data inter & sufficency

Upload: tanya-hughes

Post on 14-Oct-2015

98 views

Category:

Documents


0 download

TRANSCRIPT

43

CONTENTS:1. Introduction2. Table Charts3. Bar Charts4. Pie Charts5. Line Graph6. Data Sufficiency

Data Interpretation Data Interpretation, the one of the easiest, time taking and scoring topic of the Bank Exams. Everybody knows this fact... but people pay less attention on this area. But unfortunately in SBI PO Exam, the complete aptitude section will depend on Data Interpretation.

In this section , we shall discuss about the basics Data Interpretation. The Data Interpretation is also called as comprehension of mathematics. Because, in reading comprehension, we have to study the passage and answer the questions followed by that passage. In the same way, in Data Interpretation, some data is given in the form of graphs, charts and tables followed by questions. We have to study, understand and analyze the data to solve the questions. Here we have to keep in mind that, even a 10th standard boy can solve these problems. But you've to solve these problems in time

now lets come to our topic

Data :Data is a collection of facts, such as values or measurements. It can be numbers, words, measurements, observations or even just descriptions of things.

Information :Information refers to data being arranged and presented in a systematic or an organise form, so that some useful inference can be drawn from the same. By data we generally mean quantities, figures, statistics, relating to any event.

So what is this Data Interpretation?

The Data Interpretation is the extraction (or usage) of maximum information from a given set of data or information. The data can be presented either in the form of a table or a bar chart or a pie chart or a line graph or as a combination of one of these formats.

now lets have a look at some tips in solving the Data Interpretation Problems :

Before starting DI section one should be very comfortable with numbers, calculations, fractions, percentages, averages, ratios. It helps in reducing the time required for solving the questions.

Scan the data briefly to see what it is about, but here do not attempt to analyse it in too much detail before reading a question. Focus on only those aspects of the data that are necessary to answer the question.

Be sure to read all notes related to the data.

When possible, try to make visual comparisons of the data given in a graph and estimate products and quotients rather than perform involved computations. Remember that these questions are to be answered only on the basis of the data given, everyday facts (such as the number of days in a year), and your knowledge of mathematics.

Do not make use of specific information you recall that might relate to the particular situation on which the questions are based unless that information can be derived from the date provided.

Now lets have a look at the types of the DIAGRAMS which are used ind data Interpretations and shall do some problems on them. (Click on the name of the Data Interpretation model for thedescriptionand model problems.

Bar Diagrams Multiple Bar DiagramsSubdivided / Component Bar Diagrams Line Graphs Pie Charts TablesBar Diagrams The Bar Diagram is the basic model of the Data Interpretation Problems.The bar diagram is a two dimensional graphic representation where the elementary graphic objects are a set of rectangles or bars drawn in parallel so that the extension of the same is proportional to the magnitude they intend to represent.

Here the rectangles, or bars, can be either horizontally or vertically positioned.

If only one bar is given in the graph, then that diagram is called a simple bar diagram.

Have a look at the Following bar diagram. It gives us the information of the production of a company in various years.

Now lets have a look at a problem based on this Simple Bar diagram.

What is the average production of the company over the years ? (followed by some options)

Now just find out the average of the production.

So here, 333 is the answer. ( Remember, here you should add all the terms mentally and put that 2000 on paper and then divided that with 6. Subdivided / Component Bar Diagrams The Sub Divided / Component bar diagrams are used to represent data in which the total magnitude (bar) is divided into different parts or components. In these type of diagrams,first they make simple bars for each class taking total magnitude in that class and then divide these simple bars into parts in the ratio of various components. With an example we shall try to understand the Concept.

Assume that you have to give the data of the production of vehicles of 3 companies (name them P, Q and R) over the years 1994 to 2000.

The questions will be like this. What is the difference between the production of Q in the years 1997 and 1999 ? (followed by some options)

Sol :

The Production of Q in 1997 is (40 -17.5) = 22.5 thousand.

TheProduction of Q in 1999 is (32.5-12.5) = 20 thousand.

The Difference = 22500 - 20000 = 2500

So, the answer is 2500.Line Graphs The line graph is another important type of graph. The line graph displays information as a series of data points connected by some straight line segments (or simply lines). You can simply say that the Line Graph is the graph which uses points connected by lines to show how something changes in value. Lets have a look at an example Line Graph so that we can understand the topic in detail.

Single Line Graph :

The following Line Graph gives the production of a company over the years 1999 to 2005.

Now the problem question will be like this.In how many of the following years was the production of the company above the average? (followed by some options)

Sol :

The Average Production =

So clearly it is visible that the production is above average in 3 years.

Multiple Line Graph :

The following Graph shows the profit of two companies A and B (In Lakhs) over the years 2000 to 2005.

Now the question will be like this.What is the difference between the average profit of the companies A and B over the years? (followed by some options)

Sol :

So 3.33 Lakhs is the answer :) Pie Chart You might have observed the Pie Charts while reading about Budget.The pie chart is a circular chart which is sectors. In a pie chart, the arc length of each sector (and consequently its central angle and area), is proportional to the quantity it represents. As we've already said, these charts are moreusefulwhile showing the percentages and ratios. Lets discuss these type of problems with an example. The following Pie - Chart shows the differentcolorsof cars using by the 7200 people of a town.

Tables All of us know what the TABLE is.... Here the Data is given in the form of rows and columns. A row is a series of cells going horizontally across the table. A column is a series of cells going vertically or up and down the table. We have to analyze these rows and columns and should answer the questions according to them. Lets have a look at an example. The followingtable gives the data of the number of computers produced by five companies namely P, Q, R, S and T over the years 2004 to 2009 (the production is in Thousands).

Now the question will be like,The percentage lead in the production of computers by company R from 2005 to 2006 was ? (followed by some options)

So the Answer is 50%

Now the question will be like, How many persons are using REDcolorcars ? (followed by some options)

Sol : The Number of persons using Red color cars is

so the answer is 1440.

This is all about D.I friends Lets discuss problems based on this topic

1. Table charts

SOLVED

EXAMPLE

I . The following table gives the percentage distribution of population of five states, P, Q, R, S and T on the basis of poverty line and also on the basis of sex.StatePercentage of Population below the Poverty LineProportion of Males and Females

Below Poverty LineAbove Poverty Line

M : FM : F

P355 : 66 : 7

Q253 : 54 : 5

R241 : 22 : 3

S193 : 24 : 3

T155 : 33 : 2

1.If the male population above poverty line for State R is 1.9 million, then the total population of State R is?A.4.5 millionB.4.85 million

C.5.35 millionD.6.25 million

Answer: Option D

Explanation:Let the total population of State R be x million.Then, population of State R above poverty line = [(100 - 24)% of x] million =76x xmillion

100

And so, male population of State R above poverty line =2x76x xmillion

5100

But, it is given that male population of State R above poverty line = 1.9 million.2x76x x= 1.9 x =5 x 100 x 1.9= 6.25.

510076 x 2

Total population of State R = 6.25 million.

2. What will be the number of females above the poverty line in the State S if it is known that the population of State S is 7 million?A.3 millionB.2.43 million

C.1.33 millionD.5.7 million

Answer: Option BExplanation:Total population of State S = 7 million.Population above poverty line = [(100 - 19)% of 7] million = (81% of 7) million = 5.67 million.And so, the number of females above poverty line in State S =3x 5.67million

7

= 2.43 million.3. What will be the male population above poverty line for State P if the female population below poverty line for State P is 2.1 million?A.2.1 millionB.2.3 million

C.2.7 millionD.3.3 million

Answer: Option DExplanation:Female population below poverty line for State P = 2.1 millionLet the male population below poverty line for State P be x million.Then, 5 : 6 = x : 21 x =2.1 x 5= 1.75.

6

Population below poverty line for State P = (2.1 + 1.75) million = 3.85 million.Let the population above poverty line for State P by y million.Since, 35% of the total population of State P is below poverty line, therefore, 65% of the total population of State P is above poverty line i.e., the ratio of population below poverty line to that above poverty line for State P is 35 : 65.35 : 65 = 3.85 : y y = 65 x 3.85= 7.15.

35

Population above poverty line for State P = 7.15 million and so, male population above poverty line for State P =6x 7.15million

13

= 3.3 million.4.If the population of males below poverty line for State Q is 2.4 million and that for State T is 6 million, then the total populations of States Q and T are in the ratio?A.1:3B.2:5

C.3:7D.4:9

Answer: Option BExplanation:For State Q:Male population below poverty line = 2.4 million.Let the female population below poverty line be x million.Then, 3 : 5 = 2.4 : x x =5 x 2.4= 4.

3

Total population below poverty line = (2.4 + 4) = 6.4 million.If Nq be the total population of State Q, then,25% of Nq = 6.4 million Nq =6.4 x 100million = 25.6 million.

25

For State T:Male population below poverty line = 6 million.Let the female population below poverty line be y million.Then, 5 : 3 = 6 : y y =3 x 6= 3.6.

5

Total population below poverty line = (6 + 3.6) = 9.6 million.If Nt be the total population of State T, then,15% of Nt = 9.6 million Nt =9.6 x 100 Million = 64 million.

15

Thus, Required ratio =Nq =25.6= 0.4 =2.

Nt645

NOW THESE ARE FOR YOU , DO IT CAREFULLY

II . Use this table to solve the questions from 1 -4Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.YearItem of Expenditure

SalaryFuel and TransportBonusInterest on LoansTaxes

1998288983.0023.483

19993421122.5232.5108

20003241013.8441.674

20013361333.6836.488

20024201423.9649.498

1. What is the average amount of interest per year which the company had to pay during this period?A.Rs. 32.43 lakhsB.Rs. 33.72 lakhs

C.Rs. 34.18 lakhsD.Rs. 36.66 lakhs

Q2 The total amount of bonus paid by the company during the given period is approximately what percent of the total amount of salary paid during this period?A.0.1%B.0.5%

C.1%D.1.25%

Q3 Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?A.62%B.66%

C.69%D.71%

. Q4The total expenditure of the company over these items during the year 2000 is?A.Rs. 544.44 lakhsB.Rs. 501.11 lakhs

C.Rs. 446.46 lakhsD.Rs. 478.87 lakhs

III. Study the following table and answer the questions 5 -9 Number of Candidates Appeared and Qualified in a Competitive Examination from Different States Over the Years.StateYear

19971998199920002001

App.Qual.App.Qual.App.Qual.App.Qual.App.Qual.

M520072085009807400850680077595001125

N7500840920010508450920920098088001020

P64007808800102078008908750101097501250

Q8100950950012408700980970012008950995

R780087076009409800135076009457990885

Q5 Total number of candidates qualified from all the states together in 1997 is approximately what percentage of the total number of candidates qualified from all the states together in 1998?A.72%B.77%

C.80%D.83%

Q6 What is the average candidates who appeared from State Q during the given years?A.8700B.8760

C.8990D.8920

Q7 In which of the given years the number of candidates appeared from State P has maximum percentage of qualified candidates?A.1997B.1998

C.1999D.2001

Q8 What is the percentage of candidates qualified from State N for all the years together, over the candidates appeared from State N during all the years together?A.12.36%B.12.16%

C.11.47%D.11.15%

Q9 The percentage of total number of qualified candidates to the total number of appeared candidates among all the five states in 1999 is?A.11.49%B.11.84%

C.12.21%D.12.57%

IV . The following table gives the percentage of marks obtained by seven students in six different subjects in an examination. Study the following table and answer the questions10 -14The Numbers in the Brackets give the Maximum Marks in Each Subject.StudentSubject (Max. Marks)

MathsChemistryPhysicsGeographyHistoryComputer Science

(150)(130)(120)(100)(60)(40)

Ayush905090607080

Aman1008080408070

Sajal906070709070

Rohit806580806060

Muskan806585955090

Tanvi707565854060

Tarun653550778080

Q10 What are the average marks obtained by all the seven students in Physics? (rounded off to two digit after decimal)A.77.26B.89.14

C.91.37D.96.11

Q11 The number of students who obtained 60% and above marks in all subjects is?A.1B.2

C.3D.None

Q12 What was the aggregate of marks obtained by Sajal in all the six subjects?A.409B.419

C.429D.449

Q13 In which subject is the overall percentage the best?A.MathsB.Chemistry

C.PhysicsD.History

Q14 What is the overall percentage of Tarun?A.52.5%B.55%

C.60%D.63%

V. Study the following table and answer the questions 15-19Classification of 100 Students Based on the Marks Obtained by them in Physics and Chemistry in an Examination.SubjectMarks out of 50

40 and above30 and above20 and above10 and above0 and above

Physics9328092100

Chemistry4216681100

Average (Aggregate)7277387100

Q15. What is the different between the number of students passed with 30 as cut-off marks in Chemistry and those passed with 30 as cut-off marks in aggregate?A.3B.4

C.5D.6

Q16 If at least 60% marks in Physics are required for pursuing higher studies in Physics, how many students will be eligible to pursue higher studies in Physics?A.27B.32

C.34D.41

Q17 The percentage of number of students getting at least 60% marks in Chemistry over those getting at least 40% marks in aggregate, is approximately?A.21%B.27%

C.29%D.31%

Q18 The number of students scoring less than 40% marks in aggregate is?A.13B.19

C.20D.27

Q19 If it is known that at least 23 students were eligible for a Symposium on Chemistry, then the minimum qualifying marks in Chemistry for eligibility to Symposium would lie in the range?A.40-45B.30-40

C.20-30D.Below 20

V1. Study the following table and answer the questions 20-24Number of Candidates Appeared, Qualified and Scheduled in a Competitive Examination from Five States Delhi, H.P, U.P, Punjab and Haryana Over the Years 1994 to 1998YearDelhiH.PU.PPunjabHaryana

APPQULSchAPPQULIScheAPPQULISchAppQualSelAppQualSel

1997800085094780081082750072078820068085640070075

1998480050048750080065560062085680060070710065075

1999750064082740056070480040048650052565520035055

2000950085090880092086700065070780072084640054060

2001900080070720085075850095080570048560450060075

Q20 For which state the average number of candidates selected over the years is the maximum?A.DelhiB.H.P

C.U.PD.Punjab

Q21 The percentage of candidates qualified from Punjab over those appeared from Punjab is highest in the year?A.1997B.1998

C.1999D.2000

Q22 In the year 1997, which state had the lowest percentage of candidates selected over the candidates appeared?A.DelhiB.H.P

C.U.PD.Punjab

Q23 The number of candidates selected from Haryana during the period under review is approximately what percent of the number selected from Delhi during this period?A.79.5%B.81%

C.84.5%D.88.5%

Q24 The percentage of candidates selected from U.P over those qualified from U.P is highest in the year?A.1997B.1998

C.1999D.2001

V11. Study the following table and answer the questions 25-29

The following table gives the sales of batteries manufactured by a company over the years.Number of Different Types of Batteries Sold by a Company over the Years (Numbers in Thousands)YearTypes of Batteries

4AH7AH32AH35AH55AHTotal

199275144114102108543

19939012610284126528

19949611475105135525

1995105901509075510

199690751357590465

19971056016545120495

199811585160100145605

Q25 What was the approximate percentage increase in the sales of 55AH batteries in 1998 compared to that in 1992?A.28%B.31%

C.33%D.34%

Q26 The total sales of all the seven years is the maximum for which battery?A.4AHB.7AH

C.32AHD.35AH

Q27 What is the difference in the number of 35AH batteries sold in 1993 and 1997?A.24000B.28000

C.35000D.39000

Q28 The percentage of 4AH batteries sold to the total number of batteries sold was maximum in the year?A.1994B.1995

C.1996D.1997

Q29 In case of which battery there was a continuous decrease in sales from 1992 to 1997?A.4AHB.7AH

C.32AHD.35AH

VIII. Study the following table and answer the questions 30-33A school has four sections A, B, C, D of Class IX students.The results of half yearly and annual examinations are shown in the table given below.ResultNo. of Students

Section ASection BSection CSection D

Students failed in both Exams28231727

Students failed in half-yearlybut passed in Annual Exams1412813

Students passed in half-yearlybut failed in Annual Exams617915

Students passed in both Exams64554676

Q30 If the number of students passing an examination be considered a criteria for comparision of difficulty level of two examinations, which of the following statements is true in this context?A.Half yearly examinations were more difficult.

B.Annual examinations were more difficult.

C.Both the examinations had almost the same difficulty level.

D.The two examinations cannot be compared for difficulty level.

Q31 How many students are there in Class IX in the school?A.336B.189

C.335D.430

Q32 Which section has the maximum pass percentage in at least one of the two examinations?A.A SectionB.B Section

C.C SectionD.D Section

Q33Which section has the maximum success rate in annual examination?A.A SectionB.B Section

C.C SectionD.D Section

Q34 which section has the minimum failure rate in half yearly examination?A.A sectionB.B section

C.C sectionD.D section

ANSWER1. D2. C3. C4. A5. C6. C7. D8. D9. B10. B11. B12. D13. A14. C15. D16. B17. C18. D19. C20. A21. D22. D23. D24. B25. D26. C27. D28. D29. B30. C31. D32. D33. A34. D

2. BAR CHARTSA style of chart used by some technical analysts, on which, as illustrated below, the top of the vertical line indicates the highest price a security traded at during..

I. SOLVED EXAMPLE The total of the first three deficit countries (in Rs. crores) = 3594.3. The total of next five deficit countries (in Rs. crores) = 2588.5. The total of the last five deficit countries (in Rs. crores)Cumulative Trade Deficit/Surplus of Countries for the Year 2006 - 2007 (All figures in Rs. Crores).

Now give the answers on the basis of Above Table1.The ratio between the difference between the highest and the lowest of the surplus countries to the difference between Bangladesh and Oman is ?3.44B.2.96

C.4.5D.3.83

Answer: Option DExplanation:The required answer will be equal to 360/94 = 3.829. 2.The average of the total deficit of the middle five deficit is closest to the deficit of which country ?A.KoreaB.South Africa

C.UAED.None of these

Answer: Option AExplanation:The middle five deficit countries are India, New Zealand, South Africa, Korea and Namibia.Their average deficit is (1946.6/5) = 389.32. Korea's deficit is close to this value.

3.The state whose surplus is nearly equal to the average of the four surplus countries isA.Sri LankaB.UAE

C.USAD.UK

Answer: Option CExplanation:The average trade surplus of the four countries is 1860.4/4 = 465.1. Of the four options, USA has the closest value. 4. The ratio of the deficit of the first five deficit countries to the overall deficit of all the deficit countries is nearly equal to ?A.0.72B.0.75

C.0.80D.0.85

Answer: Option BExplanation:The required answer is (4885.2/6517) = 0.7496 5. The net total deficit/surplus is equal to ?A.4656.6 surplusB.4656.6 deficit

C.3836.5 deficitD.None of these

Answer: Option BExplanation:Adding all surpluses and subtracting all deficits will give an overall value of deficit of 4656.6. LETS CHECK WHAT WE HAVE LEARNT II. Study the following Bar graph and answer the questions 1-5The bar graph given below shows the sales of books (in thousand numbers) from six branches of a publishing company during two consecutive years 2000 and 2001.

Sales of Books (in thousand numbers) from Six Branches - B1, B2, B3, B4, B5 and B6 of a publishing Company in 2000 and 2001.

Q1.What is the ratio of the total sales of branch B2 for both years to the total sales of branch B4 for both years?A.2:3B.3:5

C.4:5D.7:9

Q2. Total sales of branch B6 for both the years are what percent of the total sales of branches B3 for both the years?A.68.54%B.71.11%

C.73.17%D.75.55%

Q3. What percent of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?A.75%B.77.5%

C.82.5%D.87.5%

Q4. What is the average sale of all the branches (in thousand numbers) for the year 2000?A.73B.80

C.83D.88

Q5 Total sales of branches B1, B3 and B5 together for both the years (in thousand numbers) are?A.250B.310

C.435D.560

The bar graph given below shows the foreign exchange reserves of a country (in million US $) from 1991 - 1992 to 1998 - 1999.III. Study the following Bar graph and answer the questions 6-10

Foreign Exchange Reserves Of a Country. (in million US $)

Q6. The ratio of the number of years, in which the foreign exchange reserves are above the average reserves, to those in which the reserves are below the average reserves is?A.2:6B.3:4

C.3:5D.4:4

Q7. The foreign exchange reserve in 1997-98 was how many times that in 1994-95?A.0.7B.1.2

C.1.4D.1.5

Q8 .For which year, the percent increase of foreign exchange reserves over the previous year, is the highest?A.1992-93B.1993-94

C.1994-95D.1996-97

9. The foreign exchange reserves in 1996-97 were approximately what percent of the average foreign exchange reserves over the period under review?A.95%B.110%

C.115%D.125%

Q10, What was the percentage increase in the foreign exchange reserves in 1997-98 over 1993-94?A.100B.150

C.200D.620

IV. Study the following Bar graph and answer the questions 11-15The bar graph given below shows the data of the production of paper (in lakh tones) by three different companies X, Y and Z over the years..Production of Paper (in lakh tones) by Three Companies X, Y and Z over the Years.

Q11. For which of the following years, the percentage rise/fall in production from the previous year is the maximum for Company Y?A.1997B.1998

C.1999D.2000

Q12. What is the ratio of the average production of Company X in the period 1998-2000 to the average production of Company Y in the same period?A.1:1B.15:17

C.23:25D.27:29

Q13. The average production for five years was maximum for which company?A.XB.Y

C.ZD.X and Z both

Q14. In which year was the percentage of production of Company Z to the production of Company Y the maximum?A.1996B.1997

C.1998D.1999

Q15. What is the percentage increase in the production of Company Y from 1996 to 1999?A.30%B.45%

C.50%D.60%

V. Study the following Bar graph and answer the questions 16-20Out of the two bar graphs provided below, one shows the amounts (in Lakh Rs.) invested by a Company in purchasing raw materials over the years and the other shows the values (in Lakh Rs.) of finished goods sold by the Company over the years.Amount invested in Raw Materials (Rs. in Lakhs)

Value of Sales of Finished Goods (Rs. in Lakhs)

Q16.The maximum difference between the amount invested in Raw materials and value of sales of finished goods was during the year?A.1995B.1996

C.1997D.1998

Q17. The value of sales of finished goods in 1999 was approximately what percent of the sum of amount invested in Raw materials in the years 1997, 1998 and 1999?A.33%B.37%

C.45%D.49%

Q18. What was the difference between the average amount invested in Raw materials during the given period and the average value of sales of finished goods during this period?A.Rs. 62.5 lakhsB.Rs. 68.5 lakhs

C.Rs. 71.5 lakhsD.Rs. 77.5 lakhs

Q19. In which year, the percentage change (compared to the previous year) in the investment on Raw materials is same as that in the value of sales of finished goods?A.1996B.1997

C.1998D.1999

Q20. In which year, there has been a maximum percentage increase in the amount invested in Raw materials as compared to the year?A.1996B.1997

C.1998D.1999

VI. Study the following bar charts and answer the questions.21-25Foreign Trade (Imports and Exports) by countries for the year (1993 - 1994)

Q21The ratio of the maximum exports to the minimum imports was closest to ?A.64B.69

C.74D.79

Q22. How many countries exhibited a trade surplus?A.5B.4

C.3D.6

Q23.The total trade deficit/surplus for all the countries put together was?A.11286 surplusB.11286 deficit

C.10286 deficitD.None of these

Q24. The highest trade deficit was shown by which country?A.CB.G

C.HD.L

Q25. The ratio of Exports to Imports was highest for which country ?A.AB.I

C.JD.K

VII. Study the following bar charts and answer the questions.26-30The bar graph given below shows the percentage distribution of the total expenditures of a company under various expense heads during 2003.Percentage Distribution of Total Expenditure of a Company

Q26.The total amount of expenditures of the company is how many times of expenditure on research and development?A.27B.20

C.18D.8

Q27 If the expenditure on advertisement is 2.10 crores then the difference between the expenditure on transport and taxes is?A.Rs. 1.25 croresB.Rs. 95 lakhs

C.Rs. 65 lakhsD.Rs. 35 lakhs

Q28. What is the ratio of the total expenditure on infrastructure and transport to the total expenditure on taxes and interest on loans?A.5:4B.8:7

C.9:7D.13:11

Q29. If the interest on loans amounted to Rs. 2.45 crores then the total amount of expenditure on advertisement, taxes and research and development is?A.Rs. 7 croresB.Rs. 5.4 crores

C.Rs. 4.2 croresD.Rs. 3 crores

Q30. The expenditure on the interest on loans is by what percent more than the expenditure on transport?A.5%B.10%

C.20%D.40%

(VIII) Study the following bar charts and answer the questions.31-35A cosmetic company provides five different products. The sales of these five products (in lakh number of packs) during 1995 and 2000 are shown in the following bar graph.Sales (in lakh number of packs) of five different products of Cosmetic Company during 1995 and 2000

Q31. The sales of lipsticks in 2000 was by what percent more than the sales of nail enamels in 2000? (rounded off to nearest integer)A.33%B.31%

C.28%D.22%

Q32. During the period 1995-2000, the minimum rate of increase in sales is in the case of?A.ShampoosB.Nail enamels

C.Talcum powdersD.Lipsticks

Q33. What is the approximate ratio of the sales of nail enamels in 2000 to the sales of Talcum powders in 1995?A.7:2B.5:2

C.4:3D.2:1

Q34. The sales have increase by nearly 55% from 1995 to 2000 in the case of?A.LipsticksB.Nail enamels

C.Talcum powdersD.Shampoos

Q35.The sales of conditioners in 1995 were by what percent less than the sales of shampoos in 1995? (Rounded off to nearest integer)A.57%B.36%

C.29%D.25%

ANSWER1. D2. C3. D4. B5. D6. C7. D8. A9. D10. A11. A12. C13. D14. A15. D16. C17. D18. D19. B20. A21. B22. B23. B24. D25. B26. B27. D28. D29. C30. D31. C32. A33. B34. D35. B

PIE CHARTSPie Graph. A pie chart is a circular chart divided into sectors, each sector shows the relative size of each.

SOLVED EXAMPLEI. Study the following pie-diagrams carefully and answer the questions given below it:Percentage Composition of Human Body

1.What percent of the total weight of human body is equivalent to the weight of the proteins in skin in human body?

A.0.016B.1.6

C.0.16D.Data inadequate

Answer & ExplanationAnswer: Option BExplanation:Let the body weight be x kg.Then, weight of skin protein in the body=16% of1of xkg

10

=16xkg.

1000

Required percentage =16x

1000

x 100% = 1.6%.

x

2. What will be the quantity of water in the body of a person weighing 50 kg?A.20 kgB.35 kg

C.41 kgD.42.5 kg

Answer & ExplanationAnswer: Option BExplanation:Quantity of water in the body of a person weighing 50 kg= (70% of 50) kg

= 35 kg

3. What is the ratio of the distribution of proteins in the muscles to that of the distribution of proteins in the bones?A.1 : 18B.1 : 2

C.2 : 1D.18 : 1

Answer & ExplanationAnswer: Option CExplanation:Required ratio =16% of1

3

=6=2.

16% of1

6

31

4. To show the distribution of proteins and other dry elements in the human body, the arc of the circle should subtend at the centre an angle of:A.54B.126

C.108D.252

Answer & ExplanationAnswer: Option CExplanation:Percentage of proteins and other dry elements in the body= (16% + 14%)

= 30%.

Central angle corresponding to proteins and other dry elements together

= 30% of 360

= 108.

TEST TIME II. Study the following Pie charts and answer the questions.1-5The following pie-chart shows the percentage distribution of the expenditure incurred in publishing a book. Study the pie-chart and the answer the questions based on it.Various Expenditures (in percentage) Incurred in Publishing a Book

Q1.If for a certain quantity of books, the publisher has to pay Rs. 30,600 as printing cost, then what will be amount of royalty to be paid for these books?

A.Rs. 19,450B.Rs. 21,200

C.Rs. 22,950D.Rs. 26,150

Q2.What is the central angle of the sector corresponding to the expenditure incurred on Royalty?

A.15B.24

C.54D.48

Q3.The price of the book is marked 20% above the C.P. If the marked price of the book is Rs. 180, then what is the cost of the paper used in a single copy of the book?

A.Rs. 36B.Rs. 37.50

C.Rs. 42D.Rs. 44.25

Q4.If 5500 copies are published and the transportation cost on them amounts to Rs. 82500, then what should be the selling price of the book so that the publisher can earn a profit of 25%?

A.Rs. 187.50B.Rs. 191.50

C.Rs. 175D.Rs. 180

Q5.Royalty on the book is less than the printing cost by:A.5%B.33 1/5 %

C.20%D.25%

III.Study the following Pie charts and answer the questions.6-8The following pie charts exhibit the distribution of the overseas tourist traffic from India. The two charts shows the tourist distribution by country and the age profiles of the tourists . Distribution of Overseas Tourist Traffic from India.

Q6.What percentage of Indian tourist went to either USA or UK ?

A.40 %B.50 %

C.60 %D.70 %

Q7.The ratio of the number of Indian tourists that went to USA to the number of Indian tourists who were below 30 years of age is ?

A.2:1B.8:3

C.3:8D.Cannot be determined

Q8.If amongst other countries, Switzerland accounted for 25% of the Indian tourist traffic, and it is known from official Swiss records that a total of 25 lakh Indian tourists had gone to Switzerland during the year, then find the number of 30-39 year old Indian tourists who went abroad in that year ?

A.18.75 lakhB.25 lakh

C.50 lakhD.75 lakh

IV.Study the following Pie charts and answer the questions.9-11The following pie chart give the information about the distribution of weight in the human body according to different kinds of components. Study the pie charts and answer the question.

Distribution of Weight in Human Body

Q9.What percentage of proteins of the human body is equivalent to the weight of its skin ?

A.41.66 %B.43.33 %

C.44.44 %D.Cannot be determined

Q10.How much of the human body is neither made of bones or skin ?

A.40 %B.50 %

C.60 %D.70 %

Q11.What is the ratio of the distribution of proteins in the muscles to that of the distribution of proteins in the bones ?

A.2:1B.2:3

C.3:2D.Cannot be determined

V.Study the following Pie charts and answer the questions.12-16The following pie-chart shows the sources of funds to be collected by the National Highways Authority of India (NHAI) for its Phase II projects. Study the pie-chart and answers the question that follow.Sources of funds to be arranged by NHAI for Phase II projects (in crores Rs.) Q12.Near about 20% of the funds are to be arranged through:

A.SPVSB.External Assistance

C.AnnuityD.Market Borrowing

Q13.If NHAI could receive a total of Rs. 9695 crores as External Assistance, by what percent (approximately) should it increase the Market Borrowing to arrange for the shortage of funds?

A.4.5%B.7.5%

C.6%D.8%

Q14.If the toll is to be collected through an outsourced agency by allowing a maximum 10% commission, how much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs. 4910 crores?

A.Rs. 6213 croresB.Rs. 5827 crores

C.Rs. 5401 croresD.Rs. 5316 crores

Q15The central angle corresponding to Market Borrowing is

A.52B.137.8

C.187.2D.192.4

Q16.The approximate ratio of the funds to be arranged through Toll and that through Market Borrowing is

A.2 : 9B.1 : 6

C.3 : 11D.2 : 5

VI.Study the following Pie charts and answer the questions.17-21The following pie-charts show the distribution of students of graduate and post-graduate levels in seven different institutes in a town.Distribution of students at graduate and post-graduate levels in seven institutes:

Q17What is the total number of graduate and post-graduate level students is institute R?

A.8320B.7916

C.9116D.8099

Q18.What is the ratio between the number of students studying at post-graduate and graduate levels respectively from institute S?

A.14 : 19B.19 : 21

C.17 : 21D.19 : 14

Q19.How many students of institutes of M and S are studying at graduate level?

A.7516B.8463

C.9127D.9404

Q20.What is the ratio between the number of students studying at post-graduate level from institutes S and the number of students studying at graduate level from institute Q?

A.13 : 19B.21 : 13

C.13 : 8D.19 : 13

Q21Total number of students studying at post-graduate level from institutes N and P is

A.5601B.5944

C.6669D.8372

VII Study the following pie-chart and the table and answer the questions 22-25Proportion of Population of Seven Villages in 1997.

Village% Population Below Poverty Line

X38

Y52

Z42

R51

S49

T46

V58

Q22.If the population of village R in 1997 is 32000, then what will be the population of village Y below poverty line in that year?

A.14100B.15600

C.16500D.17000

Q23.The ratio of population of village T below poverty line to that of village Z below poverty line in 1997 is:

A.11 : 23B.13 : 11

C.23 : 11D.11 : 13

Q24Find the population of village S if the population of village X below poverty line in 1997 is 12160.

A.18500B.20500

C.22000D.26000

Q25If in 1998, the population of villages Y and V increase by 10% each and the percentage of population below poverty line remains unchanged for all the villages, then find the population of village V below poverty line in 1998, given that the population of village Y in 1997 was 30000.

A.11250B.12760

C.13140D.13780

VIII. Study the following pie-chart and the table and answer the questions 26-30The following pie chart shows the amount of subscriptions generated for India Bonds from different categories of investors.Subscriptions Generated for India Bonds

Q26 .In the corporate sector, approximately how many degrees should be there in the central angle ?

A.120B.121

C.122D.123

Q27.If the investment by NRI's are Rs 4,000 crore, then the investments by corporate houses and FII's together is:

A.24,000 croreB.24,363 crore

C.25,423 croreD.25,643 crore

Q28.What percentage of the total investment is coming from FII's and NRI's ?

A.33 %B.11 %

C.44 %D.22 %

Q29.If the total investment other than by FII and corporate houses is Rs 335,000 crore, then the investment by NRI's and Offshore funds will be (approximately) ?

A.274,100B.285,600

C.293,000D.Cannot be determined

Q30.If the total investment flows from FII's were to be doubled in the next year and the investment flows from all other sources had remained constant at their existing levels for this year, then what would be the proportion of FII investment in the total investment into India Bonds next year (in US $ millions) ?

A.40 %B.50 %

C.60 %D.70 %

IX The circle-graph given here shows the spendings of a country on various sports during a particular year. Study the graph carefully and answer the questions 31-35

Q31.What percent of total spending is spent on Tennis?

A.121%

2

B.221%

2

C.25%D.45%

Q32.How much percent more is spent on Hockey than that on Golf?

A.27%B.35%

C.37.5%D.75%

Q33.If the total amount spent on sports during the year be Rs. 1,80,00,000 , the amount spent on Basketball exceeds on Tennis by:

A.Rs. 2,50,000B.Rs. 3,60,000

C.Rs. 3,75,000D.Rs. 4,10,000

Q34.How much percent less is spent on Football than that on Cricket?

A.222%

9

B.27%

C.331%

3

D.371%

7

Q35.If the total amount spent on sports during the year was Rs. 2 crores, the amount spent on Cricket and Hockey together was:

A.Rs. 8,00,000B.Rs. 80,00,000

C.Rs. 1,20,00,000D.Rs. 1,60,00,000

ANSWER KEY1. C2. C3. B4. A5. D6. B7. B8. D9. A10. D11. D12. B13. C14. C15. C16. B17. D18. D19. B20. D21. C22. B23. C24. C25. B26. C27. B28. C29. A30. B31. A32. D33. A34. C35. B

LINE GRAPHSolved exampleI Study the following line graph and answer the questions 1-5Exports from Three Companies Over the Years (in Rs. crore)

1.For which of the following pairs of years the total exports from the three Companies together are equal?

A.1995 and 1998B.1996 and 1998

C.1997 and 1998D.1995 and 1996

Answer: Option DExplanation:Total exports of the three Companies X, Y and Z together, during various years are:In 1993 = Rs. (30 + 80 + 60) crores = Rs. 170 crores.In 1994 = Rs. (60 + 40 + 90) crores = Rs. 190 crores.In 1995 = Rs. (40 + 60 + 120) crores = Rs. 220 crores.In 1996 = Rs. (70 + 60 + 90) crores = Rs. 220 crores.In 1997 = Rs. (100 + 80 + 60) crores = Rs. 240 crores.In 1998 = Rs. (50 + 100 + 80) crores = Rs. 230 crores.In 1999 = Rs. (120 + 140 + 100) crores = Rs. 360 crores.Clearly, the total exports of the three Companies X, Y and Z together are same during the years 1995 and 1996.

2.Average annual exports during the given period for Company Y is approximately what percent of the average annual exports for Company Z?

A.87.12%B.89.64%

C.91.21%D.93.33%

Answer: Option DExplanation:Analysis of the graph: From the graph it is clear that1. The amount of exports of Company X (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 30, 60, 40, 70, 100, 50 and 120 respectively.2. The amount of exports of Company Y (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 80, 40, 60, 60, 80, 100 and 140 respectively.3. The amount of exports of Company Z (in crore Rs.) in the years 1993, 1994, 1995, 1996, 1997, 1998 and 1999 are 60, 90,, 120, 90, 60, 80 and 100 respectively.Average annual exports (in Rs. crore) of Company Y during the given period =1x (80 + 40 + 60 + 60 + 80 + 100 + 140) =560= 80.

77

Average annual exports (in Rs. crore) of Company Z during the given period =1x (60 + 90 + 120 + 90 + 60 + 80 + 100) =600.

77

Required percentage =80x 100% 93.33%.

3.In which year was the difference between the exports from Companies X and Y the minimum?

A.1994B.1995

C.1996D.1997

Answer: Option CExplanation:The difference between the exports from the Companies X and Y during the various years are:In 1993 = Rs. (80 - 30) crores = Rs. 50 crores.In 1994 = Rs. (60 - 40) crores = Rs. 20 crores.In 1995 = Rs. (60 - 40) crores = Rs. 20 crores.In 1996 = Rs. (70 - 60) crores = Rs. 10 crores.In 1997 = Rs. (100 - 80) crores = Rs. 20 crores.In 1998 = Rs. (100 - 50) crores = Rs. 50 crores.In 1999 = Rs. (140 - 120) crores = Rs. 20 crores.Clearly, the difference is minimum in the year 1996.

4.What was the difference between the average exports of the three Companies in 1993 and the average exports in 1998?

A.Rs. 15.33 croresB.Rs. 18.67 crores

C.Rs. 20 croresD.Rs. 22.17 crores

Answer: Option CExplanation:Average exports of the three Companies X, Y and Z in 1993 = Rs.1x (30 + 80 + 60)crores = Rs.170crores.

33

Average exports of the three Companies X, Y and Z in 1998 = Rs.1x (50 + 100 + 80)crores = Rs.230crores.

33

Difference= Rs.230-170crores

33

= Rs.60crores

3

= Rs. 20 crores.

5.In how many of the given years, were the exports from Company Z more than the average annual exports over the given years?

A.2B.3

C.4D.5

Answer: Option CExplanation:Average annual exports of Company Z during the given period =1x (60 + 90 + 120 + 90 + 60 + 80 + 100)

7

= Rs.600crores

7

= Rs. 85.71 crores.From the analysis of graph the exports of Company Z are more than the average annual exports of Company Z (i.e., Rs. 85.71 crores) during the years 1994, 1995, 1996 and 1999, i.e., during 4 of the given years.NOW LETS DO SOME QUESTIONS :II. Study the following line graph and answer the questions 1-5The following line graph gives the ratio of the amounts of imports by a company to the amount of exports from that company over the period from 1995 to 2001.Ratio of Value of Imports to Exports by a Company Over the Years.

Q1.If the imports in 1998 was Rs. 250 crores and the total exports in the years 1998 and 1999 together was Rs. 500 crores, then the imports in 1999 was ?

A.Rs. 250 croresB.Rs. 300 crores

C.Rs. 357 croresD.Rs. 420 crores

Q2.The imports were minimum proportionate to the exports of the company in the year ?

A.1995B.1996

C.1997D.2000

Q3.What was the percentage increase in imports from 1997 to 1998 ?

A.72B.56

C.28D.Data inadequate

Q4.If the imports of the company in 1996 was Rs. 272 crores, the exports from the company in 1996 was ?

A.Rs. 370 croresB.Rs. 320 crores

C.Rs. 280 croresD.Rs. 275 crores

Q5.In how many of the given years were the exports more than the imports ?

A.1B.2

C.3D.4

Study the following line graph and answer the questions 6-10Number of Vehicles Manufactured by Two companies ove the Years (Number in Thousands)

Q6What is the difference between the number of vehicles manufactured by Company Y in 2000 and 2001 ?

A.50000B.42000

C.33000D.21000

Q7.What is the difference between the total productions of the two Companies in the given years ?

A.19000B.22000

C.26000D.28000

Q8.What is the average numbers of vehicles manufactured by Company X over the given period ? (rounded off to nearest integer)

A.119333B.113666

C.112778D.111223

Q9.In which of the following years, the difference between the productions of Companies X and Y was the maximum among the given years ?

A.1997B.1998

C.1999D.2000

Q10.The production of Company Y in 2000 was approximately what percent of the production of Company X in the same year ?

A.173B.164

C.132D.97

Study the following line graph and answer the questions 11-15The following line graph gives the percent profit earned by two Companies X and Y during the period 1996 - 2001.Percentage profit earned by Two Companies X and Y over the Given Years%Profit =Income - Expenditurex 100

Expenditure

Q11The incomes of two Companies X and Y in 2000 were in the ratio of 3:4 respectively. What was the respective ratio of their expenditures in 2000 ?

A.7:22B.14:19

C.15:22D.27:35

Q12.If the expenditure of Company Y in 1997 was Rs. 220 crores, what was its income in 1997 ?

A.Rs. 312 croresB.Rs. 297 crores

C.Rs. 283 croresD.Rs. 275 crores

Q13.If the expenditures of Company X and Y in 1996 were equal and the total income of the two Companies in 1996 was Rs. 342 crores, what was the total profit of the two Companies together in 1996 ? (Profit = Income - Expenditure)

A.Rs. 240 croresB.Rs. 171 crores

C.Rs. 120 croresD.Rs. 102 crores

Q14.The expenditure of Company X in the year 1998 was Rs. 200 crores and the income of company X in 1998 was the same as its expenditure in 2001. The income of Company X in 2001 was ?

A.Rs. 465 croresB.Rs. 385 crores

C.Rs. 335 croresD.Rs. 295 crores

Q15.If the incomes of two Comapanies were equal in 1999, then what was the ratio of expenditure of Company X to that of Company Y in 1999 ?

A.6:5B.5:6

C.11:6D.16:15

Study the following line graph and answer the questions 16-20The following line graph gives the percentage of the number of candidates who qualified an examination out of the total number of candidates who appeared for the examination over a period of seven years from 1994 to 2000.Percentage of Candidates Qualified to Appeared in an Examination Over the Years

Q16.The difference between the percentage of candidates qualified to appeared was maximum in which of the following pairs of years?

A.1994 and 1995B.1997 and 1998

C.1998 and 1999D.1999 and 2000

Q17.In which pair of years was the number of candidates qualified, the same?

A.1995 and 1997B.1995 and 2000

C.1998 and 1999D.Data inadequate

Q18.If the number of candidates qualified in 1998 was 21200, what was the number of candidates appeared in 1998?

A.32000B.28500

C.26500D.25000

Q19.If the total number of candidates appeared in 1996 and 1997 together was 47400, then the total number of candidates qualified in these two years together was?

A.34700B.32100

C.31500D.Data inadequate

Q20.The total number of candidates qualified in 1999 and 2000 together was 33500 and the number of candidates appeared in 1999 was 26500. What was the number of candidates in 2000?

A.24500B.22000

C.20500D.19000

Answer the questions based on the given line graph. Study the following line graph and answer the questions 21-25Ratio of Exports to Imports (in terms of money in Rs. crores) of Two Companies Over the Years

Q21In how many of the given years were the exports more than the imports for Company A?

A.2B.3

C.4D.5

Q22.If the imports of Company A in 1997 were increased by 40 percent, what would be the ratio of exports to the increased imports?

A.1.20B.1.25

C.1.30D.cannot be determined

Q23.If the exports of Company A in 1998 were Rs. 237 crores, what was the amount of imports in that year?

A.Rs. 189.6 croresB.Rs. 243 crores

C.Rs. 281 croresD.Rs. 316 crores

Q24.In 1995, the export of Company A was double that of Company B. If the imports of Company A during the year was Rs. 180 crores, what was the approximate amount of imports pf Company B during that year?

A.Rs. 190 croresB.Rs. 210 crores

C.Rs. 225 croresD.Cannot be determined

Q25.In which year(s) was the difference between impors and exports of Company B the maximum?

A.2000B.1996

C.1998 and 2000D.Cannot be determined

Que Two different finance companies declare fixed annual rate of interest on the amounts invested with them by investors. The rate of interest offered by these companies may differ from year to year depending on the variation in the economy of the country and the banks rate of interest. The annual rate of interest offered by the two Companies P and Q over the years are shown by the line graph provided below.Study the following line graph and answer the questions 26-30Annual Rate of Interest Offered by Two Finance Companies Over the Years.

Q26.A sum of Rs. 4.75 lakhs was invested in Company Q in 1999 for one year. How much more interest would have been earned if the sum was invested in Company P?

A.Rs. 19,000B.Rs. 14,250

C.Rs. 11,750D.Rs. 9500

Q27.If two different amounts in the ratio 8:9 are invested in Companies P and Q respectively in 2002, then the amounts received after one year as interests from Companies P and Q are respectively in the ratio?

A.2:3B.3:4

C.6:7D.4:3

Q28.In 2000, a part of Rs. 30 lakhs was invested in Company P and the rest was invested in Company Q for one year. The total interest received was Rs. 2.43 lakhs. What was the amount invested in Company P?

A.Rs. 9 lakhsB.Rs. 11 lakhs

C.Rs. 12 lakhsD.Rs. 18 lakhs

Q29.An investor invested a sum of Rs. 12 lakhs in Company P in 1998. The total amount received after one year was re-invested in the same Company for one more year. The total appreciation received by the investor on his investment was?

A.Rs. 2,96,200B.Rs. 2,42,200

C.Rs. 2,25,600D.Rs. 2,16,000

Q30.An investor invested Rs. 5 lakhs in Company Q in 1996. After one year, the entire amount along with the interest was transferred as investment to Company P in 1997 for one year. What amount will be received from Company P, by the investor?

A.Rs. 5,94,550B.Rs. 5,80,425

C.Rs. 5,77,800D.Rs. 5,77,500

Study the following line graph and answer the questions 31-35In a school the periodical examination are held every second month. In a session during April 2001 - March 2002, a student of Class IX appeared for each of the periodical exams. The aggregate marks obtained by him in each perodical exam are represented in the line-graph given below.Marks Obtained by student in Six Periodical Held in Every Two Months During the Year in the Session 2001 - 2002.Maximum Total Marks in each Periodical Exam = 500

Q31In which periodical exams did the student obtain the highest percentage increase in marks over the previous periodical exams ?

A.June, 01B.August, 01

C.Oct, 01D.Dec, 01

Q32.The total number of marks obtained in Feb. 02 is what percent of the total marks obtained in April 01 ?

A.110%B.112.5%

C.115%D.116.5%

Q33.What is the percentage of marks obtained by the student in the periodical exams of August, 01 and Oct, 01 taken together ?

A.73.25%B.75.5%

C.77%D.78.75%

Q34.What are the average marks obtained by the student in all the periodical exams during the last session ?

A.373B.379

C.381D.385

Q35.In which periodical exams there is a fall in percentage of marks as compared to the previous periodical exams ?

A.NoneB.June, 01

C.Oct, 01D.Feb, 02

ANSWER1. D2. C3. D4. B5. D6. D7. C8. A9. D10. B11. C12. B13. D14. A15. D16. B17. D18. C19. D20. C21. B22. B23. D24. B25. D26. D27. D28. D29. C30. B31. C32. B33. B34. C35. A

DATA SUFFICIENCYImportant facts to keep in mind while dealing with D.S1) DS problems, we need to answer if it is sufficient information to answer, means, there should be one conclusive answer. We do not need to find the answer, just if it can be found or not?2) Some questions ask , is this true? So if we can find that the information available is enough to prove that it is not, we are still able to answer the question, that it is not true. Hence we are able to answer the question.3) Check for all possibilties, that is using one statement, using second, then only combine the two.

Have a glance at this pattern

In each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements andGive answer (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question (D) If the data given in both statements I and II together are not sufficient to answer the question and (E) If the data in both statements I and II together are necessary to answer the question.

1.Question: In which year was Rahul born ?Statements:1. Rahul at present is 25 years younger to his mother.2. Rahul's brother, who was born in 1964, is 35 years younger to his mother.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

2.Question: What will be the total weight of 10 poles, each of the same weight ?Statements:1. One-fourth of the weight of each pole is 5 kg.2. The total weight of three poles is 20 kilograms more than the total weight of two poles.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

3.Question: How many children does M have ?Statements:1. H is the only daughter of X who is wife of M.2. K and J are brothers of M.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

4.Question: How much was the total sale of the company ?Statements:1. The company sold 8000 units of product A each costing Rs. 25.2. This company has no other product line.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

5.Question: The last Sunday of March, 2006 fell on which date ?Statements:1. The first Sunday of that month fell on 5th.2. The last day of that month was Friday.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

6.Question: What is the code for 'sky' in the code language ?Statements:1. In the code language, 'sky is clear' is written as 'de ra fa'.2. In the same code language, 'make it clear' is written as 'de ga jo'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

7.Question: How many children are there between P and Q in a row of children ?Statements:1. P is fifteenth from the left in the row.2. Q is exactly in the middle and there are ten children towards his right.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

8.Question: How is T related to K?Statements:1. R's sister J has married Ts brother L, who is the only son of his parents.2. K is the only daughter of L and J.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

9.Questin: How is J related to P ?Statements:1. M is brother of P and T is sister of P.2. P's mother is married to J's husband who has one son and two daughters.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

10.Question: How is X related to Y ?Statements:1. Y and Z are children of D who is wife of X.2. R's sister X is married to Ys father.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

11.Question: Who is to the immediate right of P among five persons P, Q, R, S and T facing North ?Statements:1. R is third to the left of Q and P is second to the right of R.2. Q is to the immediate left of T who is second to the right of P.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

12.Question: On which date of the month was Anjali born in February 2004 ?Statements:1. Anjali was born on an even date of the month.2. Anjali's birth date was a prime number.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

13.Question: How is X related to Y?Statements:1. Y says, "I have only one brother".2. X says, "I have only one sister".

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

14.Question: How is F related to P?Statements:1. P has two sisters M and N.2. F's mother is sister of M's father.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

15.Question: B is the brother of A. How is A related to B ?Statements:1. A is the sister of C.2. E is the husband of A.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

16.Question: How many children are there in the row of children facing North ?Statements:1. Vishakha who is fifth from the left end is eighth to the left of Ashish who is twelfth from the right end.2. Rohit is fifth to the left of Nisha who is seventh from the right end and eighteenth from the left end.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

17.Question: How many doctors are practising in this town ?Statements:1. There is one doctor per seven hundred residents.2. There are 16 wards with each ward having as many doctors as the number of wards.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

18.Question: On which day of the week was birthday of Sahil ?Statements:1. Sahil celebrated his birthday the very next day on which Arun celebrated his birthday.2. The sister of Sahil was born on the third day of the week and two days after Sahil was born.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

19.Question: How many pages of book X did Robert read on Sunday ?Statements:1. The book has 300 pages out of which two-thirds were read by him before Sunday.2. Robert read the last 40 pages of the book on the morning of Monday.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

20.Question: How is Tanya related to the man in the photograph ?Statements:1. Man in the photograph is the only son of Tanya's grandfather.2. The man in the photograph has no brothers or sisters and his father is Tanya's grandfather.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

ANSWER1. E2. C3. D4. E5. C6. D7. E8. E9. B10. C11. C12. E13. D14. E15. C16. C17. B18. B19. E20. B

DATA SUFFICIENCYIn each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements andGive answer (A) If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question (B) If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question (C) If the data either in statement I alone or in statement II alone are sufficient to answer the question (D) If the data given in both statements I and II together are not sufficient to answer the question and (E) If the data in both statements I and II together are necessary to answer the question.1.Question: How is 'No' coded in the code language ?Statements:1. 'Ne Pa Sic Lo' means 'But No None And' and 'Pa Lo Le Ne' means 'If None And But'.2. 'Le Se Ne Sic' means 'If No None Will' and 'Le Pi Se Be' means 'Not None If All'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

2.Question: Who among P, Q, T, V and M is exactly in the middle when they are arranged in ascending order of their heights ?Statements:1. V is taller than Q but shorter than M.2. T is taller than Q and M but shorter than P.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

3.Question: Which code word stands for 'good' in the coded sentence 'sin co bye' which means 'He is good' ?Statements:1. In the same code language, 'co mot det' means 'They are good'.2. In the same code language, 'sin mic bye' means 'He is honest'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

4.Question: What is the numerical code for 'water' in a certain code ?Statements:1. The code for 'give me water' is '719'.2. The code for 'you can bring water for me' is written as '574186'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

5.Question: How many visitors saw the exhibition yesterday ?Statements:1. Each entry pass holder can take up to three persons with him/her.2. In all, 243 passes were sold yesterday.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

6.Question: Gaurav ranks eighteenth from the top in a class. What is his rank from the last?Statements:1. There are 47 students in the class.2. Jatin who ranks 10th in the same class, ranks 38th from the last.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

7.Question: What is the rank of P from the bottom in a class of 30 students ?Statements:1. M is third from the top and there are five students between M and P.2. The rank of K is fourth from the bottom and there are 17 students between K and P.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

8.Question: In a row of five buildings - P, Q, R, S and T, which building is in the middle ?Statements:1. Buildings S and Q are at the two extreme ends of the row.2. Building ,T is to the right of building R.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

9.Question: How many speeches were delivered in the two days' programme ?Statements:1. 18 speakers were invited to give at least one speech (maximum of two speech), out of which one-sixth of the speakers could not come.2. One-third of the speakers gave two speeches each.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

10.Question: Among five friends, who is the tallest ?Statements:1. D is taller than A and C.2. B is shorter than E but taller than D.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

11.Question: What time did the train leave today ?Statements:1. The train normally leaves on time.2. The scheduled departure is at 14 : 30.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

12.Question: What does '$' mean in a code language?Statements:1. '5$#3' means 'flowers are really good'.2. '7#35' means 'good flowers are available'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

13.Question: How many sons does D have ?Statements:1. A's father has three children.2. B is A's brother and son of D.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

14.Question: How is M related to N?Statements:1. P, who has only two kids, M and N, is the mother-in-law of Q, who is sister-in-law of N.2. R, the sister-in-law of M, is the daughter-in-law of S, who has only two kids, M and N.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

15.Question: What is the colour of the fresh grass ?Statements:1. Blue is called green, red is called orange, orange is called yellow.2. Yellow is called white, white is called black, green is called brown and brown is called purple.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

16.Question: Which train did Aman catch to go to office ?Statements:1. Aman missed his usual train of 10.25 a.m. A train comes in every 5 minutes.2. Aman did not catch the 10.40 a.m. train or any train after that time.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

17.Question: On which day of the week did Hitesh visit the zoo ?Statements:1. Hitesh did not visit zoo either on Tuesday or on Thursday.2. Hitesh visited zoo two days before his mother reached his house which was day after Monday.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

18.Question: The Chairman of a big company visits one department on Monday of every week except for the Monday of third week of every month. When did he visa/the Purchase department ?Statements:1. He visited Accounts department in the second week of September after having visited Purchase department on the earlier occasion.2. He had visited Purchase department immediately after visiting Stores department but before visiting Accounts department.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

19.Question: What does 'nip' stand for in a code language ?Statements:1. In the code language, 'that is very beautiful' is written as 'se nip sre num'2. In the same code language, 'my house is beautiful' is written as 'nip sto sre tip'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

20.Question: What is the monthly salary of Prashant ?Statements:1. Prashant gets 15% more than Sumit while Sumit gets 10% less than Lokesh.2. Lokesh's monthly salary is Rs 2500.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

ANSWER KEY1. A2. E3. C4. D5. D6. C7. C8. D9. E10. E11. D12. E13. D14. A15. B16. D17. B18. A19. D20. E DATA SUFFICIENCY In each of the following problems, there is one question and three statements I, II and III given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find which of the statements is/are sufficient to answer the given question. Choose the correct alternative in each question.1.Question: What is Suman's rank from the top in a class of forty students ?Statements:1. Suman is 3 ranks below Deepak from the top.2. Deepak's rank from the bottom is 23.3. Suman is 3 ranks above Deepak from the bottom.

A.Any two of the three

B.Only I and II

C.Only II and III

D.All I, II and III

E.Only II and either I or III

2.Question: Five persons - A, B, C, D and E are sitting in a row. Who is sitting in the middle?Statements:1. B is between E and C.2. B is to the right of E.3. D is between A and E.

A.Only I and II

B.Only II and III

C.Only I and III

D.All I, II and III

E.None of these

3.Question: How is 'DATE' written in the code language ?Statements:1. DEAR is written as $#@? in that code.2. TREAT is written as %?#@% in that code.3. TEAR is written as %#@? in that code,

A.Only I and II

B.Only II and III

C.All I, II and III

D.Only I and either II or III

E.None of these

4.Question: In which year was Sanjay born ?Statements:1. Sanjay is six years older than Gopal.2. Gopal's brother was born in 1982.3. Sanjay's brother is two years younger than Gopal's brother who was eight year4. younger than Gopal.

A.Only I and II

B.Only II and III

C.Only I and III

D.All I, II and III

E.None of these

5.Question: Who among Siddhartha, Nikunj, Vipul and Mukul is the youngest?Statements:1. Vipul is younger than Mukul but older than Siddhartha and Nikunj.2. Mukul is the oldest.3. Siddhartha is older than Nikunj.

A.Only I

B.Only I and II

C.Only II and III

D.Only I and III

E.None of these

6.Question: In a certain code, 'XYZ' means 'We are friends'. Which letter stands for 'We' ?Statements:1. 'PYN' means 'They are classmates'.2. 'ZMS' means 'We love them'.3. 'PX' means 'Hello friends',

A.Only II

B.Only I and III

C.All I, II and III

D.Either I only or II only

E.None of these

7.Question: Among P, Q, R, S and T, Q is the second tallest and S is immediate taller than the shortest. Who among them is in the middle when they stand in the order of their heights ?Statements:1. T is not the shortest.2. R is taller than S but shorter than Q.3. P ranks third in height above S when all are arranged in the order of height.

A.Only I and II

B.Either II only or I and III only

C.Only II

D.Only II and III

E.None of these

8.Question: Four subjects - Physics, Chemistry, Mathematics and Biology - were taught in four consecutive periods of one hour each starting from 8.00 a.m. At what time was the Chemistry period scheduled?Statements:1. Mathematics period ended at 10.00 a.m., which was preceded by Biology.2. Physics was scheduled in the last period.3. Mathematics period was immediately followed by Chemistry.

A.Only I

B.Either I only or II only

C.Only II

D.Only II and III

E.Only I and either II or III

9.Question: What is the total monthly salary of Vasu ?Statements:1. Vasu's basic salary is Rs 100 more than Rajan's salary who also serves in Vasu's company.2. Other allowances drawn by Rajan besides his basic salary are Rs 2000 per month which is Rs 50 less than Vasu's salary.3. Rajan's basic salary is Rs 1550 per month,

A.Only II

B.Only II and III

C.Only I and II

D.Only I and III

E.All I, II and III

10.Question: Who is the tallest among six boys P, T, N, D, Q and R ?Statements:1. P is taller than D and N but not-as tall as T.2. R is taller than Q but not as tall as T.3. Q is not taller than T and R.

A.Only I and II

B.Only II and III

C.Only I and III

D.All I, II and III

E.Only I and either II or III

11.Question: What does 'come' represent in a code language?Statements:1. 'pit na tac' means 'come and go' in that code language.2. 'ja ta da' means 'you are good' in that code language.3. 'na da rac' means 'you can come' in that code language.

A.Only I and II

B.Only II and III

C.Only I and III

D.All I, II and III

E.None of these

12.Question: How is the girl in the photograph related to Kunal?Statements:1. Pointing to the photograph, Kunal said, "She is the mother of my father's only granddaughter".2. Kunal has no siblings.3. Pointing to the photograph, Kunal said, "She is the only daughter-in-law of my mother."

A.Any two of the three

B.Only I and II

C.Only II and III

D.Either only III or only I and II

E.None of these

13.Question: How many sons does X have?Statements:1. Q and U are brothers of T.2. R is sister of P and U.3. R and T are daughters of X.

A.Only I and II

B.Only II and III

C.All I, II and HI

D.I, II and III together are not sufficient

E.None of these

14.Question: What is Gagan's age ?Statements:1. Gagan, Vimal and Kunal are all of the same age.2. Total age of Vimal, Kunal and Anil is 32 years and Anil is as old as Vimal and Kunal together.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

15.Question: In a certain code, '13' means 'stop smoking' and '59' means 'injurious habit'. What do '9' and '5' mean respectively in that code ?Statements:1. '157' means 'stop bad habit'.2. '839' means 'smoking is injurious'.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

16.Question: How much money do Vivek and Suman have together ?Statements:1. Suman has 20 rupees less than what Tarun has.2. Vivek has 30 rupees more than what Tarun has.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

17.Question: Among Monika, Anita, Sonal, Ratna and Tanvy, who came last for the programme ?Statements:1. Monika came after Anita but not after Tanvy.2. Ratna came after Tanvy but not after Sonal.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

18.Question: Who among P, Q, R, S and T is the lightest?Statements:1. R is heavier than Q and T but lighter than S.2. S is not the heaviest.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

19.Question: Manoj, Prabhakar, Akash and Kamal are four friends. Who among them is the heaviest ?Statements:1. Prabhakar is heavier than Manoj and Kamal but lighter than Akash.2. Manoj is lighter than Prabhakar and Akash but heavier than Kamal.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

20.Question: Vinod's and Javed's salaries are in the proportion of 4 : 3 respectively. What is Vinod's salary ?Statements:1. Javed's salary is 75% that of Vinod's salary.2. Javed's salary is Rs 4500.

A.I alone is sufficient while II alone is not sufficient

B.II alone is sufficient while I alone is not sufficient

C.Either I or II is sufficient

D.Neither I nor II is sufficient

E.Both I and II are sufficient

ANSWER

1. E2. D3. D4. D5. D6. E7. B8. E9. E10. A11. C12. D13. D14. E15. C16. D17. E18. D19. A20. B

43