TCSTCS

SAMPLE QUESTIONSSAMPLE QUESTIONS

For student’s preparationFor student’s preparation

(New Test Pattern 2010 (New Test Pattern 2010 onwards)onwards)

TCS pattern since year 2010 has TCS pattern since year 2010 has changed. From this year onwards the changed. From this year onwards the new pattern has been followed .In the new pattern has been followed .In the new pattern 35 questions have to be new pattern 35 questions have to be answered in 60 minutes time. However answered in 60 minutes time. However the significant difference is that the the significant difference is that the English part (verbal, synonyms) has English part (verbal, synonyms) has been deleted in the new test pattern; been deleted in the new test pattern; though reading comprehension is though reading comprehension is likely to continue – the test is named likely to continue – the test is named “TOUCHSTONE”.“TOUCHSTONE”.

Some notable points TCS test is computer based test. Each student will get unique questions – as

random questions will pop-up- on computer screen - so do not copy.

There will be negative marking – so do not guess. Answer the question only if you are more than 80% sure of the correctness of the answer.

You are allowed to use calculators, but not mobile phones.

Carry HB pencils, eraser, coloured pencils etc. for answering analytical reasoning questions – rough work.

In the new test pattern questions are In the new test pattern questions are equally divided amongst the three/ four equally divided amongst the three/ four types as listed below:types as listed below:

a)a) Quantitative Ability about 15 questions.Quantitative Ability about 15 questions.

b)b) Logical Reasoning about 10 questions.Logical Reasoning about 10 questions.

c)c) Analytical Reasoning about 5 questions.Analytical Reasoning about 5 questions.

d)d) Reading comprehension about 5 Reading comprehension about 5 questions.questions.

Some sample questions are Some sample questions are discussed in this discussed in this presentation to facilitate the presentation to facilitate the preparation of students. First preparation of students. First let us take the quantitative let us take the quantitative questions which can be questions which can be typified to some extent.typified to some extent.

Quantitative 1: Simple Trigonometry

Q1) If cosec 18°= sec A, then the measure of A is________

a) 18° b) 108°c) 72° d) None of these

Ans: c) 72°

SOLUTION

Cosec 18° = Cosec (90° – 72°) As, Cosec (90 – Ѳ) = Sec ѲCosec (90° – 72°) = Sec 72°

Sec 72° = Sec A

Hence, A = 72°

Quantitative 2 : Problem of Ages

Q2) After 2 years, Paul will be 2 times as old as Alice. Presently he is 4 times as old. What is the present age of Paul?

a) 1 year b) 4 years

c) 2 years d) None of these

Ans: b) 4 years

SOLUTION

Let present age of Paul be x yrs and that of Alice be y yrs

According to condition no. 1 x + 2 = 2 (y + 2)

x – 2y = 4 – 2 x – 2y = 2 -----(i)

According to condition no. 2x = 4y

Substituting x in equation (i)4y – 2y = 2

2y = 2Hence, y = 1 years

x= 4 years

Quantitative 3 : Mensuration

Q3) A vessel is in the form of a hollow cylinder mounted on a hollow hemisphere. The diameter of the hemisphere is 14 cms and the total height of the vessel is 30 cms . Find the outer surface area of the vessel. (take π = 22/7)

a) 1628 cm² b) 1528 cm²c) 1474 cm² d) None of these

Ans: c) 1474 cm²

d = 14 cmr = 7 cmHeight of the cylinder = 30 – 7 = 23 cmOuter Surface Area of the Vessel = curved

surface area of hemisphere+ curved surface area of cylinder + πr² (top surface)

= 2 πr² + 2πrh + πr² = πr (2π + 2h + r)= 22/7 * 7 ( 2*7 +2*23 + 7)= 22 (14 + 46 + 7)= 22 * 67 = 1474 cm²

SOLUTION

Quantitative 4 : Linear EquationQ4) A telephone company charges 80 paisa/ min

for first 80 min of talk , 70 paisa/ min subsequently up to 130 min and 55 paisa/min beyond 130 min. What would be the amount paid by a subscriber who has used a total of 110 min of talk time?

a) Rs. 85 b) Rs. 108.c) Rs. 64 d) None of theseAns: Rs. 85

SOLUTION

Total Charges = (80 min x 80p) + (30 min x 70p)

= 6400p + 2100p= 8500p = Rs. 85

Quantitative 5: Linear Equation

Q5) (2/3rd) of a number is 4 more than (1/6th) of the same number. What is the number?

a) 6 b)8 c)36 d)24

Ans: b) 8

SOLUTION

Let number be xThen 2/3x = 1/6x + 4 2/3x – 1/6x = 4

[(4-1)/6] x = 43x/6 = 4

x = 4x6/3 = 8

Quantitative 6 : ProbabilityQ6) Paul the octopus who has been forecasting the outcome of FIFA world cup matches with tremendous accuracy has now been invited to predict ICC world cup matches in 2011. We will assume that the world cup contenders have been divided into 2 groups of 9 teams each. Each team in a group plays with the other teams in the group. The top two teams from each group enter the semi finals ( after which the winner is decided by knockout). However, Paul has a soft spot for India and when India plays with any team, Paul always backs India. Alas, his predictions on matches involving India are right only 2 out of 3 times. In order to qualify for the semi finals, it is sufficient for India to win 7 of its group matches. What is the probability that India will win the ICC world cup?

6(b)

a) (2/3)^10 b) (2/3)^9 + 8/3 * (2/3)^9 c) 1/3 * (2/3)^9 d) (2/3)^10 + 8/3*(2/3)^9

Ans: c) 1/3 * (2/3)^9

SOLUTION1. To win semifinals India needs to win 7 matches and

can loose one.2. To win a match probability = 2/33. Probability of loosing a match = 1/34. To qualify for semifinals India needs to win 7 matches

the probability of which is (2/3)⁷5. For India to reach the semifinals the probability is

(2/3)⁷ x 1/3.

6. Now, to further win semifinals and final both probability is 2/3 X 2/3.

7. Therefore overall probability of India wining = (2/3) ⁷ x 1/3 x 2/3 x 2/3 = (2/3)⁹ x 1/3.

Note: I. If India wins all the matches i.e. 8+2=10

matches, probability = (2/3)10

2. The key is that for reaching semi finals India has to win only 7 matches out of 8 and can afford to loose one.

Quantitative 7 : ProbabilityQ7) A toy train produces 10 different tunes when

it moves around a circular toy track of radius 5 meters at 10 meters per minute. However , the toy train is defective and it now produces only two different tunes at random. What are the odds that the toy train produces 4 consecutive music tunes of the same type?

a) 1 in 16 b) 1 in 4 c) 1 in 8 d) None of these

7(b)

Ans: a) 1 in 16

SOLUTION

• A toy train produces 10 different tunes in the normal course

• But now as the toy train has become defective, it produces only 2 different tunes; so the probability of producing any one tune is ½.

• Probability of producing 4 consecutives same tunes = ½ x ½ x ½ x ½ = 1/16 or 1 in 16

Quantitative 8 : ProbabilityQ8) Six friends decide to share a big cake. Since all of

them like the cake, they begin quarreling who gets to cut the cake first and have a piece of the cake. One friend suggests that they can make a blindfold friend choose from well shuffled set of cards numbered one to six. You check and find that this method works as it should simulating a fair throw of a die. You check by performing multiple simultaneous trials of picking the cards blindfold and throwing a die. You note that the number shown by the method of picking up a card and throwing a real world die, sums to a number between 2 and 12. Which total would be likely to appear more often – 8,9 or 10?

8(b)

a) 8 b) 10c) 9 d) All are equally likely

Ans: a) 8

SOLUTION

Sum making up to number 8 in one set of throw of die and picking up the card, probable sets are = (2,6), (6,2), (4,4), (5,3), (3,5) = Total 5 sets

Sums making up to number 9, probable sets are = (4,5), (5,4), (6,3), (3,6) = Total 4 sets

Sums making up to number 10, probable sets are = (5,5), (6,4), (4,6) = Total 3 sets

So probability of 8 would be the maximum appearing more often than others

Quantitative 9 : ProbabilityQ9) A lady has fine gloves and hats in her closet- 18 blue- 32 red and 25 yellow gloves are there. The lights are out and it is totally dark . Inspite of the darkness she can make out the difference between a hat and a glove. She takes out an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each colour?a) 50 b) 8 c) 59 d) 42

9(b)

Ans: c) 59

SOLUTIONWe have to consider the worst case scenario for

being sure. Suppose 1st she takes out all 32 Red gloves (the

maximum number possible for one colour)Then all yellow gloves which are 25 in numberAnd then next 2 gloves she takes out that will

definitely be of blue colorIn this way to make sure that she has a pair of each

color, she has to take out = 32 + 25 + 2 = 59 gloves.

Quantitative 10 : Probability

Q10) There are 7 children in a family and the youngest child is a boy. What is the probability that all of them are boys ?

a) 1/2! b) 1/64c) 1/128 d) 1/8

Ans: b) 1/64

SOLUTION :The probability of a child being boy or girl is ½

(assuming it is random)The probability that all children in the family are

boys when the youngest child is a boy

= ½ x ½ x ½ x ½ x ½ x ½ x 1 = (1/2)^6= 1/64

Quantitative 11 : Number System

Q11) A number when divided by D leaves a remainder of 3 and when divided by 3D leaves a remainder of 21 . What is the remainder, when twice the number is divided by 3D?

a) 15 b) 42c) 3 d) cannot be determined

Ans: a) 15

• SOLUTION- 1. As the remainder is 21 when divided by 3D

Therefore, 3 D >21 or D>72. Let us take the next higher value i.e. D=8 & 3D = 24

(a). The first option is number 45 (=24+21)Divided by 24 it leaves a remainder of 21Divided by 8 it leaves a remainder of 5So it does not fulfill the conditions

(b). Let us try the next possibility i.e. 45+24 = 69Divided by 24 (3D) it leaves 21 as remainderBut divided by D = 8, it leaves 7 as the remainder –

so it does not fulfill the condition

3. Let us make next trial with ‘D=9’3D = 27 (a). Let first number be 48

Divided by 3D = 27 it leaves 21 as remainder

Divided by D=9 it leaves 3 as remainder So 9 is the desired number ‘D’Let us now divide double the number i.e.

96 by 3D = 27 remainder is 15So a= 15 is the correct answer

Quantitative 12 : Permutation and Combination

Q12) Alok is attending a workshop “How to do more with less” and today's theme is Working with fewer digits. The speakers discuss how a lot of miraculous mathematics can be achieved if mankind (as well as womankind) had only worked with fewer digits.The problem posed at the end of the workshop isHow many four digit numbers can be formed using the digits 1, 2,3,4 ,5 ( but with repetition) that are divisible by 4?Can you help Alok find the answer?

12 (B)

a)100 b) 125 c) 75 d) 85

Ans: b) 125

SOLUTIONA number to be divisible by 4 the last 2 digits

should be divisible by 4

To fill the last two digits that are divisible by 4 are (1,2), (2,4), (3,2), (4,4), (5,2)

Therefore there are 5 possibilities.And the rest 2 digits can be filled in ⁵P₅ ways.So total there are 5*5*5 ways = 125 ways

Quantitative 13 : Permutation and Combination

Q13) A research lab in Chennai requires 100 mice and 75 sterilized cages for a certain set of laboratory experiments. To identify the mice, the lab has prepared labels with numbers 1 to 100 , by combining tags numbered 0 to 9. The SPCA requires that the tags be made of toxin-free material and that the temperature of the cages be maintained at 27 degree Celsius. Also , not more than 2 mice can be caged together and each cage must be at least 2 sq. ft in area. The 5 experiments to be conducted by lab are to be thoroughly documented and performed only after a round of approval by authorities. The approval procedure takes around 48 hours. How many times a tag having number '4' is used by the lab in numbering these mice?

13(b)

a) 9 b) 19 c) 20 d) 21

Ans: b) 19

SOLUTION• Tag having number '4‘ are as follows• 4, 14, 24, 34, 44, 54, 64, 74, 84, 94• 40, 41, 42, 43, 45, 46, 47, 48, 49• So a total of 19 times.

Quantitative 14 : Permutation and combination

Q14) 20 people meet and shake hands. What is the maximum number of hand shakes possible if there is to be one ‘cycle’ of handshakes { a cycle of handshake is a sequence of people (a1,a2,…..ak) such that people (a1,a2),(a2,a3)…..(a(k-1),ak),(a20,a1) shake hand}

a) 18 b) 19c) 20 d) 21

Ans: c) 20

1 23

4

5

6

7

8

17

16

15

1413 1112

109

18

19

20

To make a complete cycle number of handshakes required is 20

SOLUTION

Quantitative 15 : Time and DistanceQ15) On planet korba, a solar blast has melted the ice

caps on its equator. 9 years after the ice melts, tiny planetoids called Echina start growing on the rocks. Echina grows in the form of a circle ,and the relationship between the diameter of this circle and the age of echina is given by the formulad = 4*√ (t-9) for t ≥ 9 where d represents the diameter in mm and t the number of years since the solar blast.Jagan recorded the radius of some echina at a particular spot as 7mm. How many years back did the solar blast occur?

15(b)

a) 17 b) 21.25 c) 12.25 d) 12.06

Ans: b) 21.25

SOLUTION

The relationship between the diameters of the circle and the age of Echina is given by the formula

D = 4 x √(t – 9) for t>=9If radius r is 7 mm then diameter = 7 x 2 = 14 mm

14 = 4 x √(t – 9) 14/4 = √(t – 9) 7/2 = √(t – 9)

squaring both sides49/4 = (t – 9) So t = 21.25

Q16) Ferrari S.P.A is an Italian sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari in 1928 as Scuderia Ferrari , the company sponsored drivers and manufactured race cars before moving into production of street-legal vehicles in 1947 as Ferrari S.P.A. Throughout its history, the company has been noted for its continued participation in racing, especially in Formula One where it has enjoyed great success . Rohit once bought a Ferrari . It could go 4 times as fast as Mohan's old Mercedes. If the speed of Mohan's Mercedes is 46 km/hr and the distance traveled by the Ferrari is 953 km, find the total time taken for Rohit to drive that distance.

Quantitative 16 : Time and Distance

16(b)

a) 20.72 hr b) 5.18 hr c) 238.25 hr d) 6.18 hr

Ans: b) 5.18 hr

Speed of Mohan's Mercedes = 46 km/hrSpeed of Rohit’s Ferrari = 4 times of Mohan's Mercedes

= 4 * 46 km/hr= 184 km / hr

Distance = 953 kmTime taken by Rohit’s Ferrari = Distance / Speed

= 953 km/ 184 km/hr= 5.18 hrs

The total time taken for Rohit to drive that distance will be 5.18 hrs

SOLUTION

Quantitative 17 : Pipes and CisternsQ17) There are two water tanks A and B, A is much smaller than B. While water fills at the rate of one litre every hour in A, it gets filled up like 10, 20, 40, 80, 160... Litres per hour in tank B.( At the end of first hour, B gets 10 litres , second hour it gets 20 litres more, and so on). If tank B is 1/33 filled after 5 hours, what is the time still required (in hours) to fill it completely?

a) 26 hrs b) 25 hrs c) 5 hrs d) 27 hrs

Ans: c) 5 hrs

The data has been shown in the form of a table

Hours Water filled in B in that hr (in lts)

Cumulative Water filled in B (in lts)

1 10 102 20 303 40 704 80 1505 160 310

SOLUTION

After 5 hrs the tank is 1/33 filled which is 310 liters

So applying unitary method When 1/33 is equal to 310 ltsTherefore, the total capacity of tank B will be

= 310 lts * 33= 10230 lts

Therefore, after 5 more hours the tank B will be completely filled

Hours Water filled in B in that hr (in lts)

Cumulative Water filled in B (in lts)

1 10 10

2 20 30

3 40 70

4 80 150

5 160 310

6 320 630

7 640 1270

8 1270 2550

9 2560 5110

10 5120 10230

Let us construct the chart further

Quantitative 18 : Ratio and Proportion

Q18) A researcher at Sony Computer Science laboratories is also a jazz musician. He decided to build a robot able to improvise like a pro. Named “Continuator”, the robot can duet with a live musician in real- time. It listens to a musical phrase and then computes a complementary phrase with the same playing style. If the cost of making the robot is divided between materials , labour and overheads in the ratio of 4:6:2 and if the materials cost $108. What is the cost of the robot?

18(b)

a) $270 b) $324 c) $216 d) $ 648

Ans: b) $ 324

SOLUTION

Ratio = 4:6:2Let x be the total costSince, the cost of material = 108$Which was equal to 4/(4+6+2) * x = 108 $Therefore, x = 324 $

Quantitative 19 : Ratio and Proportion with Linear Equations

Q19) In the year 2002, Britain was reported to have had 4.3million closed – circuit television (CCTV) cameras – one for every 14 people in the country . This scrutiny is supposed to deter and detect crime. In one criminal case, the police interrogates two suspects . The ratio between the ages of the two suspects is 6:5 and the sum of their ages is 55 years. After how many years will the ratio be 8:7.?

19(b)

a) 11 b) 6 c) 10 d) 5

Ans: c) 10

SOLUTIONSince, the ratio of ages is 6:5Therefore, ages can be 6x and 5x6x+5x= 55 yearsx= 5The two ages will be 30 years and 25 yearsNew ratio = 8:7No. of years required = 30+y = 8

25 +y 7On solving y = 10 yearsAfter 10 years the ratio between their ages will be

8:7.

Quantitative 20 : Average speed

Q20) A man jogs at 6 mph over a certain journey and walks back the same route at 4 mph. What is his average speed for the journey?

a) 4 mph b) 5 mph c) 2.4 mph d) 4.8 mph

Ans: d) 4.8 mph

SOLUTION

• Average speed = 2xy or (Total Distance) x+y Total Time

x = 6 mph y= 4 mph

• Average speed = 2*6*4 6 + 4

= 4.8 mph

Quantitative 21 : SimplificationQ21) Spores of a fungus, called late blight, grow and spread infection rapidly. These pathogens were responsible for the Irish potato famine of the mid-19th century. These seem to have attacked the tomato crops in England this year. The tomato crops have reduced and the price of the crop has risen up . The price has already gone up to $45 a box from $27 a box a month ago. How much more would a vegetable vendor need to pay to buy 27 boxes this month over what he would have paid last month?

21(b)

a) $27 b) $ 18 c) $45 d) $ 486

Ans: d) $ 486

SOLUTION

• Difference in two prices = $ 45 - $ 27= $ 18

Amount that the vendor needs to pay to buy 27 boxes this month over what he would have paid last month = $ 18 * 27

= $ 486

Quantitative 22 : Simplification

Q22) (40*40*40 – 31*31*31) = ? (40*40+40*31+31*31)

a) 8 b) 9c) 71 d) 51

Ans: b) 9

SOLUTION• Let x be 40 and y be 31(40*40*40 – 31*31*31) / (40*40+40*31+31*31)

Is in the form of x3 - y3 x2 + xy + y2

= (x2 + xy + y2 ) ( x – y)x2 + xy + y2

= ( x – y)= 40 – 31= 9

Quantitative 23 : CubesQ23) Susan made a block with small cubes of 8

cubic cm volume to make a block 3 small cubes long, 9 small cubes wide and 5 small cubes deep. She realizes that she has used more small cubes than she really needed. She realized that she could have glued a fewer number of cubes together to look like a block with same dimensions, if it were made hollow. What is the minimum number of cubes that she needs to make the block?

23(b)

a) 114 b) 135 c) 21 d) 71

Ans: a) 114

SOLUTION

Total number of cubes used = 3 * 9 * 5 = 135Number of cubes required to make a hollow cube

= (3*9*5)- (1*7*3)= 135 -21= 114

3

5

91

7

3

Note: Only two outer cubes on either end face will make the faces, so inner blocks can be removed to make a hollow or 1*7*3= (3-2)(9-2)(5-2) blocks can be removed from inside to make it hollow.

Quantitative 24 : Co-ordinate Geometry

Q24) Determine the distance between x-intercept and z-intercept of the plane where equation is 6x+8y-3z=72.

a)3 b)26.83c)9 d)25.63

Ans: b) 26.83

SOLUTION• 6x+8y-3z=72

x + y - z = 172/6 72/8 72/3X- intercept = (72/6, 0, 0)

= (12, 0, 0)Y- intercept = (0, 0, -72/3)

= (0, 0, -24)Distance between x-intercept and z-intercept of the

plane = √[( x1- x2)2 + (y1-y2)2 + (z1-z2)2]=√[( 12- 0)2 + (0-0)2 + (0+24)2]= 26.83

Or simplify √(x²+z² )= √(12²+ 24²) = 26.83

Quantitative 25 : Co-ordinate Geometry

Q25) The vertices of Δ ABC are point A (1,2), B(4,6), C(-4,12). Which of the following is true?

a) ABC is not a right angled Δb) It is a right angled Δ with right angle at Cc) It is a right angled Δ with right angle at Bd) It is a right angled Δ with right angle at A

Ans: c) It is a right angled Δ with right angle at B

SOLUTION

Side AB = √ [(4-1)2 + (6-2)2 ]= 5 units

Side BC = √[ (-4-4)2 + (12-6)2 ]= 10 units

Side CA = √[ (1+4)2 + (12-2)2 ]= √125 units

For a right-angled triangle H2=p2+b2 (√125)2=102 +52

CA2 = AB 2+BC2

Hence it is right angled at B

Quantitative 26 :Time and WorkQ26) A seamstress buys a certain amount of Gingham

cloth which comes in rolls that are exactly 56 inches wide. She has also bought a certain length of Seek sucker cloth which is 35 inches wide. The seamstress first focuses on the Gingham roll and discovers that she has 116 yards of Gingham and she wants to divide the gingham into 116 lengths of 1 yard each. She wants to have twice as many pieces of seek sucker as she does of the Gingham. It takes 4 seconds to cut each length of Gingham. Working non-stop, how long (in seconds) will it take her to cut all the 116 pieces?

26(b)

a) 464 secs b) 460 secsc) 463 secs d) 465 secs

Ans: b) 460 secs

SOLUTION

• It takes 4 seconds to cut each length of Gingham

• So to cut 116 pieces, total time required= (116-1) * 4= 460 sec

Quantitative 27 : Arithmetic Progression

Q27) A long thin strip of width 7 cm is kept on a flat surface. Another identical strip is kept on it in an overlapping manner such that the combined width of the two is 11 cm. What is the width of 55 such strips kept like this?

a) 224 b) 223c) 225 d) None of these

Ans: b) 223

74 4

7+4+4+4+……….+4 = 4*54+7 = 223

SOLUTION

7

Quantitative 28 : AveragesQ28) Six persons with different ages are standing

in a queue. After two years their average age will be 43 years. A seventh person joins them. The current average age has now become 45 years. Find the age of seventh person (in years)?

a) 55 years b) 59 yearsc) 69 years d) None of theseAns: c) 69 years

SOLUTION

• Present average age of group = 43-2 = 41 years• When 7th person joins the average = 45 years• Total age of 7 people = 41*6 + x• Where x is the age of the 7th person joining the

group• Average = total/ number of observations• 45 = (246 +x) / 7• On solving• X= 69 years

Quantitative 29 : Heights & distance

Q29) Two vertical poles of heights 6m and 11m stand on a plane ground. The distance between their feet is 12m. A rope is tied tightly from the top of one pole to the top of the other. Find the length of the rope (round off)?a) 14m b)13mc) 15m d) None of these

Ans: b) 13m

A2 + B2 = H2

144 + 25 = 169H = 13 m

Therefore, Length of rope = 13 m

12 m11 m

5 m

12 m

6 m

SOLUTION

Quantitative 30 : Heights & distance with Trigonometry

Q 30) Standing on top of a high building, I measure an angle of elevation of a building 25 metres away as 45 degrees. The angle of depression of the ground level of the same building is also measured as 45 degrees. How tall is that building?a) 10m b) 20mc) 25m d) 50m

Ans: d) 50m

Since Angle of Elevation = 45o

Tan 45 = p / b = BC/OB = 1p/25= 1

Therefore, P = 25m Similarly AB = 25m

Total Height of the taller building = AB + BC = 25m +

25m = 50m

Solution

45o

25

C

----------------------------------

--------

--------

--------

--------

--------

45o

2525 B

A

O

Logical reasoning-1Logical reasoning-1Q31Q31) ) One day Alice meets Pal and Byte in One day Alice meets Pal and Byte in

fairyland. She knows that Pal lies on fairyland. She knows that Pal lies on Mondays, Tuesdays and Wednesdays and Mondays, Tuesdays and Wednesdays and tells the truth on the other days of the tells the truth on the other days of the week .Byte, on the other hand, lies on week .Byte, on the other hand, lies on Thursdays, Fridays and Saturdays, but Thursdays, Fridays and Saturdays, but tells the truth on the other days of the tells the truth on the other days of the week. Now they make the following week. Now they make the following statements to Alice – Pal: “Yesterday was statements to Alice – Pal: “Yesterday was one of those days when I lie”.one of those days when I lie”.

Byte: “Yesterday was one of those days Byte: “Yesterday was one of those days when I lie too”.when I lie too”.

What day is it ?What day is it ?

1(b)1(b)

a) Thursday b) Tuesdaya) Thursday b) Tuesday

c)c) Monday d) Sunday Monday d) Sunday

AnsAns: a) Thursday: a) Thursday

SOLUTIONSOLUTION

Mon Tues Wed Thurs Fri Sat Sun

Alice √ √ √

Pal √ √ √

Logical Reasoning-2Q32Q32) Rearrange the following letters to make a ) Rearrange the following letters to make a

meaningful word and choose from the meaningful word and choose from the options given, the category in which it lies. options given, the category in which it lies.

“RAPETEKA”“RAPETEKA”

a) Bird a) Bird b) Vegetable b) Vegetable

c) City c) City d) Fruit d) Fruit

Ans: ‘PARAKEET’. a) BirdAns: ‘PARAKEET’. a) Bird

Logical Reasoning-3

Q33Q33) In the reading room of a library, there are 23 ) In the reading room of a library, there are 23 reading spots. Each reading spot consists of a reading spots. Each reading spot consists of a round table with 9 chairs placed around it. There round table with 9 chairs placed around it. There are some readers such that in each occupied are some readers such that in each occupied reading spot there are different numbers of reading spot there are different numbers of readers. If in all there are 36 readers, how many readers. If in all there are 36 readers, how many reading spots do not have even a single reader?reading spots do not have even a single reader?

a) 8 a) 8 b) 15 b) 15 c) 16 c) 16 d) None of these d) None of these

AnsAns: b) 15: b) 15  

SOLUTIONSOLUTION 23 reading spots 23 reading spots Each reading spot consists of 9 chairs Each reading spot consists of 9 chairs

placed around it so there are some readers placed around it so there are some readers such that in each occupied reading spot such that in each occupied reading spot there are different number of readers.there are different number of readers.

Soon first table 1 person will sit.Soon first table 1 person will sit. On second table 2 person will sitOn second table 2 person will sit If there are 36 readers then If there are 36 readers then 1+2+3+4+5+6+7+8=361+2+3+4+5+6+7+8=36 Only 8 tables will be occupied. Only 8 tables will be occupied. Therefore, 23-8=15 reading spots will not Therefore, 23-8=15 reading spots will not

have even a single reader.have even a single reader.

Logical reasoning-4Logical reasoning-4Q34Q34) Middle – earth is a fictional land ) Middle – earth is a fictional land

inhabited by Hobbits, Elves, dwarves and inhabited by Hobbits, Elves, dwarves and men. The Hobbits and the Elves are men. The Hobbits and the Elves are peaceful creatures who prefer slow, silent peaceful creatures who prefer slow, silent lives and appreciate nature and art. The lives and appreciate nature and art. The dwarves and the men engage in physical dwarves and the men engage in physical games. The game is as follows . A tournol is games. The game is as follows . A tournol is one where out of the two teams that play a one where out of the two teams that play a match, the one that loses get eliminated. match, the one that loses get eliminated. The matches are played in different rounds The matches are played in different rounds where in every round , half of the teams get where in every round , half of the teams get eliminated from the tournament. If there eliminated from the tournament. If there are 8 rounds played in a knock-out tournol are 8 rounds played in a knock-out tournol how many matches were played?how many matches were played?

4(b)4(b)

a) 257 a) 257 b) 256 b) 256

c) 72 c) 72 d) 255 d) 255

Ans: d) 255Ans: d) 255

SOLUTIONSOLUTIONRound No. of matches

playedNo. of

contestants8 1 27 2 46 4 85 8 164 16 323 32 642 64 1281 128 256

Total 255

Logical Reasoning-5Logical Reasoning-5Q35Q35) Consider two tumblers, the first ) Consider two tumblers, the first

containing Water and second containing Water and second containing coffee. Suppose you take containing coffee. Suppose you take one spoon of water out of the first one spoon of water out of the first tumbler and pour it into the second tumbler and pour it into the second tumbler. After stirring well you take tumbler. After stirring well you take one spoon of the mixture from the one spoon of the mixture from the second tumbler and pour it back into second tumbler and pour it back into the first tumbler. Which one of the the first tumbler. Which one of the following statement holds now? following statement holds now?

5(b)5(b)a) There is less coffee in the first tumbler a) There is less coffee in the first tumbler than water in the second tumbler.than water in the second tumbler.

b) There is more coffee in the first tumbler b) There is more coffee in the first tumbler than water in the second tumbler.than water in the second tumbler.

c) There is as much coffee in the first c) There is as much coffee in the first tumbler as there is water in the second tumbler as there is water in the second tumbler.tumbler.

d) None of the statements holds true.d) None of the statements holds true.

AnsAns: d) None of the statements holds true.: d) None of the statements holds true.

Logical reasoning-6Logical reasoning-6Q36Q36) A taxi driver commenced his journey ) A taxi driver commenced his journey

from a point and he drove 10 km towards from a point and he drove 10 km towards north and turned to his left and drove north and turned to his left and drove another 20 km. After meeting a friend another 20 km. After meeting a friend here, he turned to his right and continued here, he turned to his right and continued to drive another 10 km. In which direction to drive another 10 km. In which direction is he now with respect to the starting is he now with respect to the starting point?point?

a)Westa)West b)Southb)South

c)Northc)North d)Eastd)East

AnsAns: c) North: c) North

SOLUTIONSOLUTION

NorthNorth

10 KM10 KM

20 KM20 KM

10 KM10 KM

Logical reasoning-7Logical reasoning-7

QQ3737) A school yard contains only ) A school yard contains only bicycles and 4 wheeled wagons. On bicycles and 4 wheeled wagons. On Tuesday, the total number of wheels in Tuesday, the total number of wheels in the schoolyard was 114. What would the schoolyard was 114. What would be the possible number of bicycles?be the possible number of bicycles?

a)18a)18 b)17b)17

c)16c)16 d) 8d) 8

AnsAns: b) 17: b) 17

SOLUTIONSOLUTION

Number of wheels in a bicycle = 2Number of wheels in a bicycle = 2 Number of wheels in a wagon = 4Number of wheels in a wagon = 4 Total number of wheels Total number of wheels =114 =114

a) 18a) 18 If bicycles are 18 then the number of wheels in bicycle If bicycles are 18 then the number of wheels in bicycle

= 36= 36 Remaining wheels = 114-36=78Remaining wheels = 114-36=78 Now this should be divisible by four because the Now this should be divisible by four because the

remaining wheels are of wagons 78/4 = 19.5remaining wheels are of wagons 78/4 = 19.5 Solution not feasible.Solution not feasible.

b)17b)17 Number of wheels in bicycle = Number of wheels in bicycle =

17×2=3417×2=34 Now 114 – 34=80/4 = 20Now 114 – 34=80/4 = 20

c) 16c) 16

16×2 = 3216×2 = 32 114-32 = 82/4 =20.5114-32 = 82/4 =20.5

d) 8d) 8

8×2 = 16 8×2 = 16 114-16 =98 = 24.5114-16 =98 = 24.5

Logical reasoning-8Logical reasoning-8

Q38Q38) A pie is to be divided among 20 ) A pie is to be divided among 20 people. A man eats 3 pieces, a woman people. A man eats 3 pieces, a woman eats 2 pieces and a child eats ½ a piece eats 2 pieces and a child eats ½ a piece of pie. There are 20 pieces of pie in all. of pie. There are 20 pieces of pie in all. What is the number of men, women & What is the number of men, women & children, so that 20 people in total and children, so that 20 people in total and everyone gets pie as per his/her everyone gets pie as per his/her requirement and there is no shortage or requirement and there is no shortage or excess of pie at the end? excess of pie at the end?

8(b)8(b)

a) 7 women, 1 man, 12 childrena) 7 women, 1 man, 12 children

b) 5 women, 1 man, 14 childrenb) 5 women, 1 man, 14 children

c) 4 women, 2 men, 12 childrenc) 4 women, 2 men, 12 children

d) None of thesed) None of these

AnsAns: b) 5 women, 1 man, 14 children: b) 5 women, 1 man, 14 children

SOLUTIONSOLUTION

Number of People = 20

Pieces eaten by men = 3

Pieces eaten by women = 2

Pieces eaten by children = ½

Options Women Men Children Total no. of Pieces

Total no. of People

a 7(7×2=14) 1(1×3=3) 12(12×1/2=6) 23 20 b 5(5×2=10) 1(1×3=3) 14(14×1/2=7) 20 20 c 4(4×2=8) 2(2×3=6) 12(12×1/2=6) 20 18

Logical reasoning-9 Logical reasoning-9 (Direction)(Direction)

Q39Q39) A scientist was researching on animal ) A scientist was researching on animal behavior in his lab. He was very interested in behavior in his lab. He was very interested in analyzing the behavior of bears. For some analyzing the behavior of bears. For some reason he traveled 1mile in north direction & reason he traveled 1mile in north direction & reached at North Pole. There he saw a bear. He reached at North Pole. There he saw a bear. He then followed the bear around 1 hr with a then followed the bear around 1 hr with a speed of 2km/hr in east direction. After that he speed of 2km/hr in east direction. After that he traveled in south direction & reached at his lab traveled in south direction & reached at his lab in 2 hrs. Then what is the color of the bear? in 2 hrs. Then what is the color of the bear?

a) Blacka) Black b) Brownb) Brown

c) Whitec) White d) None of thesed) None of these

9(b)9(b)

AnsAns: c) White: c) White

Logical Reasoning-Logical Reasoning-10(Series)10(Series)Q40Q40)) When Lucy was young her father would take his When Lucy was young her father would take his

daughter to the terrace and explain about daughter to the terrace and explain about constellations to his daughter and then he leaves her constellations to his daughter and then he leaves her alone in the terrace to find few of them all by herself. alone in the terrace to find few of them all by herself. Lucy finds around 25 groups of stars that appear to Lucy finds around 25 groups of stars that appear to her as constellations. She draws 7 patterns of the her as constellations. She draws 7 patterns of the constellations in her notebook and notes down the constellations in her notebook and notes down the number of stars in each of them. She counts 5 stars number of stars in each of them. She counts 5 stars in first constellation and 15 in next. She counts a in first constellation and 15 in next. She counts a number the third time and forgets to note it down. number the third time and forgets to note it down. The next four constellations she counts are The next four constellations she counts are 51,53,159,161. Next day her father looks at the 51,53,159,161. Next day her father looks at the notebook and wants to know the number of stars in notebook and wants to know the number of stars in the third constellation. Lucy only remembers that the third constellation. Lucy only remembers that number of starts counted in each of the constellation number of starts counted in each of the constellation followed a pattern 5, 15, x, 51, 53, 159, 161.followed a pattern 5, 15, x, 51, 53, 159, 161.

10(b)10(b)

What is the value of x?What is the value of x?

a) 19 a) 19 b) 45b) 45

c) 16c) 16 d) 17d) 17

AnsAns: d) 17: d) 17

SOLUTIONSOLUTION

55 15 15 x x 51 53 159 51 53 159161161

×3 +2 ×3 +2 ×3 ×3 +2 ×3 +2 ×3 +2+2

Analytical reasoning-1

Q41) Bob, Peter, Oliver and 2 girls –Raven and Chelsey are to be seated in a row. Raven often sits to left of Bob. No girl sits at extreme positions and middle positions. Peter always sits at the extreme position. Who sits to the right of Chelsey?

a)Oliver b)Bobc)Peter/Oliver d)Peter

Ans: c)Peter/Oliver

SOLUTION

There are two possible solutions:

Peter Chelsey Oliver Raven Bob

Peter Raven Bob Chelsey Oliver

Oliver Peter

Analytical reasoning-2

Q42) A man is standing in front of a painting of a man, and he tells us the following: “ Brothers and sisters have I none, but this man’s father is my father’s son”. Who is on the painting?

a) The man himselfb) The man’s son c) The man’s fatherd) Can’t be determined

2(b)

Ans: b) The man’s son

SOLUTION

Father

Man’s Father

Man

Analytical reasoning-3

Q43) There are 5 materials to make a perfume: Lilac, Balsalmic, Lemon, Woody and Mimosaic. To make a perfume that is in demand the following conditions are to be followed: Lilac and Balsalmic go together. Woody and Mimosaic go together but one of any one group does not go with any other of the other group together. Lemon can be added with any material. All of the following combinations are possible to make a perfume EXCEPT:

3(b)

a) Balsalmic and Lilacb) Woody and Lemonc) Mimosaic and Woodyd) Mimosaic and Lilac

Ans: Mimosaic and Lilac.

SOLUTION

LILAC ----------------BALSAMIC

WOODY--------------MIMOSAIC

LEMON CAN BE ADDED TO ALL

LILAC ----------------BALSAMIC x WOODY--------------MIMOSAIC

Directions for question 43: Read the passage given below and answer the questions that follow.

Analytical Reasoning-4Q44) In a certain society, there are 2 marriage groups,

red and brown. No marriage is permitted within a group. On marriage, males become part of their wife’s group; women remain in their own group. Children belong to the same group as their parents. Widowers and divorced males revert to the group of their birth. Marriage to more than one person at the same time and marriage to a direct descendant are forbidden.

4(b)i) A male born into the brown group may have

a) an uncle in either groupb) a brown daughter c) a brown sond) a son-in-law born into the red group e) a daughter-in-law in the red group

Ans: a)

MALE

FATHERMOTHER FATHERMOTHER’S

BROTHERFATHER’S BROTHER

4(c)

ii) Which of the following is not permitted under the rules as stated?

a) a brown male marrying his father’s sisterb) A red female marrying her mother’s brotherc) a man born red, who is now a widower,

marrying his brother’s widowd) a widower marrying his wife’s sisterAns: b)

SOLUTION

MALE

FATHERMOTHER FATHER

FATHER’S SISTER

MOTHER’S BROTHER

FEMALE

MOTHER

Reading Comprehension-1Q45)The recent news, that local hospitals have had to reroute seriously ill patients because the community's critical-care beds are full, is worrisome. Earlier this week, four of the six local hospitals ran out of space for the critically ill and had to turn people away.Federal law requires hospitals to treat anyone who walks in. As a result of having to treat large number of uninsured patients, the emergency rooms often become an economic drain on their hospitals. Doctors now want to set up their own free-standing ambulatory surgical facilities and diagnostic centers. Critics contend this would leave hospitals with less revenue and the same number of indigents to treat. A bill was recently introduced to phase out the need for a "certificate of public need" for non-hospital-based facilities, provided those facilities met stringent regulations and requirements. This would have made it easier to set up alternative facilities to help indigent patients. The finance committee balked at the hefty price and killed the bill, another casualty of a failed legislative session. Unfortunately, the problem of access to medical care for those of limited means is not going to go away anytime soon and, despite the well-intended regulations, full hospitals compromise everyone's welfare. Healthy competition with small neighborhood surgical and diagnostic centers may be what is necessary to help dampen rising medical costs. But under no circumstances should the hospitals be forced to care for everybody without health insurance while competitors operate free of the burden of caring for those unable to pay.

1(b)

Which of the following best describes the tone of the passage?

a) neutralb) positivec) persuasived) angrye) Reverential

Ans : c) persuasive

1(c)Which of the following is cited as a factor which has contributed to the overburdening of hospitals?

I Failure to pass legislation which would have mitigated the problem

II Limited access to medical care for the poorIII Federal lawa) I onlyb) II onlyc) III onlyd) I and IIe) I, II, and III

Ans : e) I, II, and III

1(d)

The author cites the failed legislation in order to show that

a) the legislature will never resolve this issue.b) the finance committee does not care about the

uninsured citizens.c) there will continue to be uninsured hospital

patients for a long time to come.d) the legislature does not have the decision to

resolve this issue.e) the doctors successfully lobbied the finance

committee.

Ans : c) there will continue to be uninsured hospital patients for a long time to come.

1(e) Which of the following is a conclusion supported by the passage?

a) If doctors want to run their own facilities, they should be required to take in at least some of the indigents.

b) The government should provide health insurance for those unable to buy their own.

c) Voters should tell the finance committee members that they will not be reelected if they do not pass some new legislation.

d) Emergency rooms that turn patients away due to overcrowding are derelict in their duty .

e) The fundamental problem facing hospitals now is that health care costs have risen dramatically in recent years

Ans : a) If doctors want to run their own facilities, they should be required to take in at least some of the indigents.

SUMMARYThe pattern of the paper can be summarized as follows:

1. In Quantitative ability the following topics are to be covered-Simple trigonometry( sin-cosine, cot-tan, cos-cosec)Problem of agesHeights & distancesMensuration ( rings, spheres etc.)Simple GeometryCo-ordinate GeometryNumber System ( simplification, factorization based on (a+b)2, (a+b)3)Arithmetic & Geometric Progression

Pipes & CisternsRatio & ProportionAveragesAverage SpeedProfit & LossCubes (volume & surface area)Simple linear equationsTime & WorkTime & DistanceProbability (atleast 3 questions will come in each paper)Permutation & Combination (atleast 2 questions will come in each paper)

2. In logical ReasoningSimple series ( at least one question)DirectionsSmall puzzles

3 You may get one or two passages on Analytical Reasoning.

4 A passage on Reading Comprehension may appear with 3 or 4 questions.

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