Q A UANTITATIVE PTITUDE Data Interpretation Data Interpretation is one of the easy putting them to use directly with com- sections of one day competitive Examinations. mon sense. It is an extension of Mathematical skill and 4. Breakdown lengthy questions into smaller accuracy. Data interpretation is nothing but parts and eliminate impossible choices. drawing conclusions and inferences from a 5. Use only the information given and your comprehensive data presented numerically in knowledge of everyday facts, such as the tabular form by means of an illustration, viz. number of hours in a day, to answer Graphs, Pie Chart etc. Thus the act of the questions based on tables and organising and interpreting data to get mean- graphs. ingful information is Data Interpretation. 6. Answer the questions asked and not what A good grasp of basic geometric as well you think the questions should be. as arithmetic formulae is must to score high 7. Be careful while dealing with units. in this section. Familiarity with graphical rep- resentation of data like Venn diagrams, graphs, 8. To make reading easier and to avoid er- pie charts, histogram, polygon etc. should be rors observe graphs keeping them thought. Once the data are grasped well, ques- straight. tions based on tables and graphs take little 9. Be prepared to apply basic mathematical time. rules, principles and formulae. In some competitive examinations data 10. Since one of the major benefits of graphs are presented in more than one table or graphs. and tables is that they present data in a The aim is to test not only quantitative skill form that enables you to readily make but also relative, comparative and analytical comparisons, use this visual attribute of ability. The crux of the matter is to find a rela- graphs and tables to help you answer the tionship between the two tables or graphs questions. Where possible, use your eyes before attempting the questions. instead of your computational skills. Some Useful tips: Tables 1. Data Interpretation questions are based Tables are often used in reports, maga- on information given in tables and graphs. zines and newspaper to present a set of These questions test your ability to inter- numerical facts. They enable the reader pret the information presented and to to make comparisons and to draw quick select the appropriate data for answer- conclusions. It is one of the easiest and ing a question. most accurate ways of presenting data. 2. Get a general picture of the information They require much closer reading than before reading the question. Read the graphs of charts and hence are difficult given titles carefully and try to under- and time consuming to interpret. stand its nature. One of the main purposes of tables is to 3. Avoid lengthy calculations generally, data make complicated information easier to interpretation questions do not require to understand. The advantage of presenting do extensive calculations and computa- data in a table is that one can see the tions. Most questions simply require read- information at a glance. ing the data correctly and carefully and While answering questions based on Q A UANTITATIVE PTITUDE tables, carefully read the table title and Solved Examples the column headings. The title of the table I. Directions (Qs. 1-5) study the following gives you a general idea of the type and table and answer the questions given often the purpose of the information pre- below it. sented. The column headings tell you the specific kind of information given in that Production of sugar by six major production column. Both the table title and the col- units of India in Million Tonnes umn headings are usually very straight PRODUCTION UNITS forward. Month A B C D E F Graphs April 310 180 169 137 140 120 There may be four types of graphs. May 318 179 177 162 140 122 1) Circle Graphs: Circle graphs are used to June 320 160 188 173 135 130 show how various sectors are in the whole. Circle graphs are sometimes July 326 167 187 180 146 130 called Pie Charts. Circle graphs usually August 327 150 185 178 145 128 give the percent that each sector receives In such representation the total quantity 1. In which month the unit B has a contribu- in question is distributed over a total tion of approximately 15% in the total sugar angle of 360°. production? While using circle graphs to find ratios a) August b) June of various sectors, don't find the c) July d) April amounts each sector received and then 2. Which of the following units shows con- the ratio of the amounts. Find the ratio tinuous increase in production of sugar over of the percents, which is much quicker. months? 2) Line Graphs: Line graphs are used to a) A b) B show how a quantity changes continu- ously. If the line goes up, the quantity is c) C d) D increasing; if the line goes down, the quan- 3. In the case of Unit E, in which of the fol- tity is decreasing; if the line is horizon- lowing pairs of months the production of sugar tal, the quantity is not changing. was equal? 3) Bar Graphs: Given quantities can be com- a) April & June b) June & July pared by the height or length of a bar c) July & August d) April & May graph. A bar graph can have either ver- tical or horizontal bars. You can compare 4. In the month of June, how many units different quantities or the same quantity have a share of more than 25% of the total at different times. In bar graph the data production of sugar? is discrete. Presentation of data in this a) one b) Three form makes evaluation of parameters c) Two d) Four comparatively very easy. 5. What was approximate percentage de- 4) Cumulative Graphs : You can compare crease in sugar production of unit B in June as several catagories by a graph of the compared to April? cumulative type. These are usually bar or line graphs where the height of the a) 8% b) 10% bar or line is divided up proportionally c) 15% d) 18% among different quantities. Q A UANTITATIVE PTITUDE Ans: 180160 20 =   100 x 100 1. (c) Total production in April  180  180 = 310+180+169+137+140+120=1056 = 11.11%  10% 15 II. Directions (Qs. 6-10): Study the following 15% of 1056 = x1056158.4 100 graph carefully and answer the questions given below it: Total Production in June 1200_______________________________A___ = 320+160+188+173+135+130 1150_______________________________B___ = 1106 1100__________________________________ 15 15% 1106 = 100 x1106165.9 RS1050__________________________________ N Total production in July E I1000__________________________________ C RI950 __________________________________ = 326+167+187+146+130=1136 P 900 __________________________________ 15 15% of 1136 = 100 x1136170.4 850 __________________________________ Total Production in August 800 __________________________________ = 327+150+185+178+145+128= 1113 Jan Feb Mar Apr May June July Aug MONTHS 15 15% of 1113 = x1113166.95167 6) What was the price difference between 100 commodity A and B in the month of April? ie, in Month July, the Unit B has a contri- a) 250 b) 150 bution of approximately 15% in the total sugar c) 100 d) 90 production. 7. What was the difference in average price 2. a) Unit A shows continuous increase in between commodity A and B from April to production of sugar over months. August? 3. d) In Unit E, the pair of months that a) 86 b) 75 shows equal sugar production is April and May. a) 95 d) 85 4. a) Total Production in June = 8. In which of the following pairs of months 320+160+188+173+135+130 = 1106 was the price of commodity A same? a) January - March b) May-June 25 25% of 1106= x1106276.5 units c) April- August d) July-August 100 9. What was the approximate percentage ie, Unit A shows more than 25% of the decrease in the price of commodity A from total production of sugar in the month June. March to April? 5. 6) In unit B, the production in June = a) 1 b) 9 c) 14 d) 12 160 the production in April = 180 units 10. What was the percentage increase in Decrease in percentage price of commodity B from January to April? a) 15 b) 20 d) 17 d) 10 Q A UANTITATIVE PTITUDE III Directions (11-15): Study the following Ans 6 (b).The price of commodity A in April graph carefully and answer the questions given = 1000 below it. The price of commodity B in April PRODUCTION OF FOODGRAIN OVER THE = 1150 YEARS (1000 TONNES) Difference = 1150 - 1000 = 150 130 7) (b). Average price of commodity A from 120 110 April to August 100 1000 1050 975 900 1000 80 = 65 5 4925 = 985 5 1993 1994 1995 1996 1997 1998 Average price of commodity B from 11) In the case of how many years was the April to August production below the average production of the given years? 1150110011001000950 = a) one b) two 5 c) three d) four 5300 = 1060 12) What was the percentage drop in produc- 5 tion from 1996 to 1997? Difference = 1060 - 985 = 75 a) 100 b) 50 8)(c)Price of commodity A in April = 1000 c) 65 d) 40 Price of commodity A in August = 1000 13) In which year was the production 50%of Therefore, in April - August the price of the total production in 1993 and 1998 together commodity A was same. a) 1994 b) 1995 9)(d)Price of commodity A in March = 1125 c) 1996 d) 1997 Price of commodity A in April = 1000 14. If the production in 1999 will be above the average production of the given years, Decrease which of the following could be the minimum production for 1999? 11251000 125 =   100 x100  1125  1125 a) 105000 b) 120000 = 11.11% 12% c) 100900 d) 130000 15. What was the approximate percentage 10)(a)Price of commodity B in January = 1000 increase in production from 1993 to 1994 Price of commodity B in April = 1150 a) 60 b) 40 11501000 Increase =   100 c) 110 d) 30  1000  150x100 = 15% 1000 Q A UANTITATIVE PTITUDE Ans:- IV. Directions (Qs. 16-20):- Study the follow- ing graph carefully and answer the questions 11.(c) Average production given below it: 80 110 100 130 65120 INCOME AND EXPENDITURE OF A = 6 COMPANY OVER THE YEARS (In lakhs Rupees) 605 = INCOME 6 EXPENDITURE = 100.833 thousand tonnes = 100900 tonnes 60 60 60 ie. production in 1993, 1995 and 1997 50 was below the average. 40 40 12.(b) Production in 1996 = 130 thousand s40 35 h tonnes. ak 30 30 30 L Production in 1997 = 65 thousand tonnes n 20 i s 20 130 65 e e  decrease=  100 p  130  u R 65 1994 1995 1996 1997 1998 = x100 = 50% 130 Years 13.(b). Total production in 1993 and 1998 16. What was the difference in profit between 1995 and 1996? = 80+120 = 200 a) Rs. 10 lakhs b) Rs. 5 lakhs 50 50% of 200 = x200100 c) Rs. 15 lakhs d) No profit 100 17. In the case of how many years was the ie, the production in 1995 was 50% of income more than the average income of the the total production in 1993 and 1998. given years? 14.(c).Average production = 100900 tonnes. a) one b) two Therefore the minimum production in c) three d) four 1999 will be 100900 tonnes 18. What was the percentage increase in 15.(b). Production in 1993 = 80 thousand tonnes. expenditure from 1996 to 1997? Production in 1994 = 110 thousand tonnes 1 a) 10 b) 33 Increase 3 2 110 80 30 c) 66 d) 20 =  100  x10040% 3  80  80 19. The income in 1996 was equal to the expenditure of which of the following years? a) 1994 b) 1995 c) 1997 d) 1998 Q A UANTITATIVE PTITUDE 20. In which of the following years was the a) Rs. 2500000 b) Rs. 3750000 profit the maximum? c) Rs. 5000000 d) Rs. 6000000 a) 1994 b) 1995 22. Out of the following, the country spent c) 1996 d) 1998 the same amount on Ans:- a) Hockey and Tennis 16.(a).Profit in 1995 = 50-30=Rs. 20 lakhs b) Golf and foot ball Profit in 1996 = 40-30 = Rs. 10 lakhs c) Cricket and Foot ball Difference in profit=20-10=Rs. 10 lakhs d) Football and Hockey 17.(c) Average income 23. Pie-chart shows that the most popular 30 50 40 60 60 240 game of the country is (on the basis of money = = 48 5 5 spent) Therefore in 1995, 1997 and 1998, the a) Cricket b) Foot ball income is more than the average income c) Basket ball d) Hockey 18.(b) Expenditure in 1996 = Rs. 30 lakh 24. The ratio of the total amount spent on Expenditure in 1997 = Rs. 40 lakh football to that spent on hockey is Increase a) 1:15 b) 1:1 40 30 10 1 c) 15:1 d) 3:20 =  100 x10033 %  30  30 3 25. If the total amount spent on sports dur- ing the year was Rs. 12000000, how much 19.(c) The income in 1996 was equal to the was spent on basket ball? expenditure in 1997 ie Rs. 40 lakhs. a) Rs. 950000 b) Rs. 1000000 20.(d) The profit is maximum in the year 1998. c) Rs. 1200000 d) Rs. 1500000 V. Directions (Qs. 21-25) The pie-chart Ans:- drawn below shows the spendings of a coun- 21.(d) The amount spent on Cricket and try on various sports during a particular year. Hockey Study the pie-chart carefully and answer the questions given below it. 15000000x40 = Rs.6000000 PERCENT OF MONEY SPENT ON VARIOUS 100 SPORTS FOR ONE YEAR 22.(d) The country spent the same amount on football and hockey Tennis Golf 10% 12.5% 23.(a) The most popular game is cricket Others 24.(b) The required ratio = 15:15 = 1:1 10% Basket ball 12.5% 25.(d) The amount spent on basket ball Cricket Foot Ball 25% 15% 12000000x12.5 Hockey = 15% 100 = Rs. 1500000 21. If the total amount spent on sports during the year was Rs. 15000000, the amount spent on cricket and hockey together was Q A UANTITATIVE PTITUDE PRACTICE TEST Directions (Qs. 6-10) : Study the following table Directions (Qs. 1-5) The table below gives the carefully and answer the questions given production capacity (in thousands units) and below it. the percent utilisation in respect of three prod- NUMBER OF STUDENTS WHO GO ABROAD ucts (A,B and C) over five years for an FOR STUDY organisation. Study the table carefully and answer the questions that follow. State/U.T. Year 1990 1991 1992 1993 1994 Product Total Maharashtra 732 840 900 920 925 Year A B C Capacity Capacity Utilisation Capacity Utilisation Capacity Utilisation(A+B+C) Kerala 1035 940 1200 1400 1500 1993 170 70% 28 75% 240 40% 438 Karnataka 750 600 830 575 900 1994 200 63% 35 60% 260 40% 495 West Bengal 500 550 450 600 525 1995 200 65% 30 80% 270 40% 500 Delhi 1500 1625 1700 1475 1800 1996 210 60% 40 50% 260 45% 510 Andhra pradesh 800 840 875 925 785 1997 225 60% 40 55% 260 50% 525 Total 5308 5395 5955 5895 6434 6. From which State/U.T, did the least num- 1. Approximately, what was the overall ber of students go abroad over the years among utilisation for all products taken together for the given States / U.T.s? the year 1993? a) Karnataka a) 50% b) 55% b) Kerala c) 60% d) 65% c) West Bengal d) Maharashtra 2. What is the approximate overall growth rate in respect of total capacity for the period 7. What was the percent increase in num- shown? ber of students from West Bengal from 1992 to 1993? a) 5% b) 10% 1 c) 15% d) 20% a) 25 b) 33 3 3. In which of the following years was the production of product A the maximum for all 2 c) 50 d) 66 period shown? 3 a) 1993 b) 1997 8. In the case of which State/ U.T. was c) 1996 d) 1994 there an increase and decrease respectively in the number of students in alternate years? 4. What is the average production of prod- a) Andhra Pradesh uct B over the period shown? b) Delhi a) 21,600 b) 24,200 c) Karnataka c) 34,600 d) 28,800 d) West Bengal 5. In which of the following years was the 9. In the case of which State/U.T. was there production of product C the minimum for the a continuous increase in the number of stu- period shown? dents over the given years? a) 1997 b) 1994 a) Delhi c) 1993 d) 1996 b) Maharashtra c) Andhra Pradesh d) Karnataka Q A UANTITATIVE PTITUDE 10. In which year did Kerala contribute ap- a) 1990 b) 1991 proximately one-fifth of the total number of c) 1992 d) 1993 students in that year? Direction (Qs. 11-15): Study the following table carefully and answer the questions given below it. NUMBER OF CANDIDATES APPEARED AND QUALIFIED UNDER VARIOUS DISCIPLINES IN AN EXAMINATION OVER THE YEARS ARTS SCIENCE COMMERCE AGRICULTURE ENGGINEERING TOTAL YEAR App. Qual. App. Qual. App. Qual. App. Qual. App. Qual. App. Qual. 1992 850 200 1614 402 750 212 614 170 801 270 4629 1254 1993 1214 315 1826 420 800 220 580 150 934 350 5354 1455 1994 975 250 1970 500 860 260 624 160 742 300 5171 1470 1995 820 196 1560 450 842 300 490 160 850 312 4562 1418 1996 1412 378 2120 625 1105 320 760 200 642 301 6039 1824 1997 738 359 3506 880 1240 308 640 210 962 400 7086 2157 11. In which of the following disciplines was percentage of qualified to the appeared ones there a continuous increase in the number of in engineering discipline the maximum? candidates appeared over the given years? a) 1994 b) 1995 a) Agriculture b) Arts c) 1997 d) 1996 c) Science d) None Direction (16-20) : Study the following graph care- 12. What was the percentage drop in num- fully and answer the questions given below: ber of candidates qualified in Science discipline from 1994 to 1995? Production of three types of vehicles by a company over the years (in thousand) a) 10 b) 20 c) 25 d) 50 Type A Type B Type C 13. The number of candidates appeared un- 40__________________________________ der Agriculture in 1995 was approximately what percentage of number of candidates quali- 35__________________________________ fied under Arts in 1994? S E 30__________________________________ L a) 400 b) 200 C c) 100 d) 20 EHI 25__________________________________ V 14. In which of the following years was the OF 20__________________________________ percentage of total number of candidates of R all the disciplines together qualified to the ap- BE 15__________________________________ M peared ones, the maximum? NU 10__________________________________ a) 1993 b) 1994 5 __________________________________ c) 1995 d) 1996 0 __________________________________ 15. In which of the following years was the 1984 '85 '86 '87 '88 '89 '90 Q A UANTITATIVE PTITUDE 16. What was the percentage increase in the 21. In which of the following years was the production of C type vehicles from 1985 to difference between the income and the ex- 1986? penditure the maximum? a) 10 b) 5 a) 1988 b) 1991 c) 20 d) None of these c) 1986 d) 1987 17. The number of A type vehicles produced 22. The income in 1987 was equal to the in 1986 was what percent of the number of C type vehicles produced in 1988? expenditure in which of the following years? 1 2 a) 33 b) 66 a) 1985 only b) 1990 only 3 3 c) 50 d) 15 c) 1985, 1989 and 1991 d) 1988 and 1989 18. In how many years was the production of A type vehicles less than its average pro- 23. What was the approximate percentage duction over the given years? drop in expenditure from 1988 to 1989? a) 2 b) 4 a) 35 b) 25 c) 75 d) 40 c) 3 d) 1 24. What was the percentage increase in in- 19. What was average number of B type ve- come from 1987 to 1988? hicles produced by the company over the a) 175 b) 75 c) 60 d) 125 years? a) 20,000 b) 25,000 25. In how many of the given years was the expenditure more than the income? c) 15,000 d) 30,000 20. In which of the following years was the a) 1 b) 3 c) 4 d) 2 total production of all the three types of ve- Directions (26-30) hicles 60,000? The pie chart given below shows the expen- a) 1985 b) 1986 diture incurred in bringing out a book, by a c) 1987 d) 1988 publisher. Directions (Qs. 21 - 25) : Study the following graph carefully and answer the questions Printing given below it. 36% Income and Expenditure of a Company over Binding the years (Rs. in crore) 12% Paper 16% INCOME Canvassing 5405 EXPENDITURE 18% RoyalMtiyscellan8eou%s 10% 40 35 Study the graph and answer the questions given below: 30 26 What is the central angle showing the 25 cost of paper? 20 a) 16° b) 32° c) 28.8°d) 57.6° 15 27. If the cost of printing is Rs. 23400, the 10 royalty is: 5 a) Rs. 6500 b) Rs. 2340 1985 '86 '87 '88 '89 '90 '91 c) Rs. 4680 d) Rs. 7840 0 YEAR Q A UANTITATIVE PTITUDE 28. If miscellaneous expenditures amount to teins in bones? Rs. 18000, the expenditure on canvassing will a) 1:2 b) 2:1 c) 18:1 d) 1:18 be: 32. What percent to the total weight of the a) Rs. 8000 b) Rs. 14400 human body is equivalent of the weight of the c) Rs. 46800 d) Rs. 40500 skin in the human body? 29. Royalty on the book is less than canvass- a) 0.016 b) 1.6 c) 0.16 ing expenditure by: d) Insufficient information a) 8% b) 80% 33. To show the distribution of proteins and other dry elements in the human body, the arc 4 c) 44 % d) None of the circle should subtend at the centre an 9 angle of 30. If 5500 copies are published and miscel- a) 126° b) 54° c) 108° d) 252° laneous expenditures amount to Rs. 36960 and the marked price is 40% above cost price, then 34. What will be the quantity of water in the the marked price of each copy is: body of a person weighing 50 kg? a) Rs. 122.50 b) Rs. 117.60 a) 35 kg b) 120 kg c) Rs. 126.40 d) Rs. 92.40 c) 71.42 kg d) 20 kg Directions (31-35) 35. What part of the human body is made of neither bones nor skin? Study the following graphs carefully and answer the questions that follow: 2 11 1 3 a) b) c) d) Distribution of proteins in human body. 5 15 40 80 Directions (36-40) Study the following graph carefully and answer the questions given be- 1/3 low muscle Skin India's Export of rice over the years (in lakh 1/10 Hormones 40 tonnes) bones enzymes and 1/6 other proteins 35 30 28 27 Graph - I 25 26 25 Distribution of Elements in the human body. 20 20 18 Protein 16% 15 15 Other dry ele- 10 ments 14% Water 70% 5 1991 1992 1993 1994 1995 1996 1997 Graph - II YEAR 36. What was the percentage increase in 31. What is the ratio of distribution of pro- export of rice from 1991 to 1992? teins in the muscles to the distribution of pro- a) 30 b) 20 c) 15 d) 25