Data Interpretation
Introduction
The Data Interpretation section of CAT 2018 Exam can be divided into two key areas.
1) Data Interpretation
This is the calculation intensive portion of the section. It consists of a myriad of graphs, charts and tables from which you will have to glean and analyze data. However, the question which often strikes Aspirants is Why you are tested in Data Interpretation? The key to cracking this area is to quickly identify the key pieces of data that you will require to work on the questions asked. It is not unknown for questionsetters of the CAT to try and bewilder students with a large amount of data, most of it unnecessary. As a rule, the more the data presented, the easier the questions that follow, so don’t lose heart if you see a table with 10 columns occupying one whole page. On the other hand, several seemingly innocuous questions may trip you up. Therefore, I would advise you to look at the questions first to get an idea of what data you need to be searching for in the graphs/charts/tables in the main question asked.
Another interesting feature of DI that you as a student can use to your advantage is that, usually, not all questions in a set are of equal difficulty. Specifically, most sets have a ‘counting’ type of question (How many companies have profits more than x%, how many people have incomes less than Rs. Y etc.). Most of these questions can be solved without calculation but by close inspection of the data presented. These I would categorize as ‘gift’ questions designed to test a student’s presence of mind, and should never be missed out on. There are other similarly easy questions in most sets, and you should practice identifying the level of difficulty of questions so you know immediately which ones to attempt and which to avoid. There is no rule that states that you need to attempt all questions in a set, so it is a perfectly valid strategy to attempt selected questions across your DI section, without perhaps completely attempting even a single set.
An unusual source of practice questions that I would recommend for DI is a GRE preparation textbook or software. These contain several graph and chart type questions, most of which are near CAT level. You can utilize these questions in the initial source of preparation to practice reading data off charts and tables, and then gradually move on to tougher questions from CAT preparation material. GRE software comes with the added advantage of an inbuilt timer that keeps you on your toes.
2) Data Sufficiency
This is the third portion of the section, and quite a few DS questions were asked in the last CAT paper. Data Sufficiency problems usually take the form of a logical puzzle, and are in the form of a question followed by two statements. You need to answer whether you can solve the problem using the statements individually, or using both, or whether you cannot solve the problem using the information provided. The key to answering such problems is to pretend like one statement does not exist, try solving the problem, and then pretend like the other statement does not exist and try solving the problem again. These problems are generally tricky, and I would recommend lots of practice and perhaps solving them near the end of your section, after you have solved the other problems.The DI/LR section is one of the higher scoring sections on the CAT, so you can look to it for help in improving your overall score as well, as long as you devote a good proportion of your time to it. Although recent CATs have had 45 question sets, be prepared for 12 question sets as well. DS questions have never appeared in sets. Important things to remember while attempting this section are that you need be quick in switching sets if you find a particular set tough, and you need to have presence of mind while solving DI/LR questions. Both of these things can be achieved with the help of practice.
Overview of the question types of the DI:
Observation based questions: These questions require simple and careful observation of the data. Interpretation and Calculation (IC) based questions: These questions require basic analysis and calculation with data. Explorative questions: These questions will pose a hypothetical scenario, and may expect you to use, observation, interpretation and calculation.
Prerequisites for the preparation of DI section
Improve your calculations
Improving your calculations is the first step to improve your Data Interpretation. You need to work on both accuracy and speed to improve this section. Speed can be increased by practicing regularly. Vedic mathematics can also help you to increase you speed. It is not necessary to follow Vedic mathematics if you are not comfortable with it.
To improve your speed try doing calculations in your mind rather than using pencil/pen. In the starting it would take some time to do calculations in mind, but slowly and gradually you will see a mark difference in your speed.
Solve different type of Graphs and Case lets
Solve different type of case lets instead of sticking to one type. Develop your skills to solve different case lets.Practice regularly
Data interpretation is not a subject to be learned instantly. It improves with practice. Interpretation of data is a process. Regular practice can do wonders in your speed as well as analyzing case lets.
Strategy while attempting DI section in CAT
Strategy for dealing with DI while attempting CAT should be very straight as well as flexible. Do not start solving any set immediately, but read all the sets first and then make a call on which set is more structured and has lesser variables in terms of conditions that can be put in a structured table or a format easily. Make a good choice across the sections and, having decided that, give all the time to that set only. There are going to be hurdles but that does not mean you leave the set and move on to another set, as you have already taken a decision and invested a lot of precious time in that set.
Hence you should make a sensible choice in picking up the right set and doing the right thing before investing any time in a particular set or just jumping from one set to another. Moving from set to set will exhaust you and kill your time. But then even if you spend eight minutes in working out the entire set and the set is very clear, you can solve it immediately. Don’t be in a hurry that every two minutes you have to mark a question. Spend time on selection of the right set.
Also Read  Ace the Data Interpretation Section of CAT
Selecting the right set
Familiarity: The difficulty level amongst sets can be gauged in order to select the easier one. For example, you have three sets. One question talks about four people playing four different games and a few conditions follow. You can still plan it in a tabular form. The second question talks about an entirely new card game. The moment we talk about a game, the advantage is to the exam setter — he can frame any rules he wants to. Pick up the one with which you have familiarity and try avoiding unseen situations.
Conditions: Very few conditions mean ambiguity and you have to work out lots of possibilities. On the other hand too many conditions, say 10 to 12, mean reading a lot. Or you read the set and every question has a new condition that virtually demands redoing the entire arrangement because it adds a new condition. Or else there is a set with four straight conditions — for example which boys sits on the right, or left etc. These are deterministic conditions. You can just work on the arrangement and answer the questions. The more standard a puzzle the more you can come up with the schemes to represent data. Each question with new condition means doing everything with a new condition. You can also monitor whether the set you have selected is right and till what level or time you should spend time on that particular set.
Reasoning: Do not make a guess on selecting a set and taking a plunge that the set is going to be easy without any reason. There should be a rationale behind selecting a set. Don’t try out all the sets. One of the biggest problem areas is that students move in a sequential way in the exam pressure type of situation. DI in most of the cases is attempted last and by that time all your strategy and time scheme plans have gone for a toss. Don’t take a chance and don’t think that the solution will be evident while trying the set. Before trying you should have a clear idea about how to go about it.
Sequence of selection: There is no suggested plan of which section should be attempted first and which should be attempted last. They should be attempted at your own competence level. Don’t keep the most difficult section for the last because it is already difficult and keeping it for the last would add to the pressure. Start with the easier section to score a few points and feel better, follow it up with the section, which you find the most difficult and then move on to the next section.
Daytoday preparation
For preparing for traditional DI, pick up any newspaper or business magazine. Some graphs are usually given and the data is captured in those graphs. So you should do some mental calculations based on that data. For example, while watching a cricket match, calculate the run rate before it is flashed. We go to a petrol station and hardly check the right amount supplied — calculate the prices and the quantity wherever you go. Such regular mental calculations would start building up the base and looking at different forms of graphs will build in understanding of the DI. Building logical ability is difficult in so far as preparation for DI section of CAT is concerned. This is not to say that logic cannot be developed but the fact is that only looking out for the solution in the puzzles will not work. If you are working on the puzzles, you should spend time with the puzzle rather than looking for solution.
Solved Questions of previous CAT Exam :
I.
Directions for questions 1 to 3 : A team of 5 players Arpit, Bimal, Chatur, Dinu and Elan participated in a ‘Freaket’ tournament and played four matches (1 to 4). The following table gives partial information about their individual scores and the total runs scored by the team in each match.
Each column has two values missing. These are the runs scored by the two lowest scorers in that match.None of the two missing values is more than 10% of the total runs scored in that match.
Match1  Match2  Match3  Match4  
Runs scored by player  Arpit  100  53  
Bimal  88  65  52  
Chatur  110  
Dinu  72  75  20  56  
Elan  60  78  
Total  270  300  240  200 
1) What is the maximum possible percentage contribution of Arpit in the total runs scored in the four matches?
A. 19.7% B. 19.9%
C. 20.1% D. 20.2%
Answer: Option A
Explanation:
Maximum possible runs scored by Arpit in Match1 = 27
Maximum possible runs scored by Arpit in Match3 = 19
Maximum possible percentage contribution:
(27+100+19+53)/(270+300+240+200)x100% = 199/1010x100%
= 19.7%
2) If the absolute difference between the total runs scored by Arpit and Chatur in the four matches is minimum possible then what is the absolute difference between total runs scored by Bimal and Elan in the four matches?
A. 32 B. 37
C. 27 D. Cannot be determined
Answer: Option B
Explanation:
Maximum possible total runs scored by Chatur in the four matches = 27 + 30 + 110 + 20 = 187.
In such a case minimum possible total runs scored by Arpit in the four matches = 23 + 100 + 13 + 53 = 189.
Difference = 189 – 187 = 2 (minimum possible) Subsequently total runs scored by Bimal in the four matches = 88 + 65 + 19 + 52 = 224.
Also, total runs scored by Elan in the four matches = 60 + 30 + 78 + 19 = 187
Absolute difference = 224 – 187 = 37
3) The players are ranked 1 to 5 on the basis of the total runs scored by them in the four matches, with the highest scorer getting Rank 1. If it is known that no two players scored the same number of total runs, how many players are there whose rank can be exactly determined?
A. 0 B. 1
C. 3 D. 5
Answer: Option C
Explanation:
Individual ranges for total score:
Arpit> 189199
Bimal> 218224
Chatur> 182187
Dinu> 223
Elan> 187188
Least total will be of Chatur (Rank 5)
2nd least will be Elan (Rank 4)
Rank 3 must be of Arpit.
It is not possible to determine the exact ranks of Bimal and Dinu.
II.
DIRECTIONS FOR QUESTIONS 1 to 5 :
RAILWAY TIMETABLE : NEW DELHI – BHUBANESWAR RAJDHANI EXPRESS
Station Name 
Arrival Time 
Departure Time 
Distance(In KM) 
New Delhi 
 
17:05 
0 
Kanpur Central 
21:48 
21:53 
440 
Mughal Sarai JN 
01:55 
02:05 
786 
Gaya JN 
04:18 
04:21 
989 
Koderma 
05:22 
05:24 
1066 
Bokaro Steel City 
07:35 
07:40 
1191 
Tatanagar JN 
10:35 
10:40 
1342 
Kharagpur JN 
12:25 
12:40 
1476 
Balasore 
14:02 
14:04 
1595 
Bhadrak 
15:12 
15:14 
1657 
Cuttack 
16:33 
16:35 
1772 
Bhubaneswar 
17:30 
 
1800 
Answer :
Station Name 
Distance(In Km) 
Time Taken(In hours) 
Speed(In kmph) 
New Delhi  Kanpur Central 
440 
4.72 
93.22 
Kanpur Central  Mughal Sarai JN 
346 
4.03 
85.86 
Mughal Sarai JN  Gaya JN 
203 
2.22 
91.44 
Gaya JN  Koderma 
77 
1.98 
38.89 
Koderma  Bokaro Steel City 
125 
2.18 
57.34 
Bokaro Steel City  Tatanagar JN 
151 
2.92 
51.71 
Tatanagar JN  Kharagpur JN 
134 
1.75 
76.57 
Kharagpur JN Balasore 
119 
1.37 
86.86 
Balasore  Bhadrak 
62 
1.13 
54.87 
Bhadrak  Cuttack 
115 
1.32 
87.12 
Cuttack  Bhubaneswar 
28 
0.92 
30.43 
1.The longest run for the train between the two successive halts is
(a) Mughal Sarai JN  Gaya JN (b) New Delhi  Kanpur Central
(c) Kanpur Central  Mughal Sarai JN (d) Balasore  Balasore
Answer : Option b
Explanation :
With the run is of 440 km, the longest run is between New Delhi  Kanpur Central.
2. The average speed that the train maintained between two successive stations was the highest between
(a) Kanpur Central  Mughal Sarai JN (b) Mughal Sarai JN  Gaya JN
(c) New Delhi  Kanpur Central (d) Bokaro Steel City  Tatanagar JN
Answer : Option c
Explanation :
The average speed of 93.22 kmph is the highest between New Delhi  Kanpur Central.
3. The average speed that the train maintained between New Delhi and Bhubaneswar was nearly equal to
(a) 72 kmph (b) 74 kmph (c) 75 kmph (d) 82 kmph
Answer :
Explanation :
The average speed that the train maintained between New Delhi and Bhubaneswar = 1800 km/25 hrs and 25 min = 70.82 kmph.
4. If we consider a journey that begins in New Delhi and ends in Bhubaneswar, the train has the longest halt at
(a) Kanpur Central (b) Mughal Sarai JN (c) Tatanagar JN (d) Kharagpur JN
Answer : Option d
Explanation :
The train has the longest halt of 15 minutes at Kharagpur JN.
5. The train begins its return journey from Bhubaneswar to New Delhi Seventeen hours after it has arrived at Bhubaneswar. If the train left New Delhi on Tuesday on what day will it have returned to New Delhi? (Assume that on the return journey that train maintains the same average speed as on the onward journey).
(a) Thursday (b) Friday (c) SaturdayAnchor (d) SundayAnchor
Answer : Option b
Explanation :
Friday
III
The following piechart shows the percentage distribution of the expenditure incurred in publishing a book. Study the piechart and the answer the questions based on it.
Various Expenditures (in percentage) Incurred in Publishing a Book
1) 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. 19,450 B. Rs. 21,200
C. Rs. 22,950 D. Rs. 26,150
Explanation:
Let the amount of Royalty to be paid for these books be Rs. r
Then, 20:15 = 30600:r
r = Rs. 30600 x 15 = Rs. 22,950.
20
2) What is the central angle of the sector corresponding to the expenditure incurred on Royalty?
A. 15º B. 24º
C. 54º D. 48º
Answer: Option C
Explanation:
Central angle corresponding to Royalty = 15% of 360º
= 15 x 360º
100
= 54º.
3) 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. 36 B. Rs. 37.50
C. Rs. 42 D. Rs. 44.25
Answer: Option B
Explanation:
Clearly, marked price of the book = 120% of C.P.
Also, cost of paper = 25% of C.P
Let the cost of paper for a single book be Rs. n.
Then, 120: 25 = 180: n
n = Rs. 25 x 180 = Rs. 37.50
120
4) 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. 187.50 B. Rs. 191.50
C. Rs. 175.00 D. Rs. 180.00
Answer: Option A
Explanation:
For the publisher to earn a profit of 25%, S.P. = 125% of C.P.
Also Transportation Cost = 10% of C.P.
Let the S.P. of 5500 books be Rs. x.
Then, 10 : 125 = 82500 : x
x = Rs. 125 x 82500 = Rs. 1031250.
10
S.P. of one book = Rs. 1031250 = Rs. 187.50
5500
5) Royalty on the book is less than the printing cost by:
A. 5.0% B. 33.5%
C. 20.0% D. 25.0%
Answer: Option D
Explanation:
Printing Cost of book = 20% of C.P.
Royalty on book = 15% of C.P.
Difference = (20% of C.P.)  (15% of C.P) = 5% of C.P.
Percentage difference = Difference x 100%
Printing Cost
= 5% of C.P. x 100%
Printing Cost
= 25%.
IIV.
Study the following table and answer the questions based on it.
Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years
Year

Item of Expenditure 

Salary 
Fuel and Transport 
Bonus 
Interest on Loans 
Taxes 

1998 
288 
98 
3.00 
23.4 
83 
1999 
342 
112 
2.52 
32.5 
108 
2000 
324 
101 
3.84 
41.6 
74 
2001 
336 
133 
3.68 
36.4 
88 
2002 
420 
142 
3.96 
49.4 
98 
1) What is the average amount of interest per year which the company had to pay during this period?
A. Rs. 32.43 lakhs B. Rs. 33.72 lakhs
C. Rs. 34.18 lakhs D. Rs. 36.66 lakhs
Answer: Option D
Explanation:
Average amount of interest paid by the Company during the given period
= Rs. 23.4 + 32.5 + 41.6 + 36.4 + 49.4 lakhs
5
= Rs. 183.3 lakhs
5
= Rs. 36.66 lakhs.
2) 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%
Answer: Option C
Explanation:
Required percentage
= (3.00 + 2.52 + 3.84 + 3.68 + 3.96) x 100%
(288 + 342 + 324 + 336 + 420)
= 17 x 100%
1710
= 1%. (Approx.)
3) 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%
Answer: Option C
Explanation:
Required percentage
= (288 + 98 + 3.00 + 23.4 + 83) x 100%
(420 + 142 + 3.96 + 49.4 + 98)
= 495.4 x 100%
713.36
= 69.45% (Approx.)
4) The total expenditure of the company over these items during the year 2000 is?
A. Rs. 544.44 lakhs B. Rs. 501.11 lakhs
C. Rs. 446.46 lakhs D. Rs. 478.87 lakhs
Answer: Option A
Explanation:
Total expenditure of the Company during 2000
= Rs. (324 + 101 + 3.84 + 41.6 + 74) lakhs
= Rs. 544.44 lakhs.
5) The ratio between the total expenditure on Taxes for all the years and the total expenditure on Fuel and Transport for all the years respectively is approximately?
A 4:7 B 10:13
C 15:18 D 5:8
Explanation:
Required ratio = (83 + 108 + 74 + 88 + 98)
(98 + 112 + 101 + 133 + 142)
= 451
586
= 1
1.3
= 10
13
V.
Study the following bar chart and answer the questions carefully.
Sales Turnover of 5 Companies (in Rs. crores)
1) What is the percentage change in the overall sales turnover of the five companies together between 2001  2002 and 2002  2003 ?
A. 17.21 % B. 14.68 %
C. 12.67 % D. 21.24 %
Answer: Option B
Explanation:
The required answer is
100  percentage value of the fraction (Absolute change/first year's value).
2) What is the absolute change in overall sales turnover of the five companies together between 2001  2002 and 2002  2003 ?
Answer: Option A
Explanation:
Absolute value of the difference between the sum of the turnover of the five companies for 2001  2002 and 2002 – 2003
3) Which of the companies shows the maximum percentage difference in sales turnover between the two years ?
A. Honda B. GM
C. Hyundai D. Maruti
Answer: Option C
Explanation:
Hyundai with 25.25 % is marginally higher than Honda with 24.5 %.
4) What should have been the sales turnover of GM in 2002  2003 to have shown an excess of the same quantum over 2001  2002 as shown by the sales turnover of Maruti ?
C. 952.76 D. 962.76
Answer: Option D
Explanation:
GM should have increased its sales turnover by Rs.49.13 crore.
Hence, the answer is 913.63 + 49.13 = 962.76.
5) What is the approximate difference between the average sales turnover of all the companies put together between the years 2001  2002 and 2002  2003 ?
A. 133.45 B. 142.48
C. 117.6 D. None of these
Answer: Option B
Explanation:
Difference between the sum of the two years divided by 5.
VI.
Study the following line graph and answer the questions
1) For which of the following pairs of years the total exports from the three Companies together are equal?
A. 1995 and 1998 B. 1996 and 1998
C. 1997 and 1998 D. 1995 and 1996
Answer: Option D
Explanation:
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 D
Explanation:
Analysis of the graph: From the graph it is clear that
 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.
 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.
 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
3) In which year was the difference between the exports from Companies X and Y the minimum?
A. 1994 B. 1995
C. 1996 D. 1997
Answer: Option C
Explanation:
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 crores B. Rs. 18.67 crores
C. Rs. 20 crores D. Rs. 22.17 crores
Answer: Option C
Explanation:
Average exports of the three Companies X, Y and Z in 1993
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. 2 B. 3
C. 4 D. 5
Answer: Option C
Explanation:
Average annual exports of Company Z during the given period
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.
Important Tips for DI preparation
Scan the Question: Most DI questions will consist of a bunch of statistics, numbers & diagrams that might look scary at first instance but are actually not at all difficult to solve. In fact the trend has been: the scarier a DI set/caselet looks, the easier it is to solve. So before you lose heart & move on to an easierlooking set/caselet, scan that scary set & the list of questions in it. There will be at least of couple of “sitters” (questions that can be easily answered).
Hone your Calculation Skills/Speed: The Date Interpretation section is calculationintensive. And by “calculations” we mean stuff like 556/874 and not 2*9=? Such calculations can eat up your time. It is imperative, therefore to get very, very comfortable with calculations. Learn shortcuts that will help you calculate in your head or better still; figure out how Vedic Math works. It will help you a lot.
Get familiar with all types of DI questions: When you have been practicing DI questions for a while, you will begin to notice that there are different types or formats of questions in this section. There will be bar charts, tables, pie charts etc. There will also be questions where a lot of text or information will be provided in a long paragraph. Work on your reading & comprehension speed. It will go a long way in helping you tackle this section. Also try reading business newspapers which have articles that are dataintensive & have graphs & piecharts etc. After reading the article, try to mentally collate & analyze the data provided in them. Such activities will help you get into the “DI mode” & stay in that mode always.
Practice, practice, practice: The last but the most important piece of advice. Copious amount of practice will help you in two ways:
 Your speed will increase considerably. You would have attempted all kinds of DI questions many number of times. You will end up attempting more questions correctly, thus increasing your score.
 Your confidence will increase considerably. You know you have practiced a lot! This will help you face tough questions with determination.
So try to solve at least three DI question every day. Refer to good books that have a lot of solved and unsolved questions for practice. Suggestions for good books have been provided in the introductory article.
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