THE DI GAME

LET’S PLAY IT…..

“An Insightful and Comprehensive Session on the Data

Interpretation section of CAT”

TABLES:

Tables refer to the arrangement of data in the form of rows and

columns.

Positives:

Data is available in compiled form, hence there is no ambiguity in

interpretation.

Data Values are directly given and hence one need not spend

time finding the accurate Values.

Negatives:

It is difficult to establish trends in the form of table.

The amount of data is huge thus one can get confused.

“ Do not get carried away by the sheer amount of data,

the set may be easy for all you know!!”

TIPS ON SOLVING TABLE CHART PROBLEMS: A: Read the data very carefully, as the smallest detail may change the

meaning of the question completely. Similarly, the instructions have to be understood carefully to prevent wasting time in calculating data that is not required, and also to find out exactly what is the answer that is sought.

B: Try to understand the data provided carefully, before jumping to answer the questions. The questions are designed to be deceptive, and proper understanding of the requirements is a must. If the Data provided is of the combined variety or if there are more than one data table/charts/graphs, try to understand the relation between the given tables.

For Example, one table may talk about absolute sales figures, while the other table may talk of sales as a percentage of production. Hence, any question on excess production or Goods in stock, will require data from both tables.

C: Be very careful of the units used in the tables, and the units in which the answers (options) are provided. A mistake in the units may yield an entirely different answer. Also be careful of whether the answer is required in decimal or percentage. Such errors are common and easily avoidable.

Check out this table:

EXAMPLE 1:

The following table shows the production of cotton (in '000 bales) by six major

cotton-producing states of India in six different years.

1. What was the approximate percentage decrease in production of cotton in Maharashtra in 2009 over the previous year?

a. 27.5 b. 21.3 c. 36.4 d. 31.7

2. In which of the following years was the total production of Cotton by all six states together the highest?

a. 2006 b. 2007 c. 2008 d. 2010

3. The difference (in '000 bales) between the productions of the cotton by Gujarat and Maharashtra for the given period was

a. 15570 b. 18715 c. 10845 d. 30215

4. How many states produced more than 20% of the total cotton produced by the six states in the year 2007?

a. 1 b. 2 c. 3 d. 4 5. How many states witnessed growth in cotton production for at least two

consecutive years? a. 0 b. 1 c. 2 d. 3

SOLUTION:

The table given below shows the production of cotton (in '000 bales) by six major cotton-producing states of India individually and together in six different

years.

1. B

The approximate percentage decrease = 2. D 3. A

The required difference (in '000 bales) = 34715 – 19145 = 15570. 4. B

20% of the total production in 2007 = There were only two states which produced more than 20% of the total cotton produced by the six states together in the year 2007 and these were Gujrat and Maharashtra.

5. C There were two such states which witnessed growth in two consecutive years and these were Gujarat and Karnataka.

EXAMPLE 2: (IIFT 2007)

1. Mark all the correct statements a. Wipro’s share in total sales of the electronics sector was lower than the

share of Tata Steel in total sales of the iron & steel sector in each given year.

b. From the group consisting of the textiles and the iron & steel sector, there were 5 companies whose salaries & wages as percent of total salaries & wages of their respective sectors increased in 2003 as compared to 2001.

c. Tata Steel’s R & D expenditure in each given year as percent of sales was lower than that of the iron and steel sector as a whole.

d. From the group consisting of the pharmaceuticals and the electronics sectors, there were 5 companies which experienced a decline in the growth rate of sales in 2003.

2. Mark all the correct statements

a. Total salaries & wages over 2001-2003 as percent of total sales of the same

period had been the highest for the iron & steel sector. b. In the year 2003, if all the companies were ranked in descending order in

terms of salaries & wages as percent of sales, Videocon International would have been ranked the lowest.

c. In the year 2002, if all companies were ranked in descending order in terms of R & D as percent of sales, Bharat Electronics Limited would have been ranked third.

d. Of all companies that made profits in each year during 2001-2003, Wipro registered the highest growth in profits for the period.

3. Mark all the incorrect statements

a. Salaries & wages of each company in the iron & steel sector were up to 13

times its losses reported in each of the loss-marking years. b. Total salaries & wages over 2001-2003 as percent of total sales of the same

period for the pharmaceuticals sector had been the minimum. c. Total salaries & wages over 2001-2003 as percent of total sales of the same

period for only two companies exceeded 20 percent. d. D. Total profits / Total Sales for all the four sectors taken together was

higher in 2002 than in 2001.

4. Mark all the correct statements

a. Tata Steel experienced the highest percent decline in R & D expenditure in any single year during the given period.

b. Of all companies which incurred R & D expenditure every year during 2001-2003, total R & D expenditure / total sales was the highest for Dr. Reddy’s Laboratories Ltd.

c. During 2001-2003, in terms of sales growth, the best performer in the pharmaceuticals sector fared better than the best performer in the iron & steel sector.

d. Videocon International Ltd experienced the second largest percent decline in salaries & wages in any single year during the given period.

SOLUTION: 1.

Statement D correct as 5 companies show decline.

2.

Statement D: Incorrect

Wipro did not make the highest profit as Indo Rama Synthetic Ltd. has made a higher growth than Wipro in the year 2001-2003. 3. B,C, D Statement A: Correct- By observation. Statement B: (Incorrect as the percentage is minimum for Electronics sector.)

Statement C: Incorrect It is incorrect as for no company; the required percentage is greater than 20%. Statement D: Incorrect In the year 2002, the ratio of total profits to total sales is –0.02880 and in the year 2001, the given ratio is – 0.0260. 4. B,C Statement A: Incorrect Because in the year 2002-2003, Cipla Ltd. had a 100% decline in the R & D expenditure. Statement B: Correct

The ratio was highest for Dr. Reddy’s. Statement C: Correct

During the year 2001-2003, in terms of sales growth, the best performer in the Pharmaceutical sector was Ranbaxy which had a 79.55% growth and no company had a growth rate greater than any company in the Iron and Steel sector. Statement D: Incorrect Arvind Mills in the year 2001-2002 and Indo Rama Synthetic Ltd. in the year 2002-2003 have greater percentage decline than Videocon in any of the given years.

PIE CHARTS They derive their name from its shape, like that of a pie divided into various portions. They always represent data in the form of a percentage of the total, with the total percentage being 100. In such a chart, the length of the arc (and therefore the angle each sector subtends at the centre) is proportional to the quantity it represents. Such charts are often used in the corporate world and in newspapers. The pie chart is used to show the break-up of one continuous variable into its component parts. The pie chart encompasses a circle of 360 degrees which represents 100 per cent of the value of the continuous variable. Thus, 3.6 degrees on the pie chart represent 1 percent of the total value of the continuous variable being represented.

**A single pie diagram can represent only one continuous variable. Hence, in terms of versatility of data representation, pie charts are less versatile than either of bar charts, x-y graphs or tables. However, their utility is in the fact that the representation of data is cleaner and it gives an immediate idea of the relative distribution of the continuous variable amongst different sectors.

Positives: More effective in calculating the percentage share of each element in the

total.

Questions based on comparisons can be effectively solved using pie charts.

One pie chart can represent only one data set. Hence, when a question pertaining to pie chart is asked, in most cases data pertaining to only one or two data sets are asked. Because of this a student need to handle only limited number of data values.

Negatives: Less accurate than tables as one may take time to establish values. Trends cannot be established in a pie-chart

EXAMPLE 1:

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

A. 0.016 B. 1.6 C. 0.16 D. Data inadequate 2. What will be the quantity of water in the body of a person weighing 50 kg? A. 20 kg B. 35 kg C. 41 kg D. 42.5 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 : 18 B. 1 : 2 C. 2 : 1 D. 18 : 1 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. 54º B. 126º C. 108º D. 252º SOLUTION : 1. B

2. B Quantity of water in the body of a person weighing 50 kg = (70% of 50) kg = 35 kg. 3.C

4. C Percentage of proteins and other dry elements in the body = (16% + 14%) = 30%. Therefore Central angle corresponding to proteins and other dry elements together = 30% of 360º = 108º. EXAMPLE 2:

1. What is the region with which India had highest total trade in 1997-98? a. USA b. Other E.U. c. OPEC d. Others 2. In 1997-98 the amount of Indian exports, in millions US $, to the region with which India had the lowest total trade, is approximately: a. 750 b. 340 c. 220 d. 440

3. In I997-98, the trade deficit with respect to India, in billions of US $, for the region with the highest trade deficit with respect to India, is approximately equal to: a. 6.0 b. 3.0 c. 4.5 d. 7.5’ 4. What is the region with the lowest trade deficit with India in 1997 - 98? a. USA b. Asia c. Others d. Other E.U. 5. What is the region to which Indian imports registered the highest percentage

growth between 1997-98 and 1998-99? ((Assume that the average monthly exports from India and imports to India

during the remaining four months of 1998-99 would be the same as that for the

first eight months of the year.))

a. Other East Europe b. USA c. Asia d. Exports have declined, no growth

SOLUTION: 1. Trade with a region is the aggregate of imports from and exports to that region. The question is about a relative position and not an absolute position and thus should involve nothing more than glancing the pie charts and at the very most some small additions that can eminently be done orally. Whatever the figures of total exports and total imports, these will not be necessary since what is asked is a relative position. Assume that the total exports is E and total imports

is I, then in the case of USA, the imports will be 9I / 100 and exports will be 19 E/ 100 and in the case of Other E.U. imports will be 12 I / 100 and exports will be14 E/ 100 . So when comparing [{ 9I /100}+ {19E/100}] with [{ 12I /100}+ {14 E/100}] can safely multiply both sides so as to get whole numbers such that comparing (9I+19E) with (12I+14E). In the present case, imports into India are USD 40779 million and one may safely take I as 4 (rounding off 40779 to the nearest ten thousand) and exports from India are USD 33979 millionone may safely take E as 3 (rounding off 33979 to the nearest ten thousand).

Comparing (9I+19E) with (12I+14E) will mean comparing (9*4+19*3) with (12*4+14*3) and hence 93 with 90 and so India’s total trade with USA is more than the total trade with Other EUs. In evaluating the options, all that one has to do is to put the percentage of imports Now the Options : (( using approximations ))

Option A: USA (9*4+19*3)=93

Option B: Other EU (12*4+14*3)=90

Option C: OPEC (23*4+10*3)=122

Option D: Others (1*4+1*3)=7

Option C is the clear choice. 2. B Others occupy 1% of the pie in both imports and exports and is the area with

the lowest total trade. Indian exports aggregate roughly 34000 million and 1%

of this is two zeroes off from 34000 and would mean 340.

Thus Option B.

3.

Assume that total imports are 100I and total exports are 100E. In case of one

region - Region 1 - the imports are A% and exports are B% and in region 2

imports are C% and exports are D%. Trade deficit in Region 1 is (AI−BE) and

in Region 2 it is (CI−DE).

If Trade deficit in Region 1 is higher than in Region 2, then (AI−BE)−(CI−DE)

should yield a positive difference and this means that (AI−BE)>(CI−DE).

Subtract CI to both sides and add BE to both sides, one would get:

(AI−CI)>(BE−DE) or I(A−C)>E(B−D).

As I is greater than E in any case.

If (A−C) is greater than (B−D) the matter is clinched because then I(A−C) is

indeed > E(B−D) and thus Trade deficit in Region 1> Trade deficit in Region 2.

{ (A−C) is some number and (B−D) is some other number. So (A−C)% of a

higher base is bound to be higher than (B−D)% of a lower base so long as

(A−C)>(B−D) }

In the present case, in all regions except OPEC and other East Europe,

exports percentages are either more than or equal to imports percentages.

Thus compare only OPEC and other East Europe and see whether (Difference

in percentages of imports)> (Difference in percentages of exports).

In the case of OPEC and other East Europe (Difference in percentages of

imports)=(23−19) and (Difference in percentages of exports)=(10−10) and

hence (Difference in percentages of imports)>(Difference in percentages of

exports) and thus trade deficit in OPEC is highest.

The trade deficit in this case works out to (0.23*41−0.1*34)=9.2−3.4=5.8

roughly.

Thus Option A: 6 billion.

4. A The lowest trade deficit can also means a negative trade deficit or trade surplus. In case of the earlier question we have seen that Other EU has the second highest trade deficit and thus it is not a likely candidate for the least trade deficit. Hence we cross out Option D.

In USA and Asia we have trade surplus. In case of others there is a deficit. When there is trade surpluses, then ignore trade deficits because a trade surplus is a negative trade deficit. So Option C is to be crossed out as well. Now left with Options 1 and 2. As seen in the earlier question, if (Difference in percentages of imports) is greater than (Difference in percentages of exports) than Trade deficit in Region 1 > Trade deficit in Region 2. Now compare USA with Asia, (Difference in percentages of imports) =(9−14)=−5 and (Difference in percentages of exports)=(19−20)=−1.

Since -5 is not higher than -1, the trade deficit in USA is lower than the trade deficit in the case of Asia and hence Option A.

5. B The pie chart for exports in 1997-98, which is for a full year and for 1998 99, which is for eight months only.

As per the additional information, we are to assume that the average monthly exports from India and imports to India during the remaining four months of 1998-99 would be the same as that for the first eight months of the year. If for eight months, the total exports have been 21436 million, the remaining four months (which is half of eight months) would have brought about an additional export equal to half of 21436 million, which is 10718 and the total exports would then have been 32154 million. Let us see the options.

Option A:

Other East Europe. 10% of 33979 has grown to 12% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of Other East Europe, exports in 1998-99/exports in 1997-98 = 12B/10A.

Option B:

USA, 19% of 33979 has grown to 23% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of USA, exports in 1998-99/exports in 1997-98 = 23B/19A.

Option C:

Asia, 20% of 33979 has grown to 19% of 32154. Let 1% of 33979 be A and 1% of 32154 be B. So in the case of Asia, exports in 1998-99/exports in 1997-98 = 18B/20A. Option D says that exports have declined or there has been no growth in any region. This has to be checked. The highest percentage growth is in the case of USA. But percentage growth is about relative growth whereas the Option D talks about absolute growth. Whether there has been no growth or decline in absolute terms can be ascertained from only absolute figures. . Since we know that in case of USA the percentage growth rate has been highest, we may just see whether there has been actual growth in this case ( choose the highest percentage growth rate to check because if there has not been absolute growth where the percentage growth is highest, then in cases of lower percentage growth, the likelihood of an absolute growth is zero).

In case of USA, export percentage grew from 19% of 33979 million to 23% of 32154 million. For determining whether there was growth, the millions are unnecessary once again. They would be needed if you were asked how much was the growth.

Round off 33979 to 34 (forget the thousands as well) and round off 32154 to 32 (forget the thousands here as well) and see whether 19% of 34 is less than 23% of 32. So exports have indeed grown in the case of USA at least and hence Option D (which if true would mean that there has not been any growth in exports in any region) does not hold water.

So Option B.

BAR GRAPHS: Bar charts are one of the easiest, graphically attractive and hence most commonly used methods of presenting all types of data. They are especially useful for representing various data series. The data series comprises the continuous variables while the values of the specific instances at which the value of the data series is measured represents the values of the discrete

variables. Positives: Trends can be easily established as compared to tables and pie-charts. Comparative type questions can be easily solved by visual inspection of

graph. Negatives:

Less accurate than tables as at times, especially when the grid lines of the graph are missing because of which exact value of the bar cannot be accurately established.

The graph may get a little complicated in case of multiple bar chart or stacked bar chart

EXAMPLE 1:

1. The ratio of the maximum exports to the minimum imports was closest to?

A. 64 B. 69 C. 74 D. 79

2.How many countries exhibited a trade surplus?

A. 5 B. 4 C. 3 D. 6

3.The total trade deficit/surplus for all the countries put together was? A. 11286 surplus B. 11286 deficit C. 10286 deficit D. None of these

4.The highest trade deficit was shown by which country?

A. C B.G C. H D. L

5.The ratio of Exports to Imports was highest for which country?

A. A B. I C. J D. K

SOLUTION : 1. B The value of maximum exports = 6045. The value of minimum imports = 87. Therefore, the required ratio (6045/87) = 69.48 = 69 (approximately).

2. B Out of a total of 12 countries, 8 showed a deficit while 4 showed a surplus

3. B Sum of exports - Sum of imports = deficit (11286).

4. D Visually it is clear that L has the highest trade deficit.

5. B I has a ratio of 4002/2744 = 1.45, which is the highest.

EXAMPLE 2 :

Many Asian countries including China, Japan, Kazakhstan, India, Singapore, Malaysia and Jordon participated in one or more sporting events held at the 2006 Asian Games. In each sporting event at least three countries participated. At the end of each sporting event, the country finishing at the first, the second and the third positions were awarded a gold, a silver and a bronze medal respectively. The following bar graph shows distribution of the three types of medals. In this graph, the parts marked by "Data Not Available" may have belonged to one or more of all the participating countries

1. Which of the following could not have been the sum of the number of silver and the number of bronze medals won by Malaysia ?

A. 142 B. 164 C. 213 D. 284

2. What was the ratio of the number of gold medals won by Singapore to the number of silver medals won by Jordon ?

A. 21 : 31 B. 4 : 5 C. 31 : 33 D. 29 : 31

3. The total number of medals won by India was at least what percentage of the total number of medals won by China?

A. 31.12% B. 75.80% C. 62.24% D. 39.50%

4. It is given that the parts of the graph marked as "Data Not Available" belonged to exactly one of the seven countries that are mentioned above but was not included in the respective bar in the graph. When arranged in an ascending order of the total number of medals won, which of the following will never be a possible case?

A. Jordon, Japan, Kazakhstan B. Malaysia, India, Singapore C. Japan, China, Singapore D. Japan, Singapore, Jordon

SOLUTION :

1. B At the end of each event exactly one each of gold, silver and bronze medals were awarded hence the total number of gold or silver or bronze medals must be the same. Let there be N number each of gold, silver and bronze medals.

Sum of the numbers of silver and bronze medals won by Malaysia: 71 N/ 200 As this sum must be an integer, it will be a multiple of 71. Accordingly 142, 213, 284 and 355 all are possible values. Only 164 is not a multiple of 71.

2. D At the end of each event exactly one each of gold, silver and bronze medals were awarded hence the total number of gold or silver or bronze medals must be the same. Let there be N number each of gold, silver and bronze medals.

Number of gold medals won by Singapore: 29N / 200 Number of Silver medals won by Jordon: 31N/ 200 Hence the required ratio is 29:31

3. C

4. D

LINE GRAPHS: Line graph represents data in the form of straight lines that connect various data values. Both line graphs and bar graphs are used to convey same things and hence can be used inter-changeably. Positives:

Trends can be even better established in Line graphs than Bar graphs. Questions pertaining to percentage change and growth rates become

easier to solve using line graphs. Negatives: It has a similar disadvantage as the Bar graph in terms of establishing the

exact values. Line graphs can only indicate the value at the end of a certain period and

not between any two values. EXAMPLE 1 : The following graph gives the relation between the total expenses and the number of units produced in a factory.

Assume that all units produced are sold and that on a normal day 200 units are produced. The selling price of each unit is Rs. 35. 1. On a particular day if 300 units are sold, find the percentage change in profit when compared to a normal day (A) 100 (B) 150 (C) 200 (D) 250 2. What is the average additional cost (in `) per unit produced in comparison to a normal day, when 350 units are produced? (A) 18 (B) 23 (C) 25 (D) 28 SOLUTION : 1.C Profit on a normal day = 7000 – 6500 = `500 Profit when 300 units are sold = 10,500 – 9000 = `1500

Required percentage ={1500 – 500 / 500} X 100 % = 200 % 2. B Cost when 200 units are produced = `6500

Cost when 350 units are produced ≃ `10,000 Additional cost /unit ={ 10,000 – 6500 / 150} = 3500 / 150 = Rs. 23 EXAMPLE 2 : A family uses the following electrical appliances– TV, Refrigerator, Geyser, Washing machine and Grinder. The monthly electricity bill generated has two components- a fixed cost of `60 and a variable cost of rs 0.35 per kWh. The family uses Refrigerator throughout the day, Geyser for 2 hours, Washing machine for 0.5 hours, Grinder 0.25 hours and watches TV for 15 hours everyday. The line graph given below shows the energy consumption of the above mentioned appliances in a week for the family-

1 → Geyser 2 → Geyser + Refrigerator 3 → Geyser + Refrigerator + TV 4 → Geyser + Refrigerator + TV + Washing machine 5 → Geyser + Refrigerator + TV + Washing machine + Grinder 1. Which of the following is true?

A. The energy consumed by TV for 3 days is more than that of Refrigerator for

3 days. B. The energy consumed by Geyser for 4 day is less than that of Grinder for 7

days. C. The energy consumed by Washing machine in a week is less than that of

Geyser for 2 weeks. D. The energy consumed by TV for 2 days is less than that of Washing

machine for a week.

2. If the fixed cost increases by 25%, then what would be the percentage increase in the total cost of energy consumption by the family in a month of 30 days. (A) 10% (B) 12.5% (C) 15% (D) 19% SOLUTION: The energy consumption of Geyser in a week is 7 kWh and as the family uses the Geyser for 2 hrs in a day. Hence for 14 hrs in a week the energy consumption is 7 kWh. Hence the energy consumption of a Geyser per day is 1 kWh. Now, energy consumption of Refrigerator in a week is 14 kWh and the family uses Refrigerator throughout the day. Hence, the energy consumption of Refrigeration per day is 2 kWh. Similarly the energy consumption for TV in a day is 2 kWh. The energy consumption for Washing machine in a day is 4/7 kwh and for grinder is 1/7 kwh 1 . C (a) Energy consumed by TV for 3 days = 6 kWh. Energy consumed by Refrigerator for 3 days = 6 kWh. Hence Choice (A) is false. (b) Energy consumed by Geyser for 4 days = 4 kWh. Energy consumed by Grinder for 7 days = 1 kWh. Hence Choice (B) is false. (c) Energy consumed by Washing Machine in a week = 4 kWh.

Energy consumed by Geyser for 2 weeks = 14 kWh. Hence Choice (C) is true. (d) Energy consumed by TV for 2 days = 4 kWh. Energy consumed by Washing machine for one week = 4 kWh Hence (D) is false

2. B The fixed cost increased by 25 %. Hence the new fixed cost is Rs. 60 + ¼ (60) = rs. 75 Hence the increment in the total cost is {15 / 60 + (.35 x 4/7 x 30)} X 100 = 12.5 %