC. accomplishedD. timid

E. non experienced22. The ____ Armada set sail on May 9, 1588.A. completeB. warlikeC. independentD. isolatedE. answer not available23. The two battles left the Spanish fleet ____.A. open to changeB. triumphantC. open to attack

D. defeatedE. discouraged24. The Armada was ___ on one side.A. closed offB. damagedC. aloneD. circledE. answer not available in this article

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The victory of the small Greek democracy of Athens over the mighty Persian empirein 490 B. C. is one of the most famous events in history. Darius, king of the Persianempire, was furious because Athens had interceded for the other Greek city-statesin revolt against Persian domination. In anger the king sent an enormous army todefeat Athens. He thought it would take drastic steps to pacify the rebellious part of

the empire. Persia was ruled by one man.In Athens, however, all citizens helped to rule. Ennobled by this participation,Athenians were prepared to die for their city-state. Perhaps this was the secret ofthe remarkable victory at Marathon, which freed them from Persian rule. On theirway to Marathon, the Persians tried to fool some Greek city-states by claiming tohave come in peace. The frightened citizens of Delos refused to believe this. Notwanting to abet the conquest of Greece, they fled from their city and did not returnuntil the Persians had left. They were wise, for the Persians next conquered the cityof Etria and captured its people. Tiny Athens stood alone against Persia. The Athenian people went to theirsanctuaries. There they prayed for deliverance. They asked their gods to expedite

their victory. The Athenians refurbished their weapons and moved to the plain ofMarathon, where their little band would meet the Persians. At the last moment,soldiers from Plataea reinforced the Athenian troops. The Athenian army attacked, and Greek citizens fought bravely. The power of themighty Persians was offset by the love that the Athenians had for their city.Athenians defeated the Persians in archery and hand combat. Greek soldiers seizedPersian ships and burned them, and the Persians fled in terror. Herodotus, afamous historian, reports that 6400 Persians died, compared with only 192Athenians.25. Athens had ____the other Greek city-states against the Persians.A. refused help to

B. intervened on behalf ofC. wanted to fightD. given orders for all to fightE. defeated26. Darius took drastic steps to ___ the rebellious Athenians.A. weakenB. destroyC. calmD. placateE. answer not available27. Their participation___to the Athenians.

A. gave comfortB. gave honorC. gave strengthD. gave fearE. gave hope28. The people of Delos did not want to ___ the conquest of Greece.A. endB. encourageC. think about

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D. daydream aboutE. answer not available29. The Athenians were ___by some soldiers who arrived from Plataea.A. welcomedB. strengthenedC. held

D. capturedE. answer not available30. Questions 30-32.

The Trojan War is one of the most famous wars in history. It is well known for theten-year duration, for the heroism of a number of legendary characters, and for the Trojan horse. What may not be familiar, however, is the story of how the war began.According to Greek myth, the strife between the Trojans and the Greeks started atthe wedding of Peleus, King of Thessaly, and Thetis, a sea nymph. All of the gods

and goddesses had been invited to the wedding celebration in Troy except Eris,goddesses of discord. She had been omitted from the guest list because herpresence always embroiled mortals and immortals alike in conflict. To take revenge on those who had slighted her, Eris decided to cause a skirmish.Into the middle of the banquet hall, she threw a golden apple marked “for the mostbeautiful.” All of the goddesses began to haggle over who should possess it. Thegods and goddesses reached a stalemate when the choice was narrowed to Hera,Athena, and Aphrodite. Someone was needed to settle the controversy by picking awinner. The job eventually fell to Paris, son of King Priam of Troy, who was said tobe a good judge of beauty.Paris did not have an easy job. Each goddess, eager to win the golden apple, tried

aggressively to bribe him.

“I'll grant you vast kingdoms to rule, “ promised Hera. “Vast kingdoms are nothingin comparison with my gift,” contradicted Athena. “Choose me and I'll see that youwin victory and fame in war.” Aphrodite outdid her adversaries, however. She wonthe golden apple by offering Helen, Zeus' daughter and the most beautiful mortal, toParis. Paris, anxious to claim Helen, set off for Sparta in Greece.Although Paris learned that Helen was married, he accepted the hospitality of herhusband, King Menelasu of Sparta, anyway. Therefore, Menelaus was outraged for anumber of reasons when Paris departed, taking Helen and much of the king'swealth back to Troy. Menelaus collected his loyal forces and set sail for Troy to begin

the war to reclaim Helen.30. Eris was known for ___both mortals and immortals.A. scheming againstB. involving in conflictC. feeling hostile towardD. ignoringE. comforting31. Each goddess tried ___to bribe Paris.

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A. boldlyB. effectivelyC. secretlyD. carefullyE. answer not stated32. Athena ___ Hera, promising Paris victory and fame in war.

A. denied the statement ofB. defeatedC. agreed withD. restated the statementE. questioned the statement

One of the most intriguing stories of the Russian Revolution concerns the identity ofAnastasia, the youngest daughter of Czar Nicholas II. During his reign over Russia,the Czar had planned to revoke many of the harsh laws established by previous

czars. Some workers and peasants, however, clamored for more rapid social reform.In 1918 a group of these people, known as Bolsheviks, overthrew the government.On July 17 or 18, they murdered the Czar and what was thought to be his entirefamily.Although witnesses vouched that all the members of the Czar's family had beenexecuted, there were rumors suggesting that Anastasia had survived. Over the years, a number of women claimed to be Grand Duchess Anastasia. Perhaps thebest – known claimant was Anastasia Tschaikovsky, who was also known as AnnaAnderson.In 1920, eighteen months after the Czar's execution, this terrified young woman wasrescued from drowning in a Berlin river. She spent two years in a hospital, where

she attempted to reclaim her health and shattered mind. The doctors and nursesthought that she resembled Anastasia and questioned heer about her background.She disclaimed any connection with the Czar's family.Eight years later, though, she claimed that she was Anastasia. She said that shehad been rescued by two Russian soldiers after the Czar and the rest of her familyhad been killed. Two brothers named Tschaikovsky had carried her into Romania.She had married one of the brothers, who had taken her to Berlin and left her there,penniless and without a vocation. Unable to invoke the aid of her mother's family inGermany, she had tried to drown herself.During the next few years, scores of the Czar's relatives, ex-servants, andacquaintances interviewed her. Many of these people said that her looks and

mannerisms were evocative of the Anastasia that they had known. Her grandmotherand other relatives denied that she was the real Anastasia, however. Tried of being accused of fraud, Anastasia immigrated to the United States in 1928and took the name Anna Anderson. She still wished to prove that she wasAnastasia, though, and returned to Germany in 1933 to bring suit against hermother's family. There she declaimed to the court, asserting that she was indeedAnastasia and deserved her inheritance.In 1957, the court decided that it could neither confirm nor deny Anastasia'sidentity. Although we will probably never know whether this woman was the Grand

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Duchess Anastasia, her search to establish her identity has been the subject ofnumerous books, plays, and movies.33. Some Russian peasants and workers___for social reform.A. longedB. cried outC. begged

D. hopedE. thought much34. Witnesses ___ that all members of the Czar's family had been executed.A. gave assuranceB. thoughtC. hopedD. convinced someE. answer not stated35. Tschaikovsky ____any connection with the Czar's family.A. deniedB. stopped

C. notedD. justifiedE. answer not stated36. She was unable to ___the aid of her relative.A. locateB. speak aboutC. call uponD. identifyE. know37. In court she ___ maintaining that she was Anastasia and deserved herinheritance.

A. finally appearedB. spoke forcefullyC. testifiedD. gave evidenceE. answer not stated

King Louis XVI and Queen Marie Antoinette ruled France from 1774 to 1789, a timewhen the country was fighting bankruptcy. The royal couple did not let France'sinsecure financial situation limit their immoderate spending, however. Even though

the minister of finance repeatedly warned the king and queen against wastingmoney, they continued to spend great fortunes on their personal pleasure. Thislavish spending greatly enraged the people of France. They felt that the royal couplebought its luxurious lifestyle at the poor people's expense.Marie Antoinette, the beautiful but exceedingly impractical queen, seemed uncaringabout her subjects; misery. While French citizens begged for lower taxes, the queenembellished her palace with extravagant works of art. She also surrounded herselfwith artists, writers, and musicians, who encouraged the queen to spend moneyeven more profusely.

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While the queen's favorites glutted themselves on huge feasts at the royal table,many people in France were starving. The French government taxed the citizensoutrageously. These high taxes paid for the entertainments the queen and her courtso enjoyed. When the minister of finance tried to stop these royal spendthrifts, thequeen replaced him. The intense hatred that the people felt for Louis XVI and MarieAntoinette kept building until it led to the French Revolution. During this time of

struggle and violence (1789-1799), thousands of aristocrats, as well as the king andqueen themselves, lost their lives at the guillotine. Perhaps if Louis XVI and MarieAntoinette had reined in their extravagant spending, the events that rocked Francewould not have occurred.38. The people surrounding the queen encouraged her to spend money ____.A. wiselyB. abundantlyC. carefullyD. foolishlyE. joyfully39. The minister of finance tried to curb these royal ___.

A. aristocratsB. money wastersC. enemiesD. individualsE. spenders

Many great inventions are greeted with ridicule and disbelief. The invention of theairplane was no exception. Although many people who heard about the firstpowered flight on December 17,1903, were excited and impressed, others reacted

with peals of laughter. The idea of flying an aircraft was repulsive to some people.Such people called Wilbur and Orville Wright, the inventors of the first flyingmachine, impulsive fools. Negative reactions, however, did not stop the Wrights.Impelled by their desire to succeed, they continued their experiments in aviation.Orville and Wilbur Wright had always had a compelling interest in aeronautics andmechanics. As young boys they earned money by making and selling kites andmechanical toys. Later, they designed a newspaper-folding machine, built a printingpress, and operated a bicycle-repair shop. In 1896, when they read about the deathof Otto Lilienthal, the brother's interest in flight grew into a compulsion.Lilienthal, a pioneer in hang-gliding, had controlled his gliders by shifting his bodyin the desired direction. This idea was repellent to the Wright brothers, however,

and they searched for more efficient methods to control the balance of airbornevehicles. In 1900 and 1901, the Wrights tested numerous gliders and developedcontrol techniques. The brothers' inability to obtain enough lift power for the glidersalmost led them to abandon their efforts.After further study, the Wright brothers concluded that the published tables of airpressure on curved surfaces must be wrong. They set up a wind tunnel and began aseries of experiments with model wings. Because of their efforts, the old tables wererepealed in time and replaced by the first reliable figures for air pressure on curvedsurfaces. This work, in turn, made it possible for them to design a machine that

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would fly. In 1903 the Wrights built their first airplane, which cost less than onethousand dollars. They even designed and built their own source of propulsion- alightweight gasoline engine. When they started the engine on December 17, theairplane pulsated wildly before taking off. The plane managed to stay aloft for twelveseconds, however, and it flew one hundred twenty feet.By 1905 the Wrights had perfected the first airplane that could turn, circle, and

remain airborne for half an hour at a time. Others had flown in balloons or in hanggliders, but the Wright brothers were the first to build a full-size machine that couldfly under its own power. As the contributors of one of the most outstandingengineering achievements in history, the Wright brothers are accurately called thefathers of aviation.40. The idea of flying an aircraft was ___to some people.A. boringB. distastefulC. excitingD. needlessE. answer not available

41. People thought that the Wright brothers had ____.A. acted without thinkingB. been negatively influencedC. been too cautiousD. had not given enough thoughtE. acted in a negative way42. The Wright's interest in flight grew into a ____.A. financial empireB. planC. need to actD. foolish thought

E. answer not in article43. Lilenthal's idea about controlling airborne vehicles was ___the Wrights.A. proven wrong byB. opposite to the ideas ofC. disliked byD. accepted byE. opposed by44. The old tables were __ and replaced by the first reliable figures for air pressureon curved surfaces.A. destroyedB. canceled

C. multipliedD. discardedE. not used45. The Wrights designed and built their own source of ____.A. force for moving forwardB. force for turning aroundC. turningD. force to going backwardE. none of the above

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Exercise 2:

Americans have always been interested in their Presidents' wives. Many First Ladieshave been remembered because of the ways they have influenced their husbands.Other First Ladies have made the history books on their own.

At least two First Ladies, Bess Truman and Lady Bird Johnson, made it theirbusiness to send signals during their husbands' speeches. When Lady Bird Johnsonthought her husband was talking too long, she wrote a note and sent it up to theplatform. It read, “It's time to stop!” And he did. Once Bess Truman didn't like whather husband was saying on television, so she phoned him and said,” If you can'ttalk more politely than that in public, you come right home.”

Abigail Fillmore and Eliza Johnson actually taught their husbands, Millard Fillmoreand Andrew Johnson, the thirteenth and seventeenth Presidents. A schoolteacher,Abigail eventually married her pupil, Millard. When Eliza Johnson married Andrew,he could not read or write, so she taught him herself.

It was First Lady Helen Taft's idea to plant the famous cherry trees in Washington,D. C. Each spring these blossoming trees attract thousands of visitors to thenation's capital. Mrs. Taft also influenced the male members of her family and theWhite House staff in a strange way: she convinced them to shave off their beards!

Shortly after President Wilson suffered a stroke, Edith Wilson unofficially took overmost of the duties of the Presidency until the end of her husband's term. Earlier,during World War I, Mrs. Wilson had had sheep brought onto the White House lawnto eat the grass. The sheep not only kept the lawn mowed but provided wool for anauction sponsored by the First Lady. Almost $100,000 was raised for the Red Cross.

Dolly Madison saw to it that a magnificent painting of George Washington was notdestroyed during the War of 1812. As the British marched toward Washington, D.C., she remained behind to rescue the painting, even after the guards had left. Thepainting is the only object from the original White House that was not burned.

One of the most famous First Ladies was Eleanor Roosevelt, the wife of PresidentFranklin D. Roosevelt. She was active in political and social causes throughout herhusband's tenure in office. After his death, she became famous for herhumanitarian work in the United Nations. She made life better for thousands ofneedy people around the world.

1. What is the main idea of this passage?

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A. The Humanitarian work of the First Ladies is critical in American government.B. Dolly Madison was the most influential president's wife.C. Eleanor Roosevelt transformed the First Lady image.D. The First Ladies are important in American culture.E. The First Ladies are key supporters of the Presidents.

Of the many kinds of vegetables grown all over the world, which remains the favoriteof young and old alike? Why, the potato, of course.

Perhaps you know them as “taters,” “spuds,” or “Kennebees,” or as “chips,”“Idahoes,” or even “shoestrings.” No matter, a potato by any other name is still apotato- the world's most widely grown vegetable. As a matter of fact, if you are anaverage potato eater, you will put away at least a hundred pounds of them each

year.

That's only a tiny portion of the amount grown every year, however. Worldwide, theannual potato harvest is over six billion bags- each bag containing a hundredpounds of spuds, some of them as large as four pounds each. Here in the UnitedStates, farmers fill about four hundred million bags a year. That may seem like a lotof “taters,” but it leaves us a distant third among world potato growers. Polishfarmers dig up just over 800 million bags a year, while the Russians lead the worldwith nearly 1.5 billion bags.

The first potatoes were grown by the Incas of South America, more than four

hundred years ago. Their descendants in Ecuador and Chile continue to grow thevegetable as high as fourteen thousand feet up in the Andes Mountains. ( That'shigher than any other food will grow.) Early Spanish and English explorers shippedpotatoes to Europe, and they found their way to North America in the early 1600s.

People eat potatoes in many ways-baked, mashed, and roasted, to name just three.However, in the United States most potatoes are devoured in the form of Frenchfries. One fast-food chain alone sells more than $1 billion worth of fries each year.No wonder, then, that the company pays particular attention to the way its fries areprepared.

Before any fry makes it to the people who eat at these popular restaurants, it mustpass many separate tests. Fail any one and the spud is rejected. To start with, onlyrusset Burbank potatoes are used. These Idaho potatoes have less water contentthan other kinds, which can have as much as eighty percent water. Once cut into“shoestrings” shapes, the potatoes are partly fried in a secret blend of oils, sprayedwith liquid sugar to brown them, steam dried at high heat, then flash frozen forshipment to individual restaurants.

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Before shipping, though, every shoestring is measured. Forty percent of a batchmust be between two and three inches long. Another forty percent has to be overthree inches. What about the twenty percent that are left in the batch? Well, a fewshort fries in a bag are okay, it seems.

So, now that you realize the enormous size and value of the potato crop, you can

understand why most people agree that this part of the food industry is no “smallpotatoes.”


A. Potatoes from Ireland started the Potato Revolution.B. The average American eats 50 lbs of potatoes a year.C. French fries are made from potatoes.D. Potatoes are a key vegetable in America.E. The various terms for potatoes have a long history.

What does the word patent mean to you? Does it strike you as being somethingrather remote from your interests? If it does, stop and think a moment about someof the commonplace things that you use every day, objects that you take for grantedas part of the world around you. The telephone, radio, television, the automobile,and the thousand and one other things (even the humble safety pin) that enrich ourlives today once existed only as ideas in the minds of men. If it had not beenpossible to patent their ideas and thus protect them against copying by others,

these inventions might never have been fully developed to serve mankind.

If there were no patent protection there would be little incentive to invent andinnovate, for once the details of an invention became known, hordes of imitatorswho did not share the inventor's risks and expenses might well flood the marketwith their copies of his product and reap much of the benefit of his efforts. Thetechnological progress that has made America great would wither rapidly underconditions such as these.

The fundamental principles in the U. S. patent structure came from England.During the glorious reign of Queen Elizabeth I in England, the expanding technology

was furthered by the granting of exclusive manufacturing and selling privileges tocitizens who had invented new processes or tools- a step that did much toencourage creativity. Later, when critics argued that giving monopoly rights to oneperson infringed on the rights of others, an important principle was added to thepatent structure: The Lord Chief Justice of England stated that society hadeverything to gain and nothing to lose by granting exclusive privileges to aninventor, because a patent for an invention was granted for something new thatsociety never had before.

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Another basic principle was brought into law because certain influential people inEngland had managed to obtain monopoly control over such age-old products assalt, and had begun charging as much as the traffic would bear. The public outcrybecame so great that the government was forced to decree that monopoly rightscould be awarded only to those who created or introduced something really unique. These principles are the mainstays of our modern patent system in the United

States.

In colonial times patent law was left up to the separate states. The inconsistency,confusion, and unfairness that resulted clearly indicated the need for a uniformpatent law, and the men who drew up the Constitution incorporated one. GeorgeWashington signed the first patent law on April 10,1790, and less than four monthslater the first patent was issued to a man named Samuel Hopkins for a chemicalprocess, an improved method of making potash for use in soapmaking.

In 1936 the Patent Office was established as a separate bureau. From the staff ofeight that it maintained during its first year of operation it has grown into an

organization of over 2500 people handling more than 1600 patent applications andgranting over 1000 every week.

The Patent Office in Washington, D. C., is the world's largest library of scientific andtechnical data, and this treasure trove of information is open for public inspection.In addition to more than 3 million U. S. patents, it houses more than 7 millionforeign patents and thousands of volumes of technical literature. Abraham Lincolnpatented a device to lift steam vessels over river shoals, Mark Twain developed aself-pasting scrapbook, and millionaire Cornelius Vanderbilt invented a shoe-shinekit.

A patent may be granted for any new and useful process, machine, article ofmanufacture, or composition of matter ( a chemical compound or combinations ofchemical compounds), or any distinct and new variety; of plant, including certainmutants and hybrids.

The patent system has also helped to boost the wages of the American worker to anunprecedented level; he can produce more and earn more with the computer,adding machines, drill press or lathe. Patented inventions also help keep pricesdown by increasing manufacturing efficiency and by stimulating the competitionthat is the foundation of our free enterprise system.

The decades of history have disclosed little need for modification of the patentstructure. Our patent laws, like the Constitution from which they grew, have stoodthe test of time well. They encouraged the creative processes, brought untoldbenefits to society as a whole, and enabled American technology to outstrip that ofthe rest of the civilized world.


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A. The patent system encourages free enterprise.B. The Constitution protects the patent system.C. The patent system in England has been influential in American patentdevelopment.D. Patents are important tools for inventors.E. Patented inventions protect the inventor, free enterprise, and the creative

process.

Most people think it's fine to be “busy as a beaver.” Little do they know. Beaversmay work hard, but often they don't get much done.

Beavers are supposed to be great tree cutters. It is true that a beaver can gnawthrough a tree very quickly. (A six-inch birch takes about ten minutes.) But then

what? Often the beaver does not make use of the tree. One expert says that beaverswaste one out of every five trees they cut.

For one thing, they do not choose their trees wisely. One bunch of beavers cut downa cottonwood tree more than one hundred feet tall. Then they found that they couldnot move it.

In thick woods a tree sometimes won't fall down. It gets stuck in the other trees. Ofcourse, doesn't think to cut down the trees that are in the way. So a good tree goesto waste.

Some people think that beavers can make a tree fall the way they want it to. Nottrue. (In fact, a beaver sometimes gets pinned under a falling tree.) When beaverscut a tree near a stream, it usually falls into the water. But they do not plan it thatway. The fact is that most trees lean toward the water to start with.

Now what about dam building? Most beaver dams are wonders of engineering. Thebest ones are strongly built of trees, stones, and mud. They are wide at the bottomand narrow at the top.

Beavers think nothing of building a dam more than two hundred feet long. Onedam, in Montana, was more than two thousand feet long. The largest one ever seen

was in New Hampshire. It stretched four thousand feet. It made a lake large enoughto hold forty beaver homes.

So beavers do build good dams. But they don't always build them in the rightplaces. They just don't plan. They will build a dam across the widest part of thestream. They don't try to find a place where the stream is narrow. So a lot of theirhard work is wasted.

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Beavers should learn that it's not enough to be busy. You have to know what you'redoing, too. For example, there was one Oregon beaver that really was a worker. Itdecided to fix a leak in a man-made dam. After five days of work it gave up. The leakit was trying to block was the lock that boats go through.


A. Beavers may be hard working animals, but they don't always choose the mostefficient mechanisms.B. Beavers are excellent dam builders.C. New Hampshire was the site of the largest beaver dam.D. Beavers are well developed tree cutters.E. Beavers are poor surveyors of aquatic environments in some cases.

The raisin business in America was born by accident. It happened in 1873 in theSan Joaquin Valley of California. Many farmers raised grapes in this valley. That year, just before the grape harvest, there was a heat wave. It was one of the worstheat waves ever known. It was so hot the grapes dried on the vines. When they werepicked, California had its first raisin crop.

People were surprised to find how good raisins were. Everybody wanted more. Sothe San Joaquin farmers went into the raisin business. Today, of course, they do

not let the grapes dry on the vines. They treat them with much more care.

In late August the grapes start to ripen. They are tested often for sweetness. Thegrowers wait until the sugar content is twenty-one percent. Then they know thegrapes are ripe enough to be picked.

Skilled workers come to the vineyards. They pick the bunches of grapes by hand. The workers fill their flat pans with grapes. They gently empty the pans ontosquares of paper. These squares lie between the long rows of vines. They sit in thesun.

Here the grapes stay while the sun does its work. It may take two weeks or longer. The grapes are first dried on one side. When they have reached the right color, theyare turned to dry on the other side. The grapes are dried until only fifteen percent ofthe moisture is left. Then they have turned into raisins.

The raisins are rolled up in the paper on which they have dried. Trucks take themfrom the fields. They are poured into big boxes called sweatboxes. Each box holdsone hundred and sixty pounds of raisins. Here, any raisins that are a bit too dry

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take moisture from those that have a bit too much. After a while they are all justmoist enough.

The big boxes are trucked next to the packaging plant. They are emptied onto aconveyor belt that shakes the raisins gently. This knocks them from their stems. Ablast of air whisks the stems away. The water bath is next. Then the plump brown

raisins have a last inspection. They are again checked for moisture and sugar. Thenthey go on a belt to packing machines. Here they are poured into packages, whichare automatically weighed and sealed. The raisins are now ready for market.


A. The creation of raisins in America was an accident.B. The process of raisin development requires multiple steps.C. Raisins on the grocery store shelf undergo a brief fermentation process.D. Raisins are cleaned thoroughly at the packing plant.E. California has been the leader in American raisin development.

In 1976, Sichan Siv was crawling through the jungle, trying to escape fromCambodia. By 1989, however, Siv was working in the White House, in WashingtonD. C., as an advisor to the President of the United States. How did this strange journey come about?

Like millions of Cambodians, Siv was a victim of a bloody civil war. One of the sidesin this war was the Cambodian government. The other was a group called theKhmer Rouge. When the Khmer Rouge won the war, the situation in Cambodia gotworse. Many people were killed, while others were forced into hard labor. Sometimesentire families were wiped out.

Siv came from a large family that lived in the capital of Cambodia. After finishinghigh school, Siv worked for a while with a Cambodian airline company. Later, hetaught English. After that, he took a job with CARE, an American group that washelping victims of the war.

Siv had hope to leave Cambodia before the Khmer Rouge took over the country.Unfortunately, he was delayed. As a result, he and his family were taken from theirhomes and forced to labor in rice fields. After a while, Siv managed to escape. Herode an old bicycle for miles, trying to reach Thailand where he would be free andsafe. For three weeks he slept on the ground and tried to hide from the soldiers whowere looking for him. Caught at last, he was afraid he would be killed. Instead, hewas put into a labor camp, where he worked eighteen hours each day without rest.After several months, he escaped again; this time he made it. The journey, however,

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was a terrifying one. After three days of staggering on foot through mile after mile ofthick bamboo, Siv finally made his way to Thailand.

Because he had worked for an American charity group, Siv quickly found work in arefugee camp. Soon he was on his way to the states. He arrived in June of 1976 andgot a job-first picking apples and then cooking in a fast-food restaurant. Siv,

however, wanted more than this; he wanted to work with people who, like himself,had suffered the hardship of leaving their own countries behind. Siv decided thatthe best way to prepare for this kind of work was to go to college. He wrote letters tomany colleges and universities. They were impressed with his school records fromCambodia, and they were impressed with his bravery. Finally, in 1980, he was ableto study at Columbia University in New York City. After finishing his studies atColumbia, Siv took a job with the United Nations. He married an American womanand became a citizen. After several more years, he felt that he was very much a partof his new country.

In 1988, Siv was offered a job in the White House working for President Reagan's

closest advisors. It was a difficult job, and he often had to work long hours. Howeverthe long hard work was worth it, because Siv got the opportunity to help refugees inhis work.


A. Persistence and courage are global ideas.B. Siv covered a large area during his life.C. Siv persevered to become an American citizenD. Siv overcame numerous challenges to come to American and help others.E. Siv persevered to become an American citizen.

When you want to hang the American flag over the middle of a street, suspend itvertically with the blue field, called the union, to the north and east-west street.When the flag is displayed with another banner from crossed staffs, the Americanflag is on the right. Place the staff of the American flag in front of the other staff.Raise the flag quickly and lower it slowly and respectfully. When flying the flag athalf-mast, hoist it to the top of the pole for a moment before lowering it to mid-pole.

When flying the American flag with banners from states or cities, raise the nation'sbanner first and lower it last. Never allow the flag to touch the ground.


A. The American flag is the symbol of American freedom.B. The American flag has fifty stars.C. Placing the American flag inappropriately will draw government intervention.

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D. American flag should be flown differently in certain situations.","The flag should be lowered quickly and respectfully.

What if someone told you about a kind of grass that grows as tall as the tallesttrees? A grass that can be made as strong as steel? A grass from which houses,furniture, boats, and hundreds of other useful things can be made? A grass that you would even enjoy eating? Would you believe that person? You should, for thatgrass is bamboo, the “wood” of 1,001 uses.

Bamboo may look like wood, but it is part of the family of plants that includeswheat, oats, and barley. It is a kind of grass. This grass is not just a material formaking useful products. Young bamboo is eaten, often mixed with other vegetables,in many Asian foods.

Bamboo grows in many parts of the world. In the United States it grows in an areafrom Virginia west to Indiana and south to Florida, Louisiana, and Texas. Mostbamboo, however, is found in warm, wet climates, especially in Asia and on theislands of the South Pacific Ocean.

In most Asian countries, bamboo is nearly as important as rice. Many Asians live inbamboo houses. They sit on bamboo chairs and sleep on bamboo mats. They fencetheir land with bamboo and use the wood for cages for chickens and pigs.

Bamboo is used to build large buildings as well as homes. When it is glued in

layers, it becomes as strong as steel. On some islands in the South Pacific, bamboois even used for water pipes. This extraordinary material has many other uses. It isused to make musical instruments, such as flutes and recorders. Paper made frombamboo has been highly prized by artists for thousands of years.

Bamboo is light and strong, and it bends without breaking. It is cheap, floats onwater, almost never wears out, and is easy to grow. Nothing else on earth growsquite so fast as bamboo. At times you can even see it grow! Botanists have recordedgrowths of more than three feet in just twenty-four hours! Bamboo is hollow andhas a strong root system that almost never stops growing and spreading. In fact,only after it flowers, an event that may happen only once every thirty years, will

bamboo die.

There are more than a thousand kinds of bamboo. The smallest is only three inchestall and one-tenth of an inch across. The largest reaches more than two hundredfeet in height and seven inches in diameter. No wonder, then, that the lives of nearlyhalf the people on earth would change enormously if there were no longer anybamboo. No wonder, too, that to many people bamboo is a symbol of happiness andgood fortune.

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A. Bamboo has at least 2,000 uses.B. Bamboo grows at an amazing rate and is found primarily in Asia.C. Bamboo is an amazing grass that can be used in multiple ways.D. There are at least a 1,000 types of bamboo.

E. Bamboo could be considered a flower in some cases.

Every year since 1986, some of the world's most daring runners have gathered inthe desert of Morocco. They are there to take part in one of the most difficult racesin the world. The Marathon of the Sands, as it is called, covers over 125 miles ofdesert and mountain wilderness. The runners complete the course in fewer thanseven days, and they run with their food, clothing, and sleeping bags on their backs.

The Marathon of the Sands was founded in 1986 by Patrick Bauer. His idea was togive the runners, who come from all over the world, a special kind of adventure.Most of the runners in this race have found that they form deep friendships with theother runners during their days and nights in the desert. Facing terrible heat andcomplete exhaustion, they learn much about themselves and each other.

For most of the runners, though, the challenge of the race is the main reason forcoming. On the first day, for example, they run fifteen miles across a desert of sand,rocks, and thorny bushes. Few runners finish the day without blistered and rawfeet. They also suffer from a lack of water. (They are allowed less than nine quarts of

water during each day of the race.) Most of all, they are exhausted when they arriveat the campsite for the night.

The second day, the runners are up at 6:00 A. M. Within a few hours, it is 100degrees F, but the runners do not hesitate. They must cover eighteen miles that day. That night, they rest. They must be ready for the next day's run.

On the third day, the runners must climb giant sand dunes- the first they havefaced. Dust and sand mix with the runners' sweat. Soon their faces are caked withmud. After fifteen miles of these conditions, the runners finally reach their nextcamp.

The race continues like this for four more days. The fourth and fifth days are theworst. On the fourth day, the runners pass through a level stretch and a beautiful,tree-filled oasis, but then, on this and on the next day, they cross more than twenty-one miles of rocks and sand dunes. The temperature soars to 125 degrees F, andmany runners cannot make it. Helicopters rush fallen runners to medical help.Runners who make it to the end of the fifth day know that the worst is over.

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On the sixth day, heat and rocks punish the racers terribly. In the Valley of Dra, thewind picks up and, as the desert heat is thrust against them with great force, theygrow more and more exhausted.

The seventh day is the last, with only twelve miles to be covered. The dusty, tired,blistered runners set out at daybreak. Near the finish line, children race along with

the runners, for everybody has caught the excitement. The ones who have run thewhole marathon know they have accomplished what most people could not evendream of . “During the hard moments,” says one contestant who has raced heretwice, “I'd think, „Why am I here?' Then I'd realize I was there to find my limits.”


A. The Marathon of the Sands race tests the limits of human endurance.B. The runners run at their own pace.C. The race causes the strong to stumble and the weak to not finish.D. The seventh day is the hardest day of the race.

E. Every runner runs the race to find their human limits.

High in the Andes Mountains in Peru stands the ancient city of Machu Picchu. Noone knows why this great city was built, nor is it likely that we will ever know.Nevertheless, the deserted city of Machu Picchu is important for what it revealsabout the ancient Inca people of South America.

The Incas once ruled a great empire that covered a large part of the South Americancontinent. The empire was more than five hundred years old when the first Spanishexplorers, looking for gold, went to that continent in the sixteenth century.

The Incas were an advanced people. They were skillful engineers who paved theirroads and built sturdy bridges. They plowed the land in such a way that rainswould not wash away valuable soil. They dug ditches to carry water into dry areasfor farming.

Even though they did not know about the wheel, the Incas were able to move hugestone blocks- some as heavy as ten tons- up the sides of mountains to build walls.

The blocks were fitted so tightly, without cement of any kind, that it would beimpossible to slip a knife blade between them! The walls have stood firm throughgreat storms and earthquakes that have destroyed many modern buildings.

The Incas were great artists, too. Today, Incan dishes and other kinds of pottery areprized for their wonderful designs. Since both gold and silver were in great supply,the Incas created splendid objects from these precious metals.

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While it is true that the Incas had no written language, they kept their accounts byusing a system of knotted strings of various lengths and colors. The sizes of theknots and the distances between them represented numbers.

At its height, the Incan empire included as many as thirty million people. Theemperor ruled them with an iron hand. He told his subjects where to live, what to

plant, how long they should work-even whom they could marry. Since he ownedeverything, the emperor gave what he wished when he wished- and in the amounthe wished -to his people.

In 1533 Spanish explorers led by Francisco Pizarro murdered the emperor of theIncas. Earlier, the heir to the Incan empire had also been killed. The Incas, who hadalways been entirely dependent on their emperor, now had no recognized leader. The Spaniards easily conquered the empire and plundered its riches.

Have the Incas disappeared from South America? Not at all. In Peru alone, once thecenter of that great empire, eighty percent of the twenty million people are

descendants of the Inca people. Evidence of the Incan empire can be found in manyother places in South America as well. You can even visit Machu Picchu. Theremains of this ancient city still stand high in the mountains of Peru, an awesometribute to this once powerful empire.


A. The Incas once inhabited the ancient city of Machu Picchu.B. Peru was the primary country of the Incas.C. The Incan empire can be found in ancient cities and was plundered by theSpanish.

D. Spanish conquerors destroyed the Incan empire in the thirteenth century.E. Machu Picchu was the capital of the Incan empire.

Exercise 3:

In 1892 the Sierra Club was formed. In 1908 an area of coastal redwood trees northof San Francisco was established as Muir Woods National Monument. In the SierraNevada mountains, a walking trail from Yosemite Valley to Mount Whitney wasdedicated in 1938. It is called John Muir Trail.

John Muir was born in 1838 in Scotland. His family name means “moor,” which is ameadow full of flowers and animals. John loved nature from the time he was small.He also liked to climb rocky cliffs and walls.

When John was eleven, his family moved to the United States and settled inWisconsin. John was good with tools and soon became an inventor. He first

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invented a model of a sawmill. Later he invented an alarm clock that would causethe sleeping person to be tipped out of bed when the timer sounded.

Muir left home at an early age. He took a thousand-mile walk south to the Gulf ofMexico in 1867and 1868. Then he sailed for San Francisco. The city was too noisyand crowded for Muir, so he headed inland for the Sierra Nevadas.

When Muir discovered the Yosemite Valley in the Sierra Nevadas, it was as if he hadcome home. He loved the mountains, the wildlife, and the trees. He climbed themountains and even climbed trees during thunderstorms in order to get closer tothe wind. He put forth the theory in the late 1860's that the Yosemite Valley hadbeen formed through the action of glaciers. People ridiculed him. Not until 1930 wasMuir's theory proven correct.

Muir began to write articles about the Yosemite Valley to tell readers about itsbeauty. His writing also warned people that Yosemite was in danger from timbermining and sheep ranching interests. In 1901 Theodore Roosevelt became president

of the United States. He was interested in conservation. Muir took the presidentthrough Yosemite, and Roosevelt helped get legislation passed to create YosemiteNational Park in 1906.Although Muir won many conservation battles, he lost a major one. He fought tosave the Hetch Valley, which people wanted to dam in order to provide water for SanFrancisco. In the late 1913 a bill was signed to dam the valley. Muir died in 1914.Some people say losing the fight to protect the valley killed Muir.

1. What happened first?

A. The Muir family moved to the United States.

B. Muir Woods was created.C. John Muir learned to climb rocky cliffs.D. John Muir walked to the Gulf of MexicoE. Muir visited along the east coast.

2. When did Muir invent a unique form of alarm clock?

A. while the family still lived in ScotlandB. after he sailed to San FranciscoC. after he traveled in YosemiteD. while the Muir family lived in Wisconsin

E. after he took the long walk

3. What did John Muir do soon after he arrived in San Francisco?

A. He ran outside during an earthquake.B. He put forth a theory about how Yosemite was formed.C. He headed inland for the Sierra Nevadas.D. He began to write articles about the Sierra Nevadas.E. He wrote short stories for the local newspaper.

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4. When did John Muir meet Theodore Roosevelt?

A. between 1901 and 1906B. between 1838 and 1868C. between 1906 and 1914D. between 1868 and 1901

E. between 1906-1907

5. What happened last?

A. John Muir died.B. John Muir Trail was dedicated.C. Muir's glacial theory was proven.D. The Sierra Club was formed.E. John's family visited him.

When using a metal file, always remember to bear down on the forward stroke only.

On the return stroke, lift the file clear of the surface to avoid dulling theinstrument's teeth. Only when working on very soft metals is it advisable to drag thefile's teeth slightly on the return stroke. This helps clear out metal pieces frombetween the teeth.

It is best to bear down just hard enough to keep the file cutting at all times. Toolittle pressure uses only the tips of the teeth; too much pressure can chip the teeth.Move the file in straight lines across the surface. Use a vice to grip the work so that your hands are free to hold the file. Protect your hands by equipping the file with ahandle. Buy a wooden handle and install it by inserting the pointed end of the fileinto the handle hole.

6. These directions show you how to-

A. work with a hammerB. use a fileC. polish a fileD. oil a viseE. repair shop tools

7. When using a file-

A. always bear down on the return strokeB. move it in a circleC. remove the handleD. press down on the forward strokeE. wear protective gloves

8. When working on soft metals, you can-

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A. remove the handleB. clear metal pieces from the teethC. bear down very hard on the return strokeD. file in circlesE. strengthen them with added wood

9. Protect your hands by-

A. dulling the teethB. dragging the teeth on the backstrokeC. using a viseD. installing a handleE. wearing safety gloves

“Old woman,” grumbled the burly white man who had just heard Sojourner Truth

speak, “do you think your talk about slavery does any good? I don't care any morefor your talk than I do for the bite of a flea.”

The tall, imposing black woman turned her piercing eyes on him. “Perhaps not,” sheanswered, “but I'll keep you scratching.”

The little incident of the 1840s sums up all that Sojourner Truth was: utterlydedicated to spreading her message, afraid of no one, forceful and witty in speech.Yet forty years earlier, who could have suspected that a spindly slave girl growingup in a damp cellar in upstate New York would become one of the most remarkablewomen in American history? Her name then was Isabella (many slaves had no last

names), and by the time she was fourteen she had seen both parents die of cold andhunger. She herself had been sold several times. By 1827, when New York freed itsslaves, she had married and borne five children.

The first hint of Isabella's fighting spirit came soon afterwards, when her youngestson was illegally seized and sold. She marched to the courthouse and badgeredofficials until her son was returned to her.

In 1843, inspired by religion, she changed her name to Sojourner(meaning “one whostays briefly”) Truth, and, with only pennies in her purse, set out to preach againstslavery. From New England to Minnesota she trekked, gaining a reputation for her

plain but powerful and moving words. Incredibly, despite being black and female(only white males were expected to be public speakers), she drew thousands to townhalls, tents, and churches to hear her powerful, deep-voiced pleas on equality forblacks-and for women. Often she had to face threatening hoodlums. Once she stoodbefore armed bullies and sang a hymn to them. Awed by her courage and hercommanding presence, they sheepishly retreated.

During the Civil War she cared for homeless ex-slaves in Washington. PresidentLincoln invited her to the White House to bestow praise on her. Later, she petitioned

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Congress to help former slaves get land in the West. Even in her old age, she forcedthe city of Washington to integrate its trolley cars so that black and white could ridetogether.

Shortly before her death at eighty-six, she was asked what kept her going. “I thinkof the great things,” replied Sojourner.

10. The imposing black woman promised to keep the white man-

A. searchingB. cryingC. holleringD. scratchingE. fleeing

11. This incident occurred in the-

A. 1760sB. 1900sC. 1840sD. 1920sE. 1700s

12. Sojourner Truth was raised in a damp cellar in-

A. New YorkB. GeorgiaC. New Jersey

D. IdahoE. Maryland

13. Isabella lost both parents by the time she was-

A. twenty-sevenB. twoC. sevenD. fourteenE. nineteen

14. When New York freed its slaves, Isabella had-

A. problemsB. no childrenC. five childrenD. an educationE. three children

15. Her change in name was inspired by-

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A. a fighting spiritB. religionC. her freedomD. officialsE. friends

16. She traveled from New England to-

A. CanadaB. CaliforniaC. MinnesotaD. AlaskaE. Virginia

17. She forced the city of Washington to-

A. integrate its trolleys

B. give land grantsC. care for ex-slavesD. provide food for ex-slavesE. clean its trolleys

18. She preached against-

A. smokingB. slaveryC. alcoholD. hoodlums

E. women having no rights

19. Sojourner Truth died at-

A. 48B. 72C. 63D. 86E. 88

The Galapagos Islands are in the Pacific Ocean, off the western coast of SouthAmerica. They are a rocky, lonely spot, but they are also one of the most unusualplaces in the world. One reason is that they are the home of some of the last gianttortoises left on earth.

Weighing hundreds of pounds, these tortoises, or land turtles, wander slowlyaround the rocks and sand of the islands. Strangely, each of these islands has its

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own particular kinds of tortoises. There are seven different kinds of tortoises on theeight islands, each kind being slightly different from the other.

Hundreds of years ago, thousands of tortoises wandered around these islands.However, all that changed when people started landing there. When people firstarrived in 1535, their ships had no refrigerators. This meant that fresh food was

always a problem for the sailors on board. The giant tortoises provided a solution tothis problem.

Ships would anchor off the islands, and crews would row ashore and seize as manytortoises as they could. Once the animals were aboard the ship, the sailors wouldroll the tortoises onto their backs. The tortoises were completely helpless once ontheir backs, so they could only lie there until used for soups and stews. Almost100,000 tortoises were carried off in this way.

The tortoises faced other problems, too. Soon after the first ships, settlers arrivedbringing pigs, goats, donkeys, dogs and cats. All of these animals ruined life for the

tortoises. Donkey and goats ate all the plants that the tortoises usually fed on, whilethe pigs. Dogs and cats consumed thousands of baby tortoises each year. Within afew years, it was hard to find any tortoise eggs-or even any baby tortoises.

By the early 1900s, people began to worry that the last of the tortoises would soondie out. No one, however, seemed to care enough to do anything about the problem.More and more tortoises disappeared, even though sailors no longer needed themfor food. For another fifty years, this situation continued. Finally, in the 1950s,scientist decided that something must be done.

The first part of their plan was to get rid of as many cats, dogs and other animals as

they could. Next, they tried to make sure that more baby tortoises would be born. Todo this, they started looking for wild tortoise eggs. They gathered the eggs and putthem in safe containers. When the eggs hatched, the scientists raised the tortoisesin special pens. Both the eggs and tortoises were numbered so that the scientistsknew exactly which kinds of tortoises they had-and which island they came from.Once the tortoises were old enough and big enough to take care of themselves, thescientists took them back to their islands and set them loose. This slow, hard workcontinues today, and, thanks to it, the number of tortoises is now increasing every year. Perhaps these wonderful animals will not disappear after all.

20. What happened first?

A. Sailors took tortoises aboard ships.B. The tortoise meat was used for soups and stews.C. Tortoises were put onto their backs.D. Settlers brought other animals to the islands.E. Pigs had been all the sailors had to eat.

21. What happened soon after people brought animals to the islands?

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A. Tortoise eggs were kept in safe containers.B. Scientists took away as many animals as they could.C. The animals ate the tortoises' food and eggs.D. The tortoises fought with the other animals.E. The tortoises continued to wander freely.

22. When did people start to do something to save the tortoises?

A. in the 1500sB. in the 1950sC. in the early 1900sD. in the 1960sE. in the 1400s

23. What happens right after the tortoise eggs hatch?

A. The scientists take the tortoises back to their islands.

B. The scientists get rid of cats, dogs, and other animals.C. The sailors use the tortoises for food.D. The scientist raised the tortoises in special pens.E. The scientist encouraged the villagers to help.

24. What happened last?

A. The tortoises began to disappear.B. The number of tortoises began to grow.C. Scientists took away other animals.D. Tortoises were taken back to their home islands.

E. The number of tortoises began to decrease.

The first person in the group starts off by naming anything that is geographical. Itcould be a city, state, country, river, lake, or any proper geographical term. Forexample, the person might say,”Boston.” The second person has ten seconds tothink of how the word ends and come up with another geographical term startingwith that letter. The second participant might say, “Norway,” since the geographicalterm has to start with “N.” The third person would have to choose a word beginningwith “ Y.” If a player fails to think of a correct answer within the time limit, thatplayer is out of the game. The last person to survive is the champion.

25. This game may help you with-

A. historyB. musicC. geographyD. sportsE. current events

26. The person trying to answer needs-

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A. no time limitB. to know geography onlyC. to ignore the last letters of wordsD. to know something about spelling and geographyE. to be a good speller

27. Before you choose your own word, think about how-

A. the last word startsB. the last word endsC. smart you areD. long the last word isE. the spelling of the first word

28. The answer must be-

A. in New York

B. within the United StatesC. proper geographical termsD. in the same regionE. along a coast line

Charles A. Lindbergh is remembered as the first person to make a nonstop soloflight across the Atlantic, in 1927. This feat, when Lindbergh was only twenty-five years old, assured him a lifetime of fame and public attention.

Charles Augustus Lindbergh was more interested in flying airplanes than he was instudying. He dropped out of the University of Wisconsin after two years to earn aliving performing daredevil airplane stunts at country fairs. Two years later, he joined the United States Army so that he could go to the Army Air Service flight-training school. After completing his training, he was hired to fly mail between St.Louis and Chicago. Then came the historic flight across the Atlantic. In 1919, a New York City hotelowner offered a prize of $25,000 to the first pilot to fly nonstop from New York toParis. Nine St. Louis business leaders helped pay for the plane Lindbergh designedespecially for the flight. Lindbergh tested the plane by flying it from San Diego toNew York, with an overnight stop in St. Louis. The flight took only 20 hours and 21

minutes, a transcontinental record.

Nine days later, on May 20,1927, Lindbergh took off from Long Island, New York, at7:52 A. M. He landed at Paris on May 21 at 10:21 P. M. He had flown more than3,600 miles in less than thirty four hours. His flight made news around the world.He was given awards and parades everywhere he went. He was presented with theU. S. Congressional Medal of Honor and the first Distinguished Flying Cross. For along time, Lindbergh toured the world as a U. S. goodwill ambassador. He met his

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future wife, Anne Morrow, in Mexico, where her father was the United Statesambassador.

During the 1930s, Charles and Anne Lindbergh worked for various airlinecompanies, charting new commercial air routes. In 1931, for a major airline, theycharted a new route from the east coast of the United States to the Orient. The

shortest, most efficient route was a great curve across Canada, over Alaska, anddown to China and Japan. Most pilots familiar with the Arctic did not believe thatsuch a route was possible. The Lindberghs took on the task of proving that it was. They arranged for fuel and supplies to be set out along the route. On July 29, theytook off from Long Island in a specially equipped small seaplane. They flew by dayand each night landed on a lake or a river and camped. Near Nome, Alaska, theyhad their first serious emergency. Out of daylight and nearly out of fuel, they wereforced down in a small ocean inlet. In the next morning's light, they discovered theyhad landed on barely three feet of water. On September 19, after two moreemergency landings and numerous close calls, they landed in China with the mapsfor a safe airline passenger route.

Even while actively engaged as a pioneering flier, Lindbergh was also working as anengineer. In 1935, he and Dr. Alexis Carrel were given a patent for an artificialheart. During World War I in the 1940s, Lindbergh served as a civilian technicaladvisor in aviation. Although he was a civilian, he flew over fifty combat missions inthe Pacific. In the 1950s, Lindbergh helped design the famous 747 jet airliner. In thelate 1960s, he spoke widely on conservation issues. He died August 1974, havinglived through aviation history from the time of the first powered flight to the firststeps on the moon and having influenced a big part of that history himself.

29. What did Lindbergh do before he crossed the Atlantic?

A. He charted a route to China.B. He graduated from flight-training school.C. He married Anne Morrow.D. He acted as a technical advisor during World War II.E. He was responsible for the fuel supply for planes.

30. What happened immediately after Lindbergh crossed the Atlantic?

A. He flew the mail between St. Louis and Chicago.B. He left college.

C. He attended the Army flight-training school.D. He was given the Congressional Medal of Honor.E. He married Anne Morrow.

31. When did Charles meet Anne Morrow?

A. before he took off from Long IslandB. after he worked for an airlineC. before he was forced down in an ocean inlet

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D. after he received the first Distinguished Flying CrossE. when visiting his parents

32. When did the Lindberghs map an air route to China?

A. before they worked for an airline

B. before Charles worked with Dr. CarrelC. after World War IID. while designing the 747E. when he was thirty

33. What event happened last?

A. Lindbergh patented an artificial heart.B. The Lindberghs mapped a route to the Orient.C. Lindbergh helped design the 747 airline.D. Lindbergh flew fifty combat missions.

E. Charles finally was given an honorary degree from college.

Always read the meter dials from the right to the left. This procedure is much easier,especially if any of the dial hands are near the zero mark. If the meter has two dials,and one is smaller than the other, it is not imperative to read the smaller dial sinceit only registers a small amount. Read the dial at the right first. As the dial turnsclockwise, always record the figure the pointer has just passed. Read the next dialto the left and record the figure it has just passed. Continue recording the figures onthe dials from right to left. When finished, mark off the number of units recorded.

Dials on water and gas meters usually indicate the amount each dial records.

34. These instructions show you how to –

A. read a meterB. turn the dials of a meterC. install a gas meterD. repair a water meterE. be prepared for outside employment

35. Always read the meter dials-

A. from top to bottomB. from right to leftC. from left to rightD. from the small to the large dialE. from the large dial to the small dial

36. As you read the first dial, record the figures

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A. on the smaller dialB. the pointer is approachingC. the pointer has just passedD. at the topE. at the bottom

37. When you have finished reading the meter, mark off-

A. the number of units recordedB. the figures on the small dialC. the total figuresD. all the zero marksE. the last reading of the month

The village of Vestmannaeyjar, in the far northern country of Iceland, is as bright

and clean and up-to-date as any American or Canadian suburb. It is located on theisland of Heimaey, just off the mainland. One January night in 1973, however,householders were shocked from their sleep. In some backyards red-hot liquid wasspurting from the ground. Flaming “skyrockets” shot up and over the houses. Theisland's volcano, Helgafell, silent for seven thousand years, was violently erupting!

Luckily, the island's fishing fleet was in port, and within twenty-four hours almosteveryone was ferried to the mainland. But then the agony of the island began inearnest. As in a nightmare, fountains of burning lava spurted three hundred feethigh. Black, baseball-size cinders rained down. An evil-smelling, eye-burning,throat-searing cloud of smoke and gas erupted into the air, and a river of lava

flowed down the mountain. The constant shriek of escaping steam was punctuatedby ear-splitting explosions.

As time went on, the once pleasant village of Vestmannaeyjar took on a weirdaspect. Its street lamps still burning against the long Arctic night, the town layunder a thick blanket of cinders. All that could be seen above the ten-foot blackdrifts were the tips of street signs. Some houses had collapsed under the weight ofcinders; others had burst into flames as the heat ignited their oil storage tanks.Lighting the whole lurid scene, fire continued to shoot from the mouth of thelooming volcano.

The eruption continued for six months. Scientists and reporters arrived from aroundthe world to observe the awesome natural event. But the town did not die thateasily. In July, when the eruption ceased, the people of Heimaey Island returned toassess the chances of rebuilding their homes and lives. They found tons of ashcovering the ground. The Icelanders are a tough people, however, accustomed to thestrange and violent nature of their Arctic land. They dug out their homes. They evenused the cinders to build new roads and airport runways. Now the new homes ofHeimaey are warmed from water pipes heated by molten lava.

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38. The village is located on the island of-

A. VestmannaeyjarB. HebridesC. HeimaeyD. Helgafell

E. Heimma

39. The color of the hot liquid was-

A. orangeB. blackC. yellowD. redE. gray

40. This liquid was coming from the –

A. mountainsB. groundC. seaD. skyE. ocean

41. The island's volcano had been inactive for-

A. seventy yearsB. seven thousand years

C. seven thousand monthsD. seven hundred yearsE. seventy decades

42. Black cinders fell that were the size of__

A. baseballsB. pebblesC. golf ballsD. footballsE. hail-stones

43. Despite the eruption-

A. buses kept runningB. the radio kept broadcastingC. the police kept workingD. street lamps kept burningE. the television kept broadcasting

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44. This volcanic eruption lasted for six ___.

A. weeksB. hoursC. monthsD. days

E. years

Answer Key

Exercise 1:

1. B2. A3. A

4. C5. C6. B7. A8. A9. B10. B11. A12. A13. C14. C15. B16. A17. B18. B19. C20. A21. B22. B23. C24. A

25. B26. C27. B28. B29. B30. B31. A32. A33. B

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34. A35. A36. C37. B38. B39. B

40. B41. A42. C43. C44. B45. A

Exercise 2:

1. D2. D

3. E4. A5. B6. D7. D8. C9. A10. C

Exercise 3:

1. C2. D3. C4. A5. B6. B7. D8. B9. D10. D

11. C12. A13. D14. C15. B16. C17. A18. B19. D

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20. A21. C22. B23. D24. B25. C

26. D27. B28. C29. B30. D31. D32. B33. C34. A35. B36. C

37. A38. C39. D40. B41. B42. A43. D44. C

Vocabulary Test

Directions: Choose the word most opposite in meaning to the capitalized word.

1. GRATUITOUS:

(A) voluntary(B) arduous(C) solicitous(D) righteous(E) befitting

2. FALLOW:(A) fatuous(B) productive

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(C) bountiful(D) pertinacious(E) opprobrious

3. METTLE:(A) ad hoc(B) perdition

(C) woe(D) trepidation(E) apathy

4. SAVANT:(A) dolt(B) sage(C) attaché(D) apropos comment(E) state of confusion

5. RIFE:(A) multitudinous(B) blemished(C) sturdy(D) counterfeit(E) sparse

6. ABRIDGE:(A) distend(B) assail(C) unfetter(D) enfeeble(E) prove

7. PRODIGAL:(A) bountiful(B) dependent(C) provident(D) superfluous(E) profligate

8. REQUIEM:(A) humility

(B) prerequisite(C) resolution(D) reign(E) hiatus

9. METE:(A) indict(B) convoke(C) hamper(D) disseminate

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(E) deviate

10. SEVERANCE:(A) continuation(B) dichotomy(C) astringency(D) disclosure

(E) remonstrance

Match each word in the first column with its definition in the second column.

1. ANATHEMA A. hard2. ANNIHILATE B. curse3. ANOMALOUS C. gully4. APATHETIC D. suffocate5. ARCHAIC E. antiquated6. ARDUOUS F. destroy7. ARROYO G. abnormal8. ASPHYXIATE H. unconcerned9. ASTRINGENT I. make amends10. ATONE J. causing

contraction


1. HYPOCRITICAL:(A) forthright(B) judicious(C) circumspect(D) puritanical(E) unorthodox

2. VOLUMINOUS:(A) obscure(B) cantankerous(C) unsubstantial(D) tenacious(E) opprobrious

3. FANATICISM:(A) delusion(B) fascism

(C) remorse(D) cynicism(E) indifference4. INTERMINABLE:(A) finite(B) jejune(C) tranquil(D) incessant(E) imprudent5. ORNATE:

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(A) Spartan(B) blemished(C) sturdy(D) counterfeit(E) temporary

6. MUTABILITY:

(A) simplicity(B) apprehension(C) frailty(D) maverick(E) tenacity

7. VIRULENT:(A) benign(B) intrepid(C) malignant(D) hyperbolic(E) tentative

8. ABSTEMIOUS:(A) timely(B) immoderate(C) bellicose(D) servile(E) irreligious

9. VERBOSE:(A) subliminal(B) myopic(C) pithy(D) dauntless(E) ubiquitous

10. VISCID:(A) subtle(B) faint(C) slick(D) vicious(E) difficult


1. BESMIRCH A. unheeded prophet2. BICAMERAL B. peevish3. BILATERAL C. pertaining to dogs4. BOOTLESS D. plot5. BRANDISH E. farce6. BURLESQUE F. display menacingly7. CABAL G. unavailing8. CANINE H. two-sided

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9. CANTANKEROUS I. having two legislative branches10. CASSANDRA J. sully


1. DERISION:

(A) urgency(B) admonishment(C) uniqueness(D) diversity(E) acclaim

2. ANTIPATHY:(A) fondness(B) disagreement(C) boorishness(D) provocation(E) opprobrium

3. CAJOLE:(A) implore(B) glance at(C) belittle(D) ennoble(E) engender

4. CENSURE:(A) prevaricate(B) titillate(C) aggrandize(D) obscure(E) sanction

5. ADULATION:(A) immutability(B) reluctance(C) reflection(D) defamation(E) indifference

6. NOISOME:

(A) salubrious(B) affable(C) multifarious(D) provident(E) officious

7. CONSECRATE:(A) curb(B) destroy(C) curse

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(D) inveigh(E) exculpate

8. ILLUSTRIOUS:(A) bellicose(B) ignoble(C) theoretical

(D) esoteric(E) immaculate

9. DEIGN:(A) inveigh(B) gainsay(C) speculate(D) reject(E) laud

10. SUBTERFUGE:(A) bewilderment(B) artlessness(C) deceit(D) felicitation(E) jeopardy


1. COMMANDEER A. seize for military use2. COMMUNION B. apologetic3. COMPATRIOT C. perfect4. CONCERTED D. accord5. CONCORD E. done together6. CONFLUENCE F. pile7. CONGERIES G. flowing together8. CONSONANT H. harmonious9. CONSUMMATE I. countryman10. CONTRITE J. fellowship


1. UPSHOT:(A) consequence(B) descent

(C)

annihilation(D) termination(E) inception

2. WHET:(A) Obscure(B) blunt(C) desiccate(D) imbibe(E) enervate

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3. PRODIGY:(A) vacuous comment(B) hegemony(C) plane(D) common occurrence(E) capitulation

4. AMBULATORY:(A) immutable(B) obdurate(C) hospitalized(D) pedantic(E) stationary

5. PLATITUDE:(A) sincere comment(B) enigmatic comment(C) hostile comment(D) disingenuous comment(E) original comment

6. SEEMLY:(A) Redoubtable(B) flaccid(C) imperceptible(D) indigenous(E) unbecoming

7. CHAMPION:(A) relinquish(B) contest(C) oppress(D) modify(E) withhold

8. AIR:(A) release(B) differ(C) expose(D) betray(E) enshroud

9. PERTURBATION:(A) impotence(B) obstruction(C) prediction(D) equanimity(E) chivalry

10: TEMPESTUOUS:(A) prodigal

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(B) reticent(C) serene(D) phenomenal(E) accountable


1. DEBUNK A. decode2. DECIPHER B. refute3. DEDUCE C. conclusive4. DEFINITIVE D. conclude5. DEFUNCT E. to draw a line around6. DELINEATE F. extinct7. DENOMINATION G. belittle8. DEPRECATE H. sect9. DESOLATE I. pertaining to debate10. DIALECTIC J. forsaken


1. CURB:(A) bridle(B) encourage(C) reproach(D) ameliorate(E) perjure

2. DOCUMENT:(A) copy(B) implement(C) gainsay(D) blanch(E) rant

3. FLUID:(A) radiant(B) smooth(C) solid(D) balky(E) craggy

4.

BOLT:(A) linger(B) refrain from(C) subdue(D) strip(E) transgress

5. TABLE:(A) Palliate(B) acclimate

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(C) garner(D) propound(E) expedite

6. HARBOR:(A) provide shelter(B) banish

(C) acquiesce(D) extol(E) capitulate

7. STEEP:(A) desiccate(B) intensify(C) pontificate(D) whet(E) hamper

8. RENT:(A) reserved(B) restored(C) razed(D) busy(E) kinetic

9. EXACT:(A) extract(B) starve(C) lecture(D) menace(E) condone


1. DORMANT A. exuberant2. DOUGHTY B. puzzling3. DUET C. comprehensive4. EBULLIENT D. asleep5. EFFEMINATE E. omission of words6. ELLIPSIS F. unmanly7. EMANCIPATE G. charm8. ENCHANT H. liberate

9. ENCYCLOPEDIC I. twosome10. ENIGMATIC J. resolute


1. DISCORD:(A) agreement(B) supposition(C) strife(D) scrutiny

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(E) antithesis

2. KEEN:(A) concentrated(B) languid(C) rash(D) caustic

(E) voracious

3. IRRELEVANT:(A) moot(B) onerous(C) impertinent(D) germane(E) true

4. FACILITATE:(A) appease(B) expedite(C) extol(D) foil(E) precipitate

5. FEND:(A) absorb(B) disperse(C) intensify(D) reflect(E) halt

6.

PORTLY:(A) ill(B) thin(C) dull(D) rotund(E) insipid

7. DEPLETE:(A) tax(B) annotate(C) replenish

(D) lecture(E) vanquish

8. INCESSANT:(A) intermittent(B) continual(C) increasing(D) enclosing(E) expanding

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9. PERJURE:(A) absolve(B) forswear(C) impeach(D) authenticate(E) mortify

10.

PLETHORA:(A) dishonor(B) paucity(C) glut(D) resolve(E) deluge


1. EXHORT A. free from blame2. EXONERATE B. strongly urge3. EXPOSTULATE C. agitator4. EXTRADITE D. untamed5. EXULT E. debacle6. FACTITIOUS F. inane7. FATUOUS G. artificial8. FERAL H. deport9. FIASCO I. rejoice10. FIREBRAND J. protest


1. ASSIMILATE:(A) strive(B) adapt(C) synchronize(D) estrange(E) officiate

2. INADVERTENT:(A) accidental(B) disingenuous(C) forthright(D) inconsiderate(E) calculated

3. ABSCOND:(A) pilfer(B) replace(C) glean(D) substitute(E) surrender

4. FOMENT:(A) exhort

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(B) dissuade(C) cower(D) abet(E) fixate

5. EXTENUATE:(A) alleviate

(B) preclude(C) worsen(D) subdue(E) justify

6. NONPAREIL:(A) consummate(B) juvenile(C) dutiful(D) ordinary(E) choice

7.

REPUDIATE:(A) denounce(B) deceive(C) embrace(D) fib(E) generalize

8. NOXIOUS:(A) diffuse(B) latent(C) beneficial(D) unique(E) unjust

9. SUFFRAGE:(A) absence of charity(B) absence of franchise(C) absence of pain(D) absence of success(E) absence of malice

10. GLEAN:(A) gaffe

(B) furor(C) gather(D) frolic(E) foist


1. GRANDIOSE A. drink2. GRIEVOUS B. pertaining to marriage3. HALCYON C. arrogance

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4. HARLEQUIN D. prejudiced5. HEDONISM E. teaching device, method6. HEURISTIC F. the pursuit of

pleasure in life7. HIDEBOUND G. clown8. HUBRIS H. serene9. HYMENEAL I. heinous

10. IMBIBE J. impressive


1. INCONGRUOUS A. harden2. INCONSPICUOUS B. relentless3. INDECOROUS C. hostile4. INDIGNANT D. cannot be fully

understood5. INDURATE E. out of place, absurd6. INEXORABLE F. not noticeable7. INIMICAL G. unseemly8. INSCRUTABLE H. resentment of injustice9. INSOUCIANT I. nonchalant10. INSUPERABLE J. insurmountable

Match each word in the first column with its definition in the second column..1. LACHRYMOSE A. trickery2. LAGGARD B. roué3. LASCIVIOUS C. very small4. LEGERDEMAIN D. tearful5. LIBERTINE E. loafer6. LILLIPUTIAN F. lustful7. LOQUACIOUS G. talkative8. MACHIAVELLIAN H. comical misuse of a word9. MAGISTERIAL I. arbitrary, dictatorial10. MALAPROPISM J. politically crafty,

cunning


1. MISCELLANY A. peerless2. MISSIVE B. to gather one‟s forces 3. MOOT C. newly coined expression4. MOUNTEBANK D. self-love5. MULTIFARIOUS E. loyal followers6. MUSTER F. letter7. MYRMIDONS G. diverse8. NARCISSISM H. charlatan9. NEOLOGISM I. disputable10. NONPAREIL J. mixture of items

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1. ORDNANCE A. a model2. ORTHODOX B. local speech

3. OUTMODED C. convulsion4. PALAVER D. stingy5. PANEGYRIC E. agent causing disease6. PARADIGM F. artillery7. PARLANCE G. conventional8. PAROXYSM H. out-of-date9. PARSIMONIOUS I. babble10. PATHOGEN J. praise


1. PHOENIX A. cliff2. PILLORY B. inclination3. PITTANCE C. warning4. PLAUDIT D. acclaim5. PLETHORA E. overabundance6. POGROM F. after death7. POSTHUMOUS G. massacre8. PRECIPICE H. rebirth9. PREDILECTION I. punish by ridicule10. PREMONITION J. trifle


1. PROTEAN A. bulge2. PROTUBERANCE B. changing readily3. PROVISIONAL C. steal4. PUNDIT D. majority5. PURLOIN E. temporary6. PURPORT F. a cessation of activity7. QUAVER G. line8. QUEUE H. tremble9. QUIETUS I. claim to be10. QUORUM J. politically astute person


1. REGIME A. vulgar2. REJOINDER B. quick reply3. REMUNERATION C. uneasy4. RENDEZVOUS D. necessary5. RENT E. miscreant6. REPROBATE F. rupture7. REQUISITE G. a meeting8. RESTIVE H. compensation

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9. RETRIBUTION I. retort10. RIBALD J. a government

Match each word in the first column with its definition in the second column.1. SCRUPLES A. figure of speech2. SCYTHE B. proper, attractive3. SEEMLY C. long, curved blade

4. SENTENTIOUS D. left-handed5. SERENDIPITY E. pertaining to the stars6. SHIBBOLETH F. signer7. SIDEREAL G. making fortunate

discoveries8. SIGNATORY H. password9. SIMILE I. misgivings10. SINISTRAL J. concise


1. STAVE A. distress2. STEVEDORE B. diligent3. STRAIT C. ward off4. STUDIOUS D. longshoreman5. SUBJUGATE E. various6. SUBTERFUGE F. overabundant7. SUNDRY G. suppress8. SUPERFLUOUS H. cunning9. SUPINE I. dreamlike10. SURREAL J. lying on the back


1. SWATCH A. to foil2. SYNOD B. anguish3. TACIT C. concise4. TALON D. provisional5. TAURINE E. agitated6. TEMPESTUOUS F. bull-like7. TENTATIVE G. claw8. TERSE H. understood without

being spoken


1. TIDINGS A. incisive2. TITER B. omnipresent3. TITULAR C. lethargic4. TORPID D. figurehead5. TRADUCE E. unrestrained6. TRENCHANT F. news7. UBIQUITOUS G. laugh nervously8. ULULATE H. ceaseless9. UNABATED I. wail

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10. UNBRIDLED J. slander


1. UNCOUTH A. disheveled2. UNDULY B. capable of

surviving

3. UNFLAGGING C. awkward4. UNKEMPT D. uncultured5. UNSTINTING E. truthfulness6. UNTENABLE F. whim7. UNWIELDY G. unrelenting8. VAGARY H. cannot be

achieved9. VERACITY I. generous10. VIABLE J. excessive

Sentence Completion

Directions for questions 1 to 25: Fill in the blanks with appropriate verbs.

1. I _____ him to come to the market with me.1) warned2) wished3) requested4) liked

2. As the floor was dirty she _____ the room quickly1) rode2) dusted3) shoved4) swept

3. He is going to start _____ around for a new job1) making2) going3) looking4) talking

4.

She _____ the tray down on a table next to the1) slowed2) kept3) set4) shock

5. We have _____ some good times together, she and I1) looked2) laughed3) smiled4) seen

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6. That girl really _____ after her mother1) takes2) talks3) goes4) backs

7. The UN has called on the warring factions to _____ aside their differences1)

keep2) put3) talk4) give

8. The pastry was so fluffy that it _____ in my mouth1) broke2) melted3) disappeared4) filled

9. I got a number of addresses _____ for the festival season1) bought2)

brought3) stitched4) borrowed

10. It was a bitter pill to _____1) swallow2) take3) eat4) make

11. We _____ the station in time but the train was an hour late1) came2) went3) reached4)

returned

12. There was a sale going on; I _____ some clothes at throw away prices1) bought on2) picked up3) stitched4) caught

13. They always _____ fault with me1) show2) tell3) say4) find

14. The principal _____ to speak to you1) wanting2) is wanting3) wants4) want

15. When I get home, my pet _____ at the door waiting for me1) sits2) has been sitting

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3) will sit4) will be sitting

16. I _____ a new car last month1) had bought2) have bought3) bought4) would have bought

17. If the _____ your plans, he will be surprised1) hears for2) would hear3) hears of4) will hear

18. She _____ unconscious since four „0‟ clock 1) is2) has been3) was4) had been

19. He had some work, so he _____ out five minutes ago1) has gone2) had gone3) went4) was going

20. We were _____ the radio all evening for news1) listening2) listening to3) hearing4)

hearing to

21. Grandma was very, very _____ because the little boy broke the vase.1) pleased2) cross3) hurt4) hated

22. The bus was so _____ that there was no place even to stand1) applied2) needed3) used4) crowded

23. The Indian team won the toss and _____ to bat first1) left2) fought3) thought4) opted

24. I _____ my fingers to the one on that particular project1) burnt2) spent

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3) worked4) tired

25. She _____ my watch when I was not looking1) protested2) stole3) knocked4) gave

Directions for questions 1 to 25: Fill in the blanks with appropriate adjectives.

1. Marijuna has few with drawl effects and this has given rise to the _____ belief that it is not anaddictive.1) mistake2) mistaken3) misunderstood4) mitigating

2. The _____ diet has too little fibre in it.1) modernistic2)

modal3) modern-day4) mock

3. An _____ crowd assembled at the gate on Monday.1) ordinary2) ornery3) ornate4) orderly

4. I have a _____ hunting knife1) raw2) rationalistic3)

raven4) razor-sharp

5. Have a sandwich; you must be _____.1) thirsty2) realistic3) accomplished4) unguarded

6. Although he is bind he is an _____ singer.1) accident prone2) accessible3) accomplished4)

unguarded

7. The disappearance of the letter made the situation all the more _____.1) piquant2) pious3) pioneering4) pitiful

8. The Afghani refugees are living in _____ conditions.1) pitch-black

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2) pivotal3) pitiable4) funny

9. America is conducting _____ raids on Afghanistan1) reticent2) metro-active3) revealing4)

retaliatory10. He is an _____ athlete who also paints very well.

1) all-rounder2) all time3) all-round4) all-star

11. She writes equally well with both hands; she is _____.1) ambivalent2) ambiguous3) ambidextrous4) articulate

12.

Mandela‟s release was a/an _____ event in South Africa‟s history 1) pithy2) pivotal3) funny4) interesting

13. This is a _____ disease1) water-born2) born and bread3) water-borne4) born-again

14. I am sure they will be _____ to rational argument1)

ambivalent2) ambitious3) amenable4) ambient

15. They put up a/an I am sure they will be _____ to rational argument performance of King Lear1) ambient2) altruistic3) amicable4) sensible

16. She was tall, blonde and I am sure they will be _____ to rational argument looking.1) interesting2)

beautiful3) athletic4) atavistic

17. Most refugees live in _____ conditions1) worst2) worse3) dirty4) atrocious

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18. His paintings are _____1) amateurish2) anaerobic3) analgesic4) antistatic

19. I think he requires a _____ diet.1) great2)

large3) hot4) nutritious

20. The _____ friends that I have are very helpful.1) little2) many3) few4) most

21. I pretended not to notice but I saw that he had given me a _____ look.1) balding2) baleful3)

balmy4) bald

22. She came In wet and _____.1) bedraggled2) becoming3) cheerful4) bereft

23. I am fed up with being _____ all the time.1) hungry2) thirsty3) broke4)

broken-hearted

24. He waged a _____ fight against crime but was unsuccessful1) ceaseless2) central3) censorious4) certain

25. I wrote a _____ note on his success1) communicable2) congratulatory3) commiseratory4) committed

Directions for questions 1 to 25: Fill in the blanks with suitable adverbs.

1. The guests were welcomed _________ by the host1) cordially2) casually3) keenly4) voluntarily

2. The sky, which thundered _________, indicated a terrible storm.

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1) radiantly2) menacingly3) vigorously4) alluringly

3. The Minister _________ stated that stringent action would be taken against the erring officials.1) ambiguously2) impudently3)

sarcastically4) categorically

4. The waiter was tipped _________ by the rich man.1) beautifully2) handsomely3) gently4) prompously

5. The man was so _________ dressed that he almost looked like a clown.1) garishly2) modestly3) decently4)

suavely

6. The brave warrior _________ fought against the enemies.1) haltingly2) valiantly3) indiscriminately4) distinctly

7. He _________ imposed strict discipline1) rigorously2) caustically3) casually4) abundantly

8. The sluggard did nothing constructive, except rambling on the strets _________.1) aimlessly2) religiously3) perversely4) spuriously

9. A country can be termed truly secular when people of all religions lived _________.1) surreptiously2) comfortable3) decently4) harmoniously

10. The wealthy old man _________ bequealthed a huge portion of his property to the orphanage.1)

magnanimously2) courteously3) graciously4) covetously

11. He glanced _________ at the document, which was supposed to be kept confidential.1) Stealthily2) threateningly3) dejectedly4) benevolently

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12. As the matter is _________ clear there is no reason for ambiguity.1) pragmatically2) practically3) explicitly4) conveniently

13. As she was thoroughly satisfied with her preparation, she entered the examination hall _________.1)

competently2) adeptly3) skillfully4) confidently

14. Although I am averse to watching movies, I _________ visit the theatre to watch plays.1) rarely2) occasionally3) fervently4) specifically

15. The rose is _________ the queen of flowers.1) controversially2)

authentically3) indisputably4) speciously

16. The boys _________ flung stones at the limping dog.1) dangerously2) casually3) mercilessly4) fearlessly

17. I drove the car _________ while negotiating the curves on the ghat road.1) cautiously2) conveniently3)

fearfully4) precariously

18. Many people wept _________ at the loss of their beloved leader.1) exclusively2) inconsolably3) intensely4) excruciatingly

19. The workers _________ demanded better wages.1) industriously2) resolutely3) persistently4)

decisively

20. The polyglot spoke many foreign languages quite _________.1) proficiently2) fluently3) enthusiastically4) incredibly

21. The thieves entered the house _________.1) Timidly

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2) docilely3) furtively4) discursively

22. As the Minister did not want to divulge the information, he replied ________ _ to the journalists‟queries.1) mockingly2) sarcastically3)

secretly4) evasively

23. One cannot form an opinion about a person by _________ looking at his face.1) trivially2) merely3) peculiarly4) intently

24. The event was so _________ planned that there was no cause for complaint.1) minutely2) meticulously3) intricately4)

nimbly

25. Although I was initially nervous to address a gathering, _________ I overcame my nervousness.1) eventually2) generally3) casually4) evidently

Directions for questions 1 to 25: Fill in the blanks with appropriate prepositions.

1. The carpet ____ the table is threadbare.1) on2)

in3) through4) under

2. He stands ____ the school gate everyday six 0‟ clock. 1) about2) up3) on4) near

3. Alcohol is injurious ____ health.1) for2) to3)

of4) with

4. Since she is my neighbour, I am acquainted ____ her.1) of2) with3) by4) at

5. Although he is not rich, he is contended ____ his lot.

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1) about2) around3) with4) of

6. I congratulate you ____ your success.1) at2) on3)

for4) before

7. The food was shared ____ ten girls.1) between2) besides3) beside4) among

8. The beggar walked ____ his dog.1) besides2) between3) beside4) near

9. The deer was killed ____ a hunter in the forest.1) with2) by3) for4) from

10. He was accused ____ forgery by his boss.1) about2) after3) of4) to

11. The dog ran ____ the road.1)

about2) in3) across4) upon

12. Sheena and her friends quarreled ____ themselves without rhyme of reason.1) between2) among3) about4) around

13. She was ____ death‟s door, when the man entered her life. 1) in2)

on3) for4) at

14. I sent the parcel to my friend ____ courier1) through2) with3) by4) into

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15. I never use a credit card; I always settle bills ____ cash.1) by2) with3) in4) to

16. He has not yet recovered ____ is illness.1) with2)

from3) over4) about

17. Mahatma Gandhi worked very hard ____ the welfare of the country1) by2) with3) for4) towards

18. ____ his father‟s death, lyotiraditya Sandia was crowned king. 1) Before2) Within3)

Behind4) After

19. He hanged himself ____ a piece of cloth.1) by2) to3) with4) around

20. We must reach our destination ____ sunset.1) besides2) by3) at4)

on

21. ____ his children, his nephews and nieces were present.1) Beside2) About3) Around4) Besides

22. I have eaten nothing ____ morning1) from2) for3) since4) till

23. He is bright boy; he is always ____ the top of his class1) in2) at3) on4) over

24. The ICICI charges interest ____ twelve percent.1) on2) for

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3) with4) at

25. ____ what I know of him, I hesitate to trust him.1) Of2) About3) From4) Since

Directions for questions 1 to 25: Fill in the blanks with appropriate prepositions.

1. This work is ___ my capacity.1) after2) beyond3) beside4) after

2. ___ this, I wash my hands off you.1) Before2) Beyond3) After4) For

3. The goods were sold ___ the auction.1) in2) behind3) around4) at

4. The programme lasted ___ the night.1) through2) around3) about4) into

5.

As he was walking on the road, he was stunned ___ a blow on the head.1) with2) by3) on4) from

6. She said something ___ leaving town.1) around2) with3) about4) of

7. Do you think this shirt is too tight ___ the shoulders?1)

around2) on3) across4) throughout

8. The party went on until ___ midnight.1) by2) through3) beyond4) about

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9. it is ___ my principles to borrow money.1) around2) about3) against4) beyond

10. The child stood ___ the curtain with only his shoes peeping out.1) beyond2)

besides3) behind4) beside5)

11. There was a ladder behind my house propped up ___ the wall.1) around2) through3) at4) against

12. My brother was working for Telco ___ 1995, when he got a job at Siemens Nixdorf.1) with2) at3)

until4) from

13. We spent the whole after noon walking ___ the town.1) about2) within3) beyond4) in

14. The fool has parked his scooter right ___ the entrance to the driveway1) beyond2) across3) within4)

on

15. ___ the span of a year, three of the town‟s biggest factories have closed down. 1) Within2) In3) Behind4) Beyond

16. He beamed ___ pleasure when he heard the news.1) in2) with3) from4) on

17. ___ all his faults, I still like him.1) In2) At3) Until4) With

18. I could see something glittering ___ the water.1) below2) beneath

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3) under4) beyond

19. They were suddenly plunged into darkness as the train went ___ the tunnel.1) into2)

through3) in4) between

20. She has been ___ a lot of pressure at work1) by2) in3) under4) beneath

21. Wait until the lights change ___ green1) into2) to3)

from4) for

22. He was standing with his back ___ me1) at2) behind3) towards4) to

23. These families are living ___ the official poverty line.1) below2) under3) beneath4)

beyond

24. Theves is a large international organization with offices ___ the world.1) through2) in3) across4) throughout

25. ___ the mist she could just make out his silhouette1) Over2) Beyond3) Through4) Across

Directions for questions 1 to 25: Fill in the blanks with appropriate conjunctions.

1. Elizabeth works hard, ____ Jane is lazy.1) and2) or3) because4) but

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2. ____ he is poor, he is contented.1) Unless2) Until3) Though4) Yet

3. I trust her ____ she always speaks the truth.1) hence2)

thus3) because4) but

4. Wait for me ____ I return.1) if2) so3) till4) as

5. I range the bell ____ no one answered1) but2) but3)

so4) if

6. He failed in the examination ____ he did not work hard.1) but2) although3) because4) therefore

7. You must not tell lies ____ your mother will punish you.1) or2) but3) and4)

unless

8. Don‟t go there ____ you are called 1) since2) therefore3) unless4) because

9. Is Rita your sister ____ your cousin?1) and2) but3) or4) because

10.

I am going to Kolkata ____ my brother is going to Chennai.1) whereas2) even3) because4) since

11. ____ he was an industrious worker, I encouraged him.1) Unless2) Though3) Before

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4) As

12. You will get late ____ you hurry to the meeting1) because2) unless3) if4) though

13.

You must be tired ____ you have walked such a long distance.1) though2) than3) but4) since

14. Not ____ I loved Caesar less, but that I loved Rome more.1) than2) if3) that4) though

15. I am in the right ____ you are in the wrong1)

because2) since3) for4) but

16. We judge ourselves by what we feel capable of doing ____ others judge us by what we havealready done.1) than2) and3) but4) except

17. ____ I have no money to spend, you have no one to spend it on.1)

When2) While3) And4) But

18. He does well, ____ that he is nervous at the beginning1) simply2) only3) and4) so

19. ____ she had given up smoking, she kept her lighter with her.1) If2)

That3) Although4) Except

20. ____ we approached the house, We heard the sound of music.1) where2) that3) if4) when

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21. I know you better ____ he does!1) that2) than3) while4) when

22. He bled so profusely ____ he died1) that2)

than3) while4) when

23. She has already packed all her belongings ____ I just have to take them to her new flat.1) but2) that3) except4) and

24. My shoes were full of water ____ I took them off1) and2) because3)

so4) that

25. It was difficult to understand people for a long time ____ eventually I got used to them.1) and2) but3) except4) because

Fill in the blanks with appropriate prepositions.

1.

She jumped ________ the river.1. into 2. in 3. on 4. onto

2.

The thief jumped ______ the wall.1. on 2. at 3. over 4. across

3. The bird flew in ____ the window.1. from 2. at 3.through 4. of

4. He is looking _________ a painting1. to 2. at 3. with 4. for

5.

They are digging the earth _______ an axe1. from 2. of 3. with 4. across

6. He has been waiting ________ the results1. with 2. of 3. off 4. for

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7.

Ravi put up _____ his friend in Mysore1. at 2. of 3. along 4. with

8. I prefer Hindi songs ________ Telugu songs1. to 2. for 3. with 4. from

9.

This house consists ________ many rooms1. with 2. for 3. of 4. between

10.

There was a quarrel _______ all members1. between 2. beside 3. with 4. among

11. Mrs. Radhika watches E Tv ________ Gemini Tv1. besides 2. beside 3. with 4. from

12. She was tired ______ the work1. with 2. of 3. from 4. in

13.

The temperature varies _________ 20 and 25 degrees1. from 2. in 3. with 4. between

14.

Children impress their parents ________ their mumbling words1. with 2. in 3. from 4. on

15. Can I have a holiday ________ Monday?1. on 2. in 3. since 4. for

16.

We are not accustomed ________ the new place

1. at 2. to 3. in 4. on

17.

Owing _________ some problems he stopped his education1. on 2. to 3. at 4. from

18. They came ________ the room slowly1. into 2. onto 3. in 4. for

19.

The girl was absorbed _________ her work1. on 2. in 3. for 4. upon

20.

The child climbed _________ the chair slowly1. into 2. from 3. onto 4. in

21. I am sorry ________ being late1. on 2. for 3. since 4. into

22. _________ his house there is a small shop1. besides 2. by 3. beside 4. at

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23.

A good judge never jumps _______ the conclusion1. to 2. at 3. on 4. for 5. with

24. Are not these slums a disgrace __________ the civic authorities1. for 2. to 3. towards 4. on

25.

Very often we do not get what we pine _______1. about 2. for 3. at 4. on

26.

The customer smashed his fist down ____ the table1. into 2. at 3. on 4. against

27. He thought that his father was not happy ______ him1. with 2. about 3. for 4. at 5. over

28. Let this be an example _________ the trouble makers1. for 2. about 2. against 4. to 4. with

29.

What you say hardly any bearing ______ the lives of tribals1. about 2. for 3. on 4. with

30.

Men have made ships that can sail _________ the sea and fly. _______ the air1. along; above 2. on; in 3. over; into 4. upon; through

31. I must hold discussions ___ you ____ that matter shortly1. about; in 2. with; in 3. with; for 4. about; for

32.

The Indian magpie indulges _____ a long flight

1. in 2. with 3. on 4. at 5. over

33.

The thunder was accompanied _________ heavy rains1. with 2. by 3. up 4. through

34. A steady mind triumphs _______ difficulties1. in 2. over 3. at 4. with

35.

He resembles ________ his mother1. with 2. in 3. at 4. None of these

36.

The teacher has no control _______ the students1. on 2. over 3. in 4. at

37. Ram is confident _____ his success1. of 2. for 3. about 4. toward

38. Your statement is very much similar mine1. to 2. of 3. about 4. on

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39.

My relations _______ Preeti are good1. to 2. on 3. with 4. against

40. I have a distaste _______ publicity1. for 2. about 3. against 4. at

41.

There is an old building ________ the rice fields.

42. The mad beggar threw stones _______ the children.1. at 2. in 3. on 4. from

43.

The car knocked against the sign post and ran _____ the road.1. across 2. over 3. on 4. from

44.

The old man walked _______ the park towards the road.1. at 2. in 3. to 4. from

45.

The car went slowly ________ the tunnel.1. through 2. in 3. to 4. from

46. They went ______ the railway line looking for the missing child.1. towards 2. to 3. at 4. from

47.

The crowd pressed ________ the gate.1. from 2. to 3. on 4. towards

48. The thief jumped ________ the wall.1. across 2. over 3. on 4. at

49. The aero plane flew _______ the clouds.1. to 2. in 3. through 4. from

50.

We are leaving ________ the school in a few minutes.1. at 2. in 3. on 4. for

51. We asked the thieves to come _________ their hiding place.1. at 2. in 3. to 4. from

52.

The meeting will be over ________about an hour.

53. The prize distribution function will be held ________17th March _______ 4 p.m.

54.

I shall wait for you ________ 5 p.m.______ 6 p.m.______ Sunday. I hope you will

come.

55. Progress reports are sent to the parents _______ the end of the month.

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56.

I am always at home _______ a Sunday morning.

57. The examinations will begin ______ the first week of May and end ______ the

15th.

58.

He has been in the hospital _________ January.

59.

He was in the hospital _______ January _________ March.60.

Our shop has announced a clearance sale __________ Durga Puja.

61.

______ the time the fire brigade arrived, the house had been reduced to ashes.

62. The next meeting will be held _______ my house _________ Model Town.

63. The train was passing ________ a bridge.

64.

Two cars collided __________ the middle of the road.

65. A boy sitting _________ the back of the class tried to disturb me.

66.

The members of his family are always quarrelling _______ themselves.

67.

Our boat was exactly ________ the bridge.

68. She stood ___________ the window and waved to me.

69.

There is a thick fog __________ the entire city.

70.

There is an almirah _________ the window and the door.

71. She had a deep cut ______ her left eye.

72.

I took off my shoes and put them _________ the table.

73.

I could see only his head _______ water.

74.

There was a fan exactly ___________ my head.

75. I stayed _______ my uncle‟s house last night.

76. He sat _____ the table to write a letter. (at, on)

76. We rested ________ a tree. (under, below)

77.

They have troubled us _______ the beginning. (since, from)

78.

Come and sit _______ me. (beside, besides)

79. Someone is knocking _______ the door. (at, on)

80.

Distribute these books ________ the two sisters. (between, among)

81. The soldiers marched __________ battlefield. (in, into)

82. The traveller was struck ________ lightning. (with, by)

83.

Father is not ________ home just now. (in, at)

84. Is the train _______ time? (in, on)

85. This book is quite different ________ that. (than, from)

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86.

She was born ________ Bombay. (at, in)

87. She peeled the vegetables _________ a knife. (by, with)

88. I have been suffering from fever ________ Monday. (since, from)

89.

I shall return your money _______ a week. (in, at)

90.

Come _________ the garden, please. (in, into)91.

The hunter killed the bird ________ a stone. (with, by)

92.

The work should be finished __________ Sunday. (by, till)

93. We travelled to Bombay ________ train. (in, by)

94. We arrived _________ the station quite ________ time. (on, at; on, in)

95.

He aimed ______ becoming a dentist.

96. The police wrongly charged him ________ murder.

97.

You need not feel anxious _________ my welfare.

98.

If you had availed yourself ________ that offer, you would have risen high in life.

99. Students complained __________ the poor food provided in the hostel.

100.

She always dreamt ________ becoming an accomplished

dancer.

101. The judge held him guilty ________ theft.

102.

The doctor insisted ________ performing the operation

immediately.

103.

I take pride ____________ being an Indian.

104.

Your complaint was referred ______ the higher authorities.

105. Our bus collided __________ a van.

106. Your essay is worthy ________ the first place.

107.

The blind man knocked _________ a wall.

108.

I requested my neighbour to send __________ a doctor.

109. He appealed ________ the High Court _______ decision of the

city magistrate.

110. He might have been blind _______ an eye but he was not blind

__________ his weakneses.

111.

If you are dealing ________ jewellery, you may have to deal

________ different customers.

112. The whole class agreed _____ this point.

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113.

Do you trust ________ God?

114. We warned the driver _______ danger ahead.

115. I enquired ________ him about your address.

116.

Maruti is superior _________ any other Indian car.

117.

They were quarrelling ________ an ordinary matter.118.

Neha is always boasting __________ her intelligence.

119.

King Humayun died _______ a fall.

120. One should always take care ________ one‟s health.

121. My father was very angry _______ me.

122.

She was annoyed _______ her son ________ behaving so

stupidly.

123. She was annoyed _____ her son‟s stupid behaviour.

124.

Bindu apologized ______ her teacher _______ her rudeness.

Choose the appropriate choice:

1.

It rained heavily while they ________ home.1. are returning 2. returning 3. were returning 4. returned

2. When the doctor touched the patient he _________1. had already died 2. already died 3. already dead 4.

has already died

3.

I bought a new house last year, but I __________ my old house yet1. did not sell 2. have not sold 3. not sell 4. have sold

4. Mary _______ in Germany for years1. has been 2. is been 3. is 4. was been

5.

The government _______________ a lot of money on welfare schemes last year1. spends 2. spending 3. spent 4. was spending

6.

When we ______________ the station the train had already left1. had reached 2. reached 3. was reaching 4. has reached

7. She never _______ in others affairs1. interferes 2. is interfering 3. had interfered 4. interfere

8. The driver will not start the bus until all vacant seats ________1. filled 2. are filled 3. had filled 4. were filled

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9.

Mr. Gopal ________ on the ice for two hours when his friends arrived1. has been skating 2. was skating 3. had been skating 4. isskating

10. They sold their old colour TV set two months ago. They ______ a new one yet.1. have not bought 2. have bought 3. had not bought 4.

did not buy

11. Ms. Revati ________ her mother1. resembles 2. is resembling 3. has resembled 4. has been resembling

12.

Children will not learn anything if they ________1. are discouraged 2. have been 3. had been 4. were

13.

If he had answered all questions well, he _________1. will have selected 2. would have beenselected

3. was selected 4. had selected

14. They asked me what __________1. is my name 2. was my name 3. has been my name 4. my name was

15. Shaker enquired the guard whether anyone _________ in his absence1. had come 2. has come 3. was coming 4. is coming

16.

He insisted on he was innocent.1. insisted on that 2. insisted that 3. insists that 4. No correction

17.

John, who studies medicine at present, hopes to go abroad after graduation.1. is studying 2. will study 3. studies 4. No correction

18. Students are attending spoken English classes since 6th February.1. were attending 2. have been attending 3. have attended 4.No correction

19. Would you please tell me when the next train comes?1. when the next train come 2. when comes the next train3. when the next train does come 4. No correction

20.

In this deteriorate condition, you should call in a good doctor.1. deteriorating 2. deteriorating 3. to deteriorated 4. No correction

21. I went to see the film as it is being directed by Satyajit Ray.1. had been directed by 2. was directed by3. had directed by 4. No correction

22.

To lock up a man and let him doing nothing is a cruel punishment.1. let him do nothing 2. letting him do nothing

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3. to let him do nothing 4. No correction

23. At last we realized what was truth.1. what was the truth 2. what the truth was 3. the truth was 4. No correction

24.

In summer, days are more warmer than night.1. more warm 2. warmer 3. warmest 4. No correction

25.

He has studied French since four years.1. since four years ago 2. from four years 3. from four years 4.for four years

26.

He had not ought to do it.1. has not ought to do 2. ought not had done 3. ought not hasdone 4. ought not have done

27.

It will depend now on they coming on time.1. their coming 2. them coming 3. theirs coming 4. they come

28.

I felt that the music was sweetly and soothingly.1. sweetly but soothingly 2. sweet and soothing3. sweetly and soothing 4. sweet but soothing

29.

He did not know the answer and I did not neither.1. and neither did I 2. and either did I 3. and neither have I 4. and either did have

Use the appropriate form of the verbs:-

42. I had to leave early next morning. So I _______ to bed early.1. go 2. went 3. am going 4. have gone

43.

She wasn‟t feeling well. So she ______ much. 1. eats 2. don‟t eat 3. ate 4. didn‟t eat

44.

We were getting late. We _____ time to wait for anybody.1. have 2. don‟t have 3. didn‟t have 4. do have time

45. How did you learn to paint? My father ________ me.1. teaches 2. teach 3. taught 4. has taught

46.

The sound system wasn‟t good. We _____ the movie. 1. enjoyed 2. were not enjoying 3. did not enjoy 4.

have enjoyed

47. I knew you were inside praying. So I _____ you.

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1. disturbed 2. didn‟t disturb 3. don‟t disturb 4.have disturbed

48. It was a noisy place. So I _____ well.1. did sleep 2. could sleep well 3. couldn‟t sleep 4.

slept

49.

Vicky wasted a lot of money yesterday. He _______ an imported camera, which ____ Out to be good.

1. purchased, turned 2. has purchased,turned3. has purchased, didn‟t turn out 4.purchased, didn‟t turn out

50. As soon as Dick______ the message over his radio, he ____ off towards the site ofthe accident.1. hears, shot 2. heard, is shooting 3. heard, shot 4. heard, is shooting

51.

Your performance in most of the subjects is good. But why----- poor marks inscience?1. did you secure 2. didn‟t secure 3. have you secured4. secured

52. She ______ for more than two hours. She must be quite tired by now.1. sang 2. was singing 3. has been singing 4. is singing

53.

It _____ so hard since yesterday that all the rooftops have turned totally white.1. Snowed 2. is snowing 3. has been snowing 4. had been snowing

54.

Since when _____ medicines from this chemist?1. you are purchasing 2.you have purchased3. have you been purchasing 4. you purchased

55.

A: Any interesting news?B: Sorry. I ______ the newspaper yet.1. did not read 2. have not read 3. have not been reading 4. don‟t read

56.

When is Anil leaving for office?He _____ .

1. is already leaving 2. is already left 3. has already left 4.

has been leaving

57.

I ____ that you have resigned your job.1. hear 2. am hearing 3. will hear 4. will have heard

58. I_______ he will come.1. am doubting 2. doubt 3. will doubt 4. shall be doubting

59. The car you _______ at ________ to my father.

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1. are looking, belonged 2. are looking, belongs3. looked, is belonging 4. looks, belongs

60. The captain was the last man ______ the sinking ship.1. left 2. to leave 3. to be leaving 4. has left

61.

_______ her work, she went to sleep.1. completing 2. having to complete 3. having completed 4. aftercompleted

Directions (Questions 62-92): Fill in the blanks with the correct form of the verbsgiven in brackets:

62. If it ____________ hot today, I‟ll stay at home. (be)

63. The police _________ you if you spread rumors. (arrest)

64.

How much will he be fined if he ____________ the traffic rules? (break)

65.

If the cake is spoiled, _________ me. (not blame)

66. You ________ a lot of time if you use a calculator. (save)

67.

If you need the services of a nurse, please ____________ this button. (press)

68. ___________ this job if you get a better one? (you resign)

69. I would certainly see this movie if tickets ___________ available. (be)

70.

Would he be granted leave if he ______ for it? (apply)

71. ___________ if I kept this book a little longer? (you mind)

72.

If god granted you two boons, what _____________? (you ask)

73.

If she dressed carefully, she __________ pretty. (look)

74. If someone hijacked the plane, what ___________? (you do)

75. If you pressed that knob, the machine ___________ working. (start).

76.

He would have won the race if he __________. (not slip)

77. If the paper __________ easier, he would have got very good marks. (be)

78.

The soup would have tasted better if you ___________ more salt in it. (put)

79.

If I had found the samples satisfactory, I ________ a huge order. (place)80. Had I seen the red signal, I _________ the car. (stop)

81.

If the farmers had used good quality seeds, there __________ a rich crop. (be)

82.

If the army ____________ a little longer, it might have won the battle. (persist)

83. If the voltage suddenly rises, the fuse ________ off. (blow)

84.

If you ___________ that funny cartoon, you would have laughed heartily. (see)

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85.

You _________ if you repeat the mistake. (repent)

86. ___________ if I pressed this button? (the machine stop)

87. If the water level ___________ the danger mark, low-lying areas would have got

flooded. (cross)

88.

If you ____________ you lunch, let me ask for the bill. (finish)89.

If you are satisfied, __________ others. (tell)

90.

If you were satisfied, ________ others? (you tell)

91. If you ____________ satisfied, you should have complained to us. (not feel)

92. If she had been less proud, she __________ happier. (be)

Sentence Correction

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Exercise 1:

Identify the underlined part that has an error

1.

Many a man have succumbed to this temptation, inviting his own downfall

and1 2 3 4

destruction.

2. Neither the chairman nor the directors is present at the crucial meetingbetween

1 2 3 4workers and the officers.

3. We have helped them not only with money and also with a body of workers, all

1 2 3 4well-trained and experienced.

4. Euclid proved that the sum of the three angles of a triangle are equal to thetwo right 1 2 3 4

angles.

5. Loosing the favour of his master, Ramesh was dismissed from his high office.1 2 3 4

6.

Were an angel to tell me such a thing of you, I will not believe it.1 2 3 4

7.

Even though Miss India lost the beauty contest, she was still more prettierthan the

1 2 3 4other girls in the pageant.

8. Before the advent of television, the common man seldom never had an1 2

opportunity to see as well as listen to his favourite singer‟s live performances.3 4

9. In order for one to achieve the desired results in this examination, it isnecessary

1 2 3that he work as hardly as possible.

4

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10.

The purpose of the United Nations is to maintain peace and security and1 2 3

encouraging respect for human rights.4

11.

The introduction of tea and coffee and such other beverages have not been

without some effect.

12. Each of the scholars have done well in the seminar.

13.

Anyone who wish to participate in our slogan competition may do so by fillingthe coupon supplied along with every bottle of our beverage purchased.

14. Either one of the three top rankers in the class is eligible for a scholarshiponly after going through an elimination process.

15.

Chand will probably buy some more computer software when he will get paid

his annual dues.

16. Every student needs an identification number so he can get a universitylibrary card made to gain access to valuable.

17. The Marwaries are not least enterprising than any other business communityin India.

18.

She is wonder and an example of what a human being in spite of infirm healthis capable.

19.

Laxmi, accompanied by her brother on the piano, were given a standingovation at the talent search contest.

20. Professor Sarcar tol his class that the best way to achieve distinction inbiochemistry is to practice the structures of the compounds.

21.

In a survey conducted by the market research agency. DRISHTI, a sample of4000 students who had just given their class X examination, were questionedabout their future plans. Surprisingly it was found that more than 3400students replied that they had not taken any decision, they are still thinkingout.

1. they are still thinking out 2. they are still thinking.3. they are still over thinking it. 4. they are still thinking it over.

22. Hurry up lest you should not miss the train.1. not miss the train 2. miss the train 3. miss the train not 4. not miss train

23.

Most of the members of management committee were in favour of AlternativeB as this idea is definitely more preferable to Alternative A.

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1. More preferable to Alternative A 2. preferable to Alternative A3. highly preferable to Alternative A 4. to be preferable

24. When asked about the appearance of stranger, the Innkeeper replied, “Heappeared to be a tall man with a slight limp.” 1. a tall man with a slight limp 2. tall and had a slight limp

3. tall and limping slightly 4. limping slightly but tall

25. The Principal, knowing about my interest in music, asked me that would liketo perform during the public celebrations.1. that I would like to perform 2. that I might like to perform3. if I would like to perform 4. if I should like to perform

26. John Higginbotham is a man of many ideas and who knows how to expressthem appropriately.1. of many ideas and who knows how to express them appropriately.2. who has many ideas and who knows how to express them?

3. of many ideas and knows to express them appropriately.4. who has many ideas and who knows how to express them appropriately?

27. Radha wishes that she took English at high school.1. Radha wishes that she took English at high school.2. Radha wishes that she had taken English at high school.3. Radha wishes that she would have taken English at high school.4. Radha wished that she take English that high school.

28. My son says that he almost has written twenty compositions this year.1. he almost has written twenty competitions.

2. he almost has written twenty pieces of composition.3. he almost has written twenty composition pieces.4. he has written almost twenty compositions.

29.

When only a baby, my father took me to the circus.1. When only a baby, my father took me to the circus.2. Being a baby, my father took me to the circus.3. When only a baby, I was taken to the circus by my father.4. Being a baby, my father, to the circus, took me.

30. The criminal was caught, convicted and hanged in a short period of time.

1. The criminal was caught, convicted and hanged in a short period of time.2. The criminal was caught, convinced and hung in a short period of time.3. The criminal was applauded, acquitted and hung in a short period of time.4. The criminal was caught, convicted and hung in a short period of time.

31. I hate sitting along him as he always smells of garlic.1. along 2. besides 3. beside 4. at

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32.

Although we are free for last forty-five years or so, yet we continue to beeconomically backward.1. Although we are free 2. Even through we arefree3. Although we have been free 4. Though we are free

33.

Neither the famine or the subsequent fire was able to destroy the spirit of thepeople.1. Neither the famine or the subsequent fire was able to destroy the spirit ofthe people2. The famine and the subsequent fire was able to destroy the spirit of thepeople.3. Neither the famine or the subsequent fire was not able to destroy the spiritof the people.4. Neither the famine nor the subsequent fire was able to destroy the spirit ofthe people.

34.

He sent a word to me that he would be coming late.1. He sent word to me that he will come late.2. He had sent a word to me that he would be coming late.3. He sent word to me that he would be coming late.4. He passed on a word to me that he would be coming late.

35.

The company does to great length to ensure that employee can be comfortablein their work environment.1. The company goes to great length to ensure that employees can becomfortable in their work environment.2. The company goes to great length to ensure that employees will be

comfortable in their work environment.3. The company goes to great length to ensure that employees are comfortablein their work environment.4. The company goes to great length to ensure that employees should becomfortable in their work environment.

36.

He sat until he was chilled with cold, dancing occasionally at the figure of theold woman peering into the window.1. He sat until he was chilled with cold, glancing occasionally at the figure ofthe old woman peering into the window.2. He sat until he was chilled with cold, glancing occasionally at the figure of

the old woman peering up the window.3. He sat until he was chilled with cold, glancing occasionally at the figure ofthe old woman peering at the window.4. He sat until he was chilled with cold, glancing occasionally at the figure ofthe old woman peering in through the window.

37. The winter this year has been severe specially.1. The winter this year has been severe specially2. The winter this year has been specially severe.

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3. The winter this year has been severe especially.4. The winter this year has been especially severe.

38. We received an invitation to the palace; we are going to go there now.1. we are going to go there now.2. and therefore we are going to go there now.

3. we are going there now4. and therefore we are going there now

39.

My husband wanted to buy two floor carpets yesterday, but he forgot to takehis money purse.1. buy two floor-carpet yesterday, but he forgot to take his money-purse.2. buy to carpet yesterday, but he forgot to take his money purse.3. buy two floor-carpets yesterday, but he forgot to take his purse.4. buy two carpets yesterday, but he forgot to take his purse.

40.

Competition has taken a lot of his business; he is finding it difficult to make

both his ends meet.1. he is finding it difficult to make both his ends meet.2. he is finding making both his ends meet difficult.3. he is finding it difficult to make both ends meet.4. he is finding the difficulty to making both ends meet.

41.

Scarcely had he gone a few steps that he was told by someone on the way thathis mother was no more.

42. If I was a despot, even though I knew my territory was crammed with fanaticalrevolutionaries, would not repress freedom of speech. No error

43.

Napoleon dimly saw what Mahatma Gandhi demonstrated ……………. That thespirit was more strong than the sword. No error

44.

Gandhiji was a social scientist who tried to analyze the ills of society and finda cure of them in the context of all the facts and personalities involved. Noerror

45. I listened attentively to his long rambling speech, but could not make out

what he was driving. No error

46.

These two young people were to be married, but the young woman changedher mind and now the engagement is broken up. No error

47. Efforts are being made by the government to create further employmentopportunities in the wake of the growing abyss of employment in the country.No error.

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48.

If properly entrapped, the direct taxes of various types and income tax inparticular can prove to be a source of substantial revenue. No error

49. Some remarks casually dropped by a woman put the police on the right scentand they soon discovered the whole gang of brigands. No error

50.

If the city falls a prey before the enemy, it remains to be seen what flag will flyover the citadel. No error

51.

This Youngman would not follow his father‟s occupation of wood-carving butinsist on preparing himself for clerkship. No error

52. The Prime Minister sometimes makes an important statement in Parliament inorder that through the comments made on it in the public press he may feelthe pulse of the nation. No error

53.

I was in the tunnel when the train came up before I was aware, but I squeezed

myself close to the wall and escaped. Not till the last coach passed I breathedfreely. No error

54. You have made a very important proposal to me. I will turn the thing up in mymind and give you an answer tomorrow. No error

55.

Boling broke at first paid homage to King Richard, but when his cause grewstronger, he threw up the mask and claimed the crown. No erro

56.

A fascinating feature of the Indian tradition is the interchange between

classical art tradition and folk craft tradition. No error

57. The Bar councils, which are entrusted the responsibility of discipliningmembers in addition to enrolling and maintaining the roll of lawyers, mustwake up to the need for reform at the bar. No error

58. He is one of the few younger painters of to day who practice their art withabsolute sincerity and deep introspective concentration. No error

59. I thus made an intimate study of the hard condition of the Indian settlers, not

only by reading and hearing of it, but by personal experience. No error

60.

The D T C management took special care to see that there was no place fordiscourtesy at any level. No error

61. Tension ran high to-day in Upper Assam‟s Dibrugarh district following from aclash between two linguistic groups. No error

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62.

The University in a determined effort to restore its clean image of yester years,is all set out to mount a multi-pronged attack on unfair means atexaminations. No error

63. Fidel Castro wrested power from Batista 26 years ago and set up the first andthe only communist government in the western hemisphere. No error

64.

We judge ourselves by what we feel capable of doing, when others judge us bywhat we have already done. No error

65.

The present speech is mild contrasted to his past utterances on the samesubject. No error

66. In case of his dying without an issue, his nephew would inherit the wholeproperty. No error

67. It is said to Akbar that he rarely had slept more than three hours at a time,even during those three hours he was unconsciously awake and vigilant. No

error

68. Nelson had done his duty; Captain Hardy congratulated him on him havinggained a complete victory. No error

69.

The enquiry revealed that the accident was due to the engine-driverdisregarding the signals. No error

70. He is the representative of the king, and as therefore we are bound to honourhim. No error

71. A few clothes they had were all tattered and torn, but they did not worry andwent ahead with their preparation to stage a show with the improvisedmaterial. No error

72. Pope professed to have learned his poetry from Dryden, who whenever anopportunity was presented he praised throughout his life with unvariedliberality. No error

73.

With whatever luxuries a bachelor may be surrounded he will always find hishappiness incomplete until he has a wife and children. No error

74. Weather permitted, there will be a garden party at government Housetomorrow. No error

75.

There are many truths of which the full meaning can not be realized unlesspersonal experience has bought it home. No error

76.

The man who eats in a hurry loses both the pleasure of eating as well as theprofit of digestion.No error

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77.

Neither life nor property were safe, and the poor and the weak were oppressedby the strong. No error

78.

The Restoration crushed for a time the Puritan party besides placed supreme

power in the hands of a libertine. No error

79. As long as he lived, he was the guiding-star of a brave nation; while he died,the little children cried in the streets. No error

80.

There never can be prosperity in any country until all the numerouscultivators of the soil are permanently depressed and injured. No error

81.

I instruct you to remain here and not to budge an inch so long as I returnfrom my inspection of the other formation. No error

82.

Sentinels were posted and every other precaution taken lest the camp may betaken by surprise. No error

83. I must refuse your request, in as much I believe it unreasonable. No error

84. This technological breakthrough, according to the scientists, would be highlybeneficient in various areas including electric locomotion. No error

85.

The formal agreement between India and Pakistan to set up a jointcommission willundoubtly inject momentum into the ongoing efforts to establish peace and

amity on the sub-continent. No error

86.

New Delhi has disclosed last year its intention of borrowing from the A D B forthe first time since it became a member of that institution. No error

87. The government announced a state of emergency in Lima on Wednesday andplaced the capital‟s six million residents under limited martial law. No error

88.

Huge land slides blocked the coming up convoy of vehicles includingpassenger buses on the Srinagar-Jammu national high way. No error

89.

Five persons were killed and seven others injured when a lorry in which theywere travelling fell in a ditch. No error

90. Four armed miscreants have looted Rs.1 lakh from the Nagri branch of Bankof India, under Ratu Police station yesterday. No error

91. With the lever of hiked oil price being exercised by the Arab countries, there isa scramble for alternate sources of energy. No error

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92.

Four dacoits were killed and three captured living by villagers and policemen.No error

93.

The criminal investigational agency claims to have busted three inter-stategangs of automobile lifters. No error

94.

Despite of an increase in postal rates in 1982-1983 the postal loss this year

has substantially grown. No error

95. Before half a century, judges were reluctant to apply the principles of liabilityof the manufacturer towards the consumer. No error

96.

The chairman of the Board accepted that they had received complaints andwill take action on the basis of records submitted to them. No error

97.

The African leader asked the countries in the region of the Indian Ocean not tohelp the super powers in their design for expanding their spheres of influence.No error

98.

Prince Faisal said the unability of the non-aligned countries to find anamicable solution to the Iran-Iraq war had undermined the cohesiveness ofthe movement. No error

99. A secular state cannot be of much help to a community as far as the solutionof these two problems is concerned. No error

100.

External Affairs Minister of India and Pakistan ForeignMinister to-day signed an agreement setting up the Indo-Pakistan JointCommission as had previously been agreed. No error

Exercise 2:

1. Everyone in the bank-including the manager and the tellers, ran to the door when the fire alarmrang.

A. tellers, ranB. tellers:ran

C. tellers, had runD. tellers-ranE. tellers' ran”

2. To no ones surprise, Joe didn't have his homework ready.

A. no ones surpriseB. noones surpriseC. no-ones surprise

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D. no ones' surpriseE. no one's surprise

3. If he would have read “The White Birds,” he might have liked William Butler Yeats's poetry.

A. would have readB. could have read

C. would of readD. could of readE. had read

4. After the hurricane, uprooted trees were laying all over the ground.

A. were layingB. lyingC. were lyingD. were laidE. was laid

5. Ralph Waldo Emerson (1803-1882), the great Transcendentalist philosopher, wrote in his essay

“Self -Reliance” of the need for an individual to develop his capacities.

A. essay “Self–Reliance”B. essay, “Self -Reliance”C. essay: Self-RelianceD. essay, Self-RelianceE. essay; “Self -Reliance”

6. The recently built children's amusement park has been called “ a boon to the community “ by itssupporters and “an eyesore” by its harshest critics.

A. and “an eyesore” by its harshest

B. and, “ an eyesore,” by its harshestC. and, an eyesore; by its harshestD. and-an eyesore- by its' harshestE. and-“an eyesore”- by its' harshest

7. I always have trouble remembering the meaning of these two common verbs, affect (to change” or“to influence”) and effect (“to cause” or “ to accomplish ) . “

A. “ to accomplish ). “B. “ to accomplish” ).C. “to accomplish).D. To accomplish.E. ( “ to accomplish. “ )

8. My class just finished reading- “ The Fall of the House of Usher “, a short story by Edgar Allen Poe.

A. reading- “ The Fall of the House of Usher”,B. reading, The Fall of the House of Usher,C. reading “The Fall of the House of Usher, “D. reading, The Fall of the house of Usher, “E. reading: The Fall of the House of Usher-

9. After it was repaired it ran perfect again.

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A. ran perfectB. ran perfectlyC. could run perfectD. could of run perfectE. would run perfectly

10. "Are there two e's in beetle," asked Margo?

A. there two e's in beetle," asked Margo?B. their two e's in beetle?" asked Margo.C. there two e's in beetle," asked Margo?D. there two e's in beetle?" asked Margo.E. there two e's in beetle, asked Margo?

11. The circus audience received a well-deserved round of applause for the perfectly timed acrobaticstunt.

A. audience received a well-deservedB. audience gave a well deservedC. audience did receive a well deserved

D. audience gave a well-deservedE. audience did get a well-deserved

12. Looking directly at me, my Mother said, “ These are your options: the choice is yours.”

A. Mother said, “ These are your options: the choice isB. Mother said- these are your options, the choice isC. Mother had said, These are your options; the choice isD. Mother had said, “These are your options; the choice isE. Mother said, “These are your options; the choice is

13. Porcupine is from Latin porcus, “pig,” and spina, “spine.”

A. porcu s, “pig,” and spina, “spine.”B. Porcus- pig and spina, “spine.” C. Porcus- pig, and Spina, “spine.” D. Porcus-Pig-,Spina-spine. E. Porcus, “pig,” and spina “spine”.

14. Seeing the dolphins, some sharks, a killer whale, and a Moray eel made the visit to the marinepark worthwhile.

A. a killer whale, and a Moray eel made the visitB. a killer whale, and a moray eel made the visitC. a killer whale and a moray eel makes the visit

D. a killer whale and a Moray eel makes the visitE. a killer whale and a moray eel made the visit

15. Still, the fact that a planet exists outside our solar system encourages hope that other solarsystems exist, and in them, perhaps, a planet that does support life.

A. that a planet exists outside our solar system encourages hope that other solar systems exist, andB. that a Planet exists out side our solar system encourages hope that other solar systems exist andC. could be that a planet exists outside our solar system encourages hope that other solar systemsexist, and

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D. that a planet exist outside our solar systems encourage hope that other solar systems exist, andE. that a planet does exists out side our solar system encourages hope that other solar systems exist,and

16. Mail-order shopping can be convenient and timesaving with appropriate precautions, it is safe aswell.

A. can be convenient and timesavingB. can be convenient and timesaving;C. should be convenient and time saving;D. could be convenient and time saving;E. can be convenient and time-saving;

17. Among the many fields of science, no matter what turns you on, there are several fields of study.

A. science, no matter what turns you on,B. Science, no matter what turns you on,C. Science, no matter which you chose,D. Science, no matter which of these you chose-E. science, no matter which you choose,

18. The fact that boxing is known to cause head injuries and brain damage should lead us to informthe public and push for a ban on boxing.

A. should lead us to informB. could lead us to informC. should of led us to informD. will lead us to informE. should have led us to inform,

19. The first part of the test was on chemistry, the second on mathematics, and the third on english.

A. on mathematics, and the third on english.B. on mathematics; and the third on English.C. on Mathematics; and the third on English.D. on mathematics, and the third on English.E. on mathematics: and the third on English.

20. The Diary of Anne Frank showed a young girl's courage during two years of hiding.

A. showed a young girl's courageB. shows a young girl's courageC. did show a young girls courageD. has shown a young girl's courageE. showed a young girl's courage

21. In August my parents will be married for twenty-five years.

A. will be married for twenty-five years.B. shall have been married for twenty-five years.C. will have been married for twenty-five years.D. will be married for twenty five years.E. will have married for twenty-five years.

22. Hours of driving laid ahead of us.

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A. laidB. have lainC. layD. has layE. lie

23. By the time we get to the picnic area, the rain will stop.

A. will stopB. shall stopC. will has stoppedD. shall have stoppedE. will have stopped

24. If Judy would not have missed the deadline, the yearbook delivery would have been on time.

A. would not have missedB. should have not missedC. wouldn't have missedD. had not missed

E. would have not missed

25. We spent Sunday afternoon wandering aimless in the park.

A. wandering aimlessB. wandering aimlesslyC. wandering without purposeD. wandering in an aimless mannerE. wandering almost aimlessly

26. Only after I went home did I remember my dental appointment.

A. went homeB. had went homeC. had gone homeD. gone homeE. should go home

27. By this time next year Johanna will begin classes at the University of Colorado.

A. will begin classesB. will have begun classesC. has began classesD. should begin classesE. should have begun classes

28. After comparing my air conditioner with the one on sale, I decided that mine was the mostefficient.

A. was the most efficient.B. should be the most efficient.C. was the more efficient.D. was, by far the most efficientE. should be considered the most efficient.

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29. I would have liked to have gone swimming yesterday.

A. to have gone swimmingB. to go swimmingC. to had gone swimmingD. to go to swimE. to of gone swimming

30. I wish I read the chapter before I tried to answer the questions.

A. read the chapterB. would read the chapterC. should of read the chapterD. could have read the chapterE. had read the chapter

31. Nathanael West said that he'd never have written his satirical novel if he had not visitedHollywood.

A. have written hisB. would have written hisC. could of written hisD. could have written hisE. should of written his

32. The smell from the paper mill laid over the town like a blanket.

A. laidB. has lainC. will lieD. layE. has laid

33. When I was halfway down the stairs, I suddenly knew what I had wanted to have said.

A. to have saidB. too sayC. to have been saidD. to had sayE. to say

34. I would be more careful if I had been you.

A. had beenB. could have beenC. wasD. wereE. could have been

35. They read where the governor has appointed a special committee to improve the school calendar.

A. whereB. howC. that of where

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D. of whereE. where-

36. In study hall I sit besides Paul Smith, who is captain of the swim team and one of the bestswimmers in the state.

A. sit besides

B. sat besideC. have set besideD. sit besideE. have sit beside

37. This classic has been read with enjoyment for nearly two hundred years.

A. has been readB. will have been readC. shall have been readD. is being readE. was read

38. Many nineteenth-century biographers rely on their imagination, not on real facts.

A. rely on their imagination,B. relied on their imagination,C. have relied on their imaginationD. could have relied on their imagination,E. could rely on their imaginations:

39. The private lives of politicians, generals, and other notables fascinates the reading public.

A. fascinates the readingB. have fascinated the reading

C. will fascinate the readingD. fascinate the readingE. has fascinate the reading

40. That small man chose a seat near the door and carefully sat down.

A. satB. will sitC. could of satD. have sit downE. set down

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Time and Distance

Speed:

We have the relation between speed, time and distance as follows:

Speed = distance / time.

So the distance covered in unit time is called speed.

This forms the basis for Time and Distance. It can be re-written as Distance = Speed X Time or

Time = Distance / Speed.

Units of Speed:

The units of speed are kmph (km per hour) or m / s.

1 kmph = 5 / 18 m / s

1 m / s = 18 / 5 kmph

Average Speed:

When the travel comprises of various speeds then the concept of average speed is to be applied.

Average Speed = Total distance covered / Total time of travel

Note: In the total time above, the time of rest is not considered.

Example 1:

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If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph find its average speed.

Soln:

Average Speed = Total distance / Total time.

Let each side of square be x km. Then the total distance = 4x km.

The total time is sum of individual times taken to cover each side.

To cover x km at 100 kmph, time = x / 100.

For the second side time = x / 200.

Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph.

Example 2:

A man if travels at 5/6 th of his actual speed takes 10 min more to travel a distance. Find his usual time.

Soln:

Let s be the actual speed and t be the actual time of the man.

Now the speed is (5/6)s and time is (t+10) min. But the distance remains the same.

So distance 1 = distance 2 => s X t = (5/6)s X (t+10) => t = 50 min.

Example 3:

If a person walks at 30 kmph he is 10 min late to his office. If he travels at 40 kmph then he reaches to his office 5 min

early. Find the distance to his office.

Soln:

Let the distance to his office be d. The difference between the two timings is given as 15 min = 1 / 4 hr.

Now if d km are covered at 30 kmph then time = d/30. Similarly second time = d/40.

So, d/30 – d/40 = 1 / 4 => d = 30 km.

Note:

When two objects move with speeds s1 and s2

a.

In opposite directions their combined speed = s1 + s2 b.

In same direction their combined speed = s1 ~ s2.

Example 4:

Two people start moving from the same point at the same time at 30 kmph and 40 kmph in opposite directions. Find the

distance between them after 3 hrs.

Soln:

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Speed = 30 + 40 = 70 kmph (since in opposite directions)

Time = 3 hrs

So distance = speed X time = 70 X 3 = 210 km.

Example 5:

A starts from X to Y at 6 am at 40 kmph and at the same time B starts from Y to X at 50 kmph. When will they meet if X

and Y are 360 km apart?

Soln:

Distance = 360 km

Speed = 40 + 50 = 90 kmph.

Time = distance / speed = 360 / 90 = 4hrs from 6 am => 10 am.

Example 6:

A starts from X to Y at 6 am at a speed of 50 kmph. After two hours B starts from Y to X at 60 kmph. When will they meet

if X and Y are 430 km apart?

Soln:

By the time B started A traveled for 2 hrs => 2 X 50 = 100 km.

So at 8 am, distance = 430 – 100 = 330 km

Speed = 50 + 60 = 110 kmph.

Time = distance / speed = 330 / 110 = 3 hrs from 8 am => 11 am.

Note:

When a train crosses a negligible length object (man / pole / tree) the distance that it has to travel is its own length.

When a train has to cross a lengthy object (train / bridge / platform) the distance it has to travel is the sum of its length and

the length of the object.

Example 7:

If a train traveling at 40 kmph crosses another train of length 100m traveling at 14 kmph in opposite direction in 30 s find

the length of the train.

Soln:

Let length of train be d.

Distance to be covered = d + 100.Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s

Time = 30 s.

Distance = speed X time => d+100 = 15 X 30 => d = 350 m.

Note:

If a man rows a boat along the stream flowing at speed S2 then it is termed downstream speed and is given by

S down = S1 + S2 , where S1 is speed of boat in still water.

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If a man rows a boat opposite to the stream flowing at S2 then it is termed upstream and is given by

S up = S1 – S2.

Exercise:1.

A car moves at a speed of 80km/hr. What is the speed of the car in meters per second?

1)9

212 2)

9

222

3)9

120 4)

2

921

2.

If a man can cover 12 meters in one second, how many kilo meters can be cover in 3 hours 45 minutes?

1) 168 km 2) 162 km

3) 150 km 4) 156 km

3. If a man running at 15 kmph. Crosses a bridge in 5 minutes, then the length of the bridge is

1) 1230 m 2) 1240 m

3) 1250 m 4) 1220 m

4.

Walking atth

4

3of his usual speed a man is late by 2 hours 30 minutes. The usual time would have been

1)2

17 hrs 2)

2

13 hrs

3)4

13 hrs 4)

8

7 hrs

5. In a 1 km race, A beats B by 100 m and C by 150 m. In a 2700 m race, by how many meters does B beat C?

1) 100 m 2) 120 m

3) 150 m 4) 180 m

6.

Traveling at a speed of 8 kmph a student reaches school from his house 10 minutes early. If he travels at 6

kmph, he is late by 20 minutes. Find the distance between the school and the house.

1) 12 km 2) 1 km

3) 10 km 4) 13 km

7.

A man takes 5 hours 45 minutes in walking to a certain place and riding back. He could have gained 2 hours

by riding both ways. The time he would take to walk both ways is _________

1) 12 hrs 2) 11 hrs 45minutes

3) 7 hrs 45 minutes 4) 3 hrs

8.

The ratio between rates of walking of two persons is 3:4. If the time taken by nd2 person to cover a certain

distance is 36 minutes, then the time taken by the first person to cover the same distance is ___________


3) 27 minutes 4) none

9.

If the speed of a vehicle changes in the ratio a : b, then the ratio of times taken is

1) a : b 2)1b

a

3) b : a 4)1a

b

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10.

A car driver makes his journey by the speed of 75km/hr and returns to initial place with 50 km/hr. Then his

average speed of journey is ___________

1) 30 km/hr 2) 40 km/hr

3) 50 km/hr 4) 60 km/hr

11. A vehicle travels 715 km at a uniform speed. If the speed of the car is 10 kmph more, it takes 2 hours less to

cover the same distance. The original speed was _______________

1) 45 kmph 2) 65 kmph

3) 55 kmph 4) 75 kmph

12.

Two persons P and Q run at 8 kmph and 12 kmph on a circular track of length 6 km in the same direction

starting at same time from same place. After how many hours will they meet each other any where on the

track?

1) 1.5 hours 2) 2 hours

3) 2.5 hours 4) 3.5 hours

13.

A car driver driving at a speed of 68kmph locates a truck 40 meters ahead of him. After 10 seconds, the truck

is 60 meters behind. The speed of truck is ____________

1) 30 km/hr 2) 32 km/hr

3) 23 km/hr 4) 3 km/hr

14.

Rajan is traveling on his cycle and has calculated to reach a point at 2 p.m. if he travels at 10 kmph. He wouldreach there by 12 noon if he travels at 15 kmph. At what speed must he travel to reach the same place at

1.p.m?

1) 12 kmph 2) 14 kmph

3) 15 kmph 4) 13 kmph

15.

Two persons start running simultaneously around a circular track of length 300m from the same point at

speeds 15 and 25km/hr. When will they meet first time on the track, when move in opposite direction?

1) 21 sec 2) 22 sec

3) 27 sec 4) 24 sec

16. A robber steals a Maruthi car at 2.30 pm and drives at 60 kmph. The theft is discovered at 3 p.m. and the

owner sits in Police jeep running at 75 kmph. When will he catch the thief?

1) 5.30 pm 2) 5.15 pm3) 5 pm 4) 5.45 pm

17.

Two planes move along a circle of circumference 1.2 km with constant speeds. When they move in different

directions they meet every 15 sec and then they move in the same direction one plane over takes the other

every 60 sec. The speed of slower plane is

1) 0.04 km/s 2) 0.03 km/s

3) 0.05 km/s 4) 0.02 km/s

18.

A 150 m long train crosses a man walking at a speed of 6 kmph in his opposite direction in 6 sec. The train (in

kmph) is:

1) 66 2) 84

3) 96 4) 106

19.

A train of length 150 m takes 10 sec to pass over another train 100 m long coming from the opposite direction.If the speed of the train is 30 kmph. Then the speed of the second train in kmph is _________

1) 54 2) 60

3) 72 4) 36

20.

If a train 110m long passes a signal pole in 3 sec. Then the time taken by it to cross a railway platform 165m

long is :

1) 3secs 2) 4secs

3) 7.5secs 4) 5secs

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21.

An Engine of 10 m length travels at 60 kmph. How long does it take to cross another train 170 m long,

running at 54 kmph in the same direction?

1) 16 sec 2) 16.8 sec

3) 108 sec 4) none

22. Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross

each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

1) 9:11 2) 11:9

3) 10:9 4) 9:10

23.

A train M leaves Mumbai at 5am. And reaches Delhi at 9am. Another train leaves Delhi at 7am. And reaches

Mumbai at 11.00am. At what time do the two trains across each other?

1) 8 a.m. 2) 9 a.m.

3) 7 a.m. 4) 6 a.m.

24.

Train P leaves Hyderabad at 6.00am. And reaches Vijayawada at 10.00am. Train Q leaves Vijayawada at

7.00am. And reaches Hyderabad at 1.00pm. At what time do the trains meet?

1) 8.48 a.m. 2) 8.12 a.m.

3) 8.42 a.m. 4) 9.00 a.m.

25. A train running at 52kmph takes 36 seconds to pass a platform. Next it takes 24 seconds to pass a man

walking at 10 kmph in the same direction. Find the length of the train and that of the platform?

1) 800 m; 440 m 2) 280 m; 440 m

3) 280 m; 240 m 4) 420 m; 300 m

26.

Two trains running in the same direction at 40 kmph and 22 kmph completely pass one another in 60 seconds.

If the length of the first train is 125 meters, then the length of second train is?

1) 125 m 2) 128 m

3) 175 m 4) 900 m

27. Two trains 220 meters and 380 meters in length respectively are running in opposite direction. One at the rate

of 35 kmph and other at 25 kmph. In what time they will cross each other?

1) 36 seconds 2) 30 seconds3) 60 seconds 4) None

28.

A man misses a train by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the

train by 10minutes. What is the minimum speed required to catch the train on time?

1) 44 kmph 2) 45 kmph

3) 48 kmph 4) 49 kmph

29.

A boat traveled from A to B and back to A from B in 5 hours. If the speed of boat in still water and the speed

of stream be 7.5 kmph and 1.5 kmph, then what is the distance between A and B?

1) 80 km 2) 45 km

3) 18 km 4) 19 km

30.

A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water andthe speed of stream (in kmph)

1) 13; 3 2) 15; 3

3) 12; 6 4) 14; 4

31.

A man can row at 9 kmph in still water. He takes 4 ½ hours to row from P to Q and back. What is the

distance between P and Q if the speed of the stream is 1 kmph?

1) 32 km 2) 28 km

3) 20km 4) 24 km

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32.

A man can row 30 km downstream in 3 hours 45 minutes, and 11 km upstream in 2 hours 12 minutes. What is

the speed of the man in still water and speed of stream (in kmph)?

1) 6; 2 2) 6.8; 1.8

3) 6.5; 1.5 4) 7; 3

33. A man rows 22 km upstream in 4 hours and 45 km downstream in 6 hours. In 10 hours how much more

distance can he row downstream than the distance he can row upstream?

1) 24 km 2) 22 km

3) 20 km 4) 18 km

34.

A person can row 10 km in 1 hour in still water. If the speed of the water current is 2 kmph and it takes two

hours for him to go to a certain place and back. Find the distance he traveled in upstream?

1) 9 ½ km 2) 9.6 km

3) 48 km 4) 5 km

35.

A person can row5

3 of a km in upstream in 10 minutes and return in 6 minutes. Find the speed of man in still

water?

1) 4.4 kmph 2) 4.5 kmph3) 4.8 kmph 4) 4.9 kmph

36. A boat can travel 10 kmph in still water. It traveled 91 km downstream and then returned, taking altogether 20

hours. Find speed of the stream?

1) 4 kmph 2) 5 kmph

3) 8 kmph 4) 3 kmph

37.

The time taken for a boat to cover certain distance in upstream is equal to the time taken by the boat to cover

three times the distance in downstream. If the speed of current is 5 kmph, what is the speed of boat in still

water?

1) 14 kmph 2) 15 kmph

3) 10 kmph 4) 19 kmph

38.

The time taken by a person to row upstream is twice the time taken by him to row the same distance

downstream. If the speed of the boat in still water is 42 kmph, find the speed of current?

1) 14 kmph 2) 32 kmph

3) 12 kmph 4) 8 kmph

39. A man rows his boat to a certain place covering a distance of 72 km and back again in 15 hours. He finds that

he takes same time to row 3 km in downstream as much he takes for 2 km in upstream. Find the speed of the

stream?

1) 4 kmph 2) 3 kmph

3) 1 kmph 4) 2 kmph

40.

A man can row 6 km/hr in still water. If the speed of stream is 2km/hr, it takes him 3 hours to row to a place

and back. How far is the place?

1) 16 km 2) 10 km3) 12 km 4) 8 km

Time and Work

If a person can complete a work in ‘n’ days then he can do 1/n part of the work in one day.

The amount of work done be a person in 1 day is called his efficiency.

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Example:

A can do a work in 10 days. Then the efficiency of A is given by A = 1 / 10.

Note:

Number of days required to do a work = work to be done / work per day.

Example 1:

If A can do a work in 10 days, B can do it in 20 days and C in 30 days in how many days will the three together do

it?

Soln:

The efficiencies are A = 1/10, B = 1/20 and C = 1/30

So work done per day by the three = 1/10 + 1/20 + 1/30 = 11/60 => No of days = 60/11 = 5.45 days.

Example 2:

If A and B can do a work in 10 days , B and C can do it in 20 days and C and A can do it in 40 days in what time all

the three can do it?

Soln:

A+B = 1/10

B+C = 1/20

C+A = 1/40

Adding all the three we get 2(A+B+C) = 7/40 => A+B+C = 7/80 => No of days = 80/7 days.

Note:

If all the people do not work for all the time then the principle below can be used:

mA + nB + oC = 1. (1 is the total work)

Here, m=no of days A worked

n=no of days B worked

o=no of days C worked

A,B,C = efficiencies

Example 3:

If A can do a work in 12 days, B can do it in 18 days and C in 24 days. All the three started the work. A left after two

days and C left three days before the completion of the work. How many days are required to complete the work?

Soln:

Let the total no of days be x.

A worked only for 2 days, B worked for x days and C worked for x-3 days.

So, mA + nB + oC = 1

2(1/12) + x(1/18) + (x-3)(1/24) = 1

12 + 4x + 3(x-3) = 72

x = 69 / 7 days.

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Note:

The ratio of dividing wages = ratio of efficiencies = ratio of parts of work done

Example 4:

A can do a work in 10 days and B can do it in 30 days and C in 60 days. If the total wages for the work is Rs. 1800

what is the share of A?

Soln:

Ratio of wages = 1/10 : 1/30 : 1/60 = 6 : 2 : 1 (Multiplying each term by LCM 60)

So total 9 equal parts in Rs. 1800 => each part = Rs. 200 => share of A = 6 parts = Rs. 1200.

Note:

When pipes are used filling the tank they are treated similar to the men working but some outlet pipes emptying the

tank are present whose work will be considered negative.

Example 5:

A pipe can fill a tank in 5 hrs but because of a leak a the bottom it takes 1 hr extra. In what time can the leak alone

empty the tank?

Soln:

Let the filling pipe be A.

A = 1 / 5.

But with the leak L, A – L = 1 / 6 ( A-L because leak is outlet)

So, 1/L = 1 / 5 – 1/ 6 = 1/30 => Leak can empty the tank in 30 hrs.

Example 6:

A pipe A can fill the tank in 10 hrs, B can fill it in 20 hrs and C can empty in 40 hrs. All are opened at the same time.

After how many hours shall the pipe B be closed such that the tank can be filled in 10 hrs?

Soln:

Let the pipe B be closed after x hrs.

Then A worked for 10 hrs, B worked for x hrs and C worked for 10 hrs.

mA + nB – oC = 1 (since C is outlet)

10(1/10) + x(1/20) – 10(1/40) = 1

x = 5 hrs.

Exercise:

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1.

A alone can complete the work in 12 days while A and B together can complete the same work in 8 days. The

number of days that B will take to complete the work alone is ___________

1) 10 2) 24

3) 20 4) 9

2. A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work.

1) 7.5 2) 5.4

3) 3.6 4) 3

3.

A can do a piece of work in 4 hours, B and C can do it in 3hrs, A and C can do it in 2hrs. How long will B alone

take to do it?

1) 10hrs 2) 12hrs

3) 8hrs 4) 24hrs

4.

10 men and 15 women finish a work in 6 days. One man alone finishes that work in 100 days. In how many

days will a woman finish the work?

1) 125 2) 150

3) 90 4) 225

5. A completes a work in 12 days; B completes the some work in 15 days. A started working alone and after 3 days

B joined him. How many days will they now take together to complete the remaining work?1) 5 2) 8

3) 6 4) 4

6.

10 men can complete a piece of work in 15 days & 15 women can complete the same work in 12 days. If all the

10 men & 15 women work together, in how many days will the work get completed?

1) 6 2)3

27

3)3

26 4) None of these

7. A can do a certain work in the same time in which B & C together can do it. If A and B together could do it in

10 days and C alone in 50 days then B alone could do the work in

1) 15 days 2) 20 days

3) 25 days 4) 30 days

8.

A& B under took to do a piece of work for Rs.4,500. A alone could do it in 8 days and B alone in 12 days. With

the assistance of C they finished the work in 4 days. Then C’s share of the money is ____________

1) Rs.2,250 2) Rs.1,500

3) Rs.750 4) Rs.375

9.

A can finish a work in 24 days, B in 9 days and C in 12 days. B & C start the work but are forced to leave after 3

days. The remaining work is done by A in _____________

1) 5 days 2) 6 days

3) 10 days 4)2

110 days

10.

If 3 men (or) 4 women can plough a field in43 days, how long will 7 men and 5 women take to plough it.

1) 10 days 2) 11 days

3) 9 days 4) 12 days

11.

A can doth

4

3 of a work in 12 days. In how many days can he finish

th

8

1 of work?

1) 1 day 2) 2 days

3) 4 days 4) 8 days

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12.

If 72 men can build a wall 280m. long in 21 days, how many men will take 18 days to build a similar type of

wall of length 100m.?

1) 30 2) 10

3) 18 4) 28

13. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they

can finish the work in 2 days. B can do the work alone in


3) 8 days 4) 6 days

14. A does5

4 of a piece of work in 20 days; he then calls in B and they finish the remaining work in 3 days. How

long will B alone take to do the whole work?

1)2

137 days 2) 37 days

3) 40 days 4) 23 days

15. A does half as much work as B in 1/6 of the time. If together they take 10 days to complete a work, how many

days shall B take to do it alone?

1) 15 days 2) 30 days

3) 40 days 4) 50 days

16.

A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days

and a boy alone can do it in 18 days, how long will a woman alone take to complete the work.


3) 24 days 4) 27 days

17. If the wages of 6 men for 15 days be Rs.700, then the wages of 9 men for 12 days will be ___________

1) Rs.700 2) Rs.840

3) Rs.1050 4) Rs.900

18.

A man is paid Rs.20 for each day he works, and forfeits Rs.3 for each day he is idle. At the end of 60 days he

gets Rs.280. Then he was idle for _____________


19.

A team of 10 men can complete a particular job in 12 days. A team of 10 women can complete the same job in 6

days. How many days are needed to complete the job if the two teams work together?

1) 4 2) 6

3) 9 4) 18

20. A contractor undertook to finish a certain work in 124 days and employed 120 men on it. After 64 days, he

found that he had already donerd

3

2of the work. How many men he can discharge now so that the work may

finish in time

1) 24 2) 56

3) 64 4) 80

21. A work could be completed in 100 days. However, due to the absence of 10 workers, it was completed in 110

days. The original number of workers was ___________

1) 100 2) 110

3) 55 4) 50

22.

A contractor under takes to make a road in 40 days and employs 25 men. After 24 days, he finds that only one-

third of the road is made. How many extra men should he employ so that he is able to complete the work 4 days

earlier?

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1) 100 2) 60

3) 75 4) none of these

23.

30 men complete one third of a work in 30 days. How many more men should be employed to finish the rest of

the work in 40 more days?

1) 15 2) 45

3) 20 4) 25

24.

A and B under took to do a piece of work for Rs.900. A alone could do it in 60 days and B in 30 days. If A & B

work together and complete the work, then the share of B _______

1) Rs.600 2) Rs.400

3) Rs.300 4) Rs.200

25.

5 men or 6 women or 10 boys can do a work in 15 days. How long will it take to complete the work by a group

of 5 men, 6 women and 10 boys?

1) 5 days 2) 6 days

3) 10 days 4) 45 days

26. A can do a piece of work in 30 days. B in 15 days and C in 10 days. They started the work all together but B put

2

1

time daily and C put 3

1

time daily to help A in doing the work. The work will last in ______________

1) 30 days 2) 10 days

3) 20 days 4) 25 days

27. A can do a work in 15 days & B the same work in 12 days. B started the work and was joined by A, 5 days

before the end of work. The work lasted for _____ days.

1) 8 2) 12

3) 13 4) 24

28.

A and B can do a piece of work in 40 days while C & A can do it in 60 days. If B is twice as good as C, then C

alone will do the work in ___________ days.

1) 120 2) 1003) 80 4) 24

29. A hostel has provision for 800 men for 24 days at the rate of 2 kg per man per day. For how many men is the

provision sufficient, for 20 days at the rate of 1.5 kg per man per day?

1) 1280 2) 1000

3) 1820 4) 1240

30. 12 men can do a work in 15 days working 8 hours a day. In how many days can 9 men do the same work,

working 10 hours a day?

1) 10 2) 16

3) 18 4) 24

31.

Two taps A and B can separately fill a tank in 20 and 30 hours respectively. If both the pipes are openedsimultaneously, how much time will be taken to fill the tank?

1) 10 hrs 2) 11 hrs

3) 18 hrs 4) 12 hrs

32. A tap can fill a tank in 12 minutes and another tap in 15 minutes, but a third tap can empty it in 6 minutes. The

three taps are kept open together. Find when the cistern is emptied or filled?

1) 60 min. to fill 2) 30 min. to fill

3) 60 min to empty 4) 30 min to empty

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33.

Two taps A & B can fill a cistern in 12 and 16 minutes respectively. Both fill taps are opened together, but 4

minutes before cistern is full, one tap A is closed. How much time will the cistern take to fill?

1) 9 1/7 min. 2) 3 1/7 min.

3) 11 1/7 min. 4) None.

34. A ship 55 km from the shore springs a leak which admits 2 tonnes of water in 6 minutes. 80 tonnes would suffer

to sink her, but the pumps can throw out 12 tonnes an hour. Find the average rate of sailing that she may just

reach the shore as she begins to sink.

1) 5.5 kmph 2) 2.5 kmph

3) 1.8 kmph 4) 4 kmph

35.

A tap can fill a swimming pool in h hours. What part of the pool is filled in y hours?

1) yh 2) y

h

3)h

y 4) h – y

36. Three pipes A, Band C can fill a tank in 30 min, 40 min and 60 min respectively. A and B work in alternative

minutes, A beginning the work whereas C works continuously. In how many minutes will the tank be filled?1) 16.4 2) 21.8

3) 18.2 4) 19.6

37.

A tank has a leak, which would empty it in 8 hrs. A tap is turned on which admits 6 litres of water a minute into

the tank and it is now emptied in 12 hrs. How many litres does the tank hold?

1) 8640 2) 8460

3) 8064 4) 8406

38.

A cistern is normally filled with water in 10 hours but takes 5 hours longer to fill because of a leak in its

bottom. If the cistern is full, then the leak will empty the cistern in

1) 20 hours 2) 40 hours

3) 50 hours 4) 30 hours

39. Two pipes A and B can separately fill a cistern in 60 and 75 minutes respectively. There is a third pipe at the

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