◆ DILR · Data Interpretation

Charts, Bar / Line / Pie, approach

Reading-and-approximation method for visual DI: grouped & stacked bars, line-graph trends and slopes, and pie charts worked in degrees. Drill the approach here, then apply it on the tabular and caselet sets.

3approach cards

3CAT sets

10questions

↩ All DI Approach Sheet CAT Sets

Approach & Concept Sheet

Method cards for chart-based DI, bars, lines and pies.

1Bar & column charts

Single bar = one series; grouped/clustered bar = compare items side-by-side; stacked bar = part-to-whole within each period.
100% stacked = percentage contributions; totals scale to 100%.
Read heights against the gridlines; estimate to the nearest gridline when exact labels are missing.
For stacked bars, a segment's value = its top minus its bottom, not just its top.

2Line graphs

Best for trends over time; x-axis usually time, y-axis quantity/percentage.
Slope = rate of change. Steeper line ⇒ faster growth; downward slope ⇒ decline.
Multiple lines let you compare trends and spot where series cross (one overtakes another).
"When did growth start to decline?" = where the slope starts decreasing, not where the value falls.

3Pie charts, work in degrees

Whole circle = 360° = 100% = the given total. One pie shows only one parameter.
Ratio principle: value = (slice° ÷ 360) × total
Shortcut: 36° = 10% of total; differences/percentages can be answered in degrees alone, no absolute values needed.
Missing slice = 360° − (sum of all given slices).

CAT Previous-Year Sets

Real CAT chart-based sets, reproduced faithfully. Difficulty: Easy Moderate Hard. Click any question to reveal the book's solution.

Bar & Line Graphs

CAT 2003. Directions (Q. 22 to 24): Answer the questions on the basis of following information. The first bar graph shows the per capita availability of tea (in gms) in a country called Chaidesh during the period 1995 to 1999. The second bar graph shows the production of tea (in million kg) and the export of tea (in million kg) for the same five years. (Note: Availability is defined as production less export.)

Data from the chart, Per Capita Availability of Tea (gms)
Year	Per capita availability (gms)
1995	487
1996	464
1997	510
1998	544
1999	566

Data from the chart, Production & Export (million kg)
Year	Production	Export
1995	421	207
1996	561	189
1997	587	209
1998	645	215
1999	660	220

ModerateCAT 2003

22. In which year during the period 1996-1999 was Chaidesh's export of tea, as a proportion of tea produced, the highest?

(1) 1996
(2) 1997
(3) 1998
(4) 1999

Show solution

(2) 1997. Compute Export ÷ Production for each year: 1996 = 189/561 = 0.337; 1997 = 209/587 = 0.356; 1998 = 215/645 = 0.333; 1999 = 220/660 = 0.333. The proportion is maximum in 1997.

ModerateCAT 2003

23. In which of the following years was the production of Chaidesh the lowest?

(1) 1995
(2) 1996
(3) 1997
(4) 1999

Show solution

(1) 1995. Availability = Production − Export, so per capita availability ∝ (Production − Export) ÷ Total production. Evaluating the ratio (Production − Export) ÷ per capita availability for each year: 1995 = (421 − 207)/487 = 0.44; 1996 = (561 − 189)/464 = 0.8; 1997 = (587 − 209)/510 = 0.74; 1998 = (660 − 220)/556 = 0.79. The smallest figure, 1995, corresponds to the lowest production.

ModerateCAT 2003

24. The area under tea cultivation continuously decreased in all four years from 1996 to 1999, by 10%, 7%, 4% and 1%, respectively. In which year was tea productivity (production per unit of area) the highest?

(1) 1999
(2) 1998
(3) 1997
(4) 1996

Show solution

(1) 1999. Tea productivity = Production ÷ Area. Production is maximum in 1999 (660 million kg), and the area under cultivation is least in 1999 (it falls every year). A maximum numerator divided by a minimum denominator gives the highest productivity, so productivity is highest in 1999.

CAT 2003. Directions (Q. 29 to 32): Answer the questions on the basis of following information. Purana and Naya are two brands of kitchen mixer-grinders available in the local market. Purana is an old brand that was introduced in 1990, while Naya was introduced in 1997. For both these brands, 20% of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that 10 Purana mixer-grinders were disposed off in 1997. The following grouped bar graph shows the number of Purana and Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

Data from the chart, mixer-grinders in operation (end of year)
Brand	1995	1996	1997	1998	1999	2000
Purana	120	162	182	222	236	236
Naya	0	0	30	80	124	134

ModerateCAT 2003

29. How many Naya mixer-grinders were disposed off by the end of 2000?

(1) 10
(2) 16
(3) 22
(4) Cannot be determined from the data

Show solution

(2) 16. 20% of the mixers bought in a year are junked exactly two years later. Naya disposed off by end of 2000 = (30 × 20 ÷ 100) + (50 × 20 ÷ 100) = 6 + 10 = 16.

ModerateCAT 2003

30. How many Naya mixer-grinders were purchased in 1999?

(1) 44
(2) 50
(3) 55
(4) 64

Show solution

(2) 50. Total Naya in operation in 1999 = 124. Naya disposed off in 1999 = 30 × 20 ÷ 100 = 6. So Naya purchased in 1999 = (124 + 6) − 80 = 50, where 80 is the number in operation at the end of 1998.

HardCAT 2003

31. How many Purana mixer-grinders were purchased in 1999?

(1) 20
(2) 23
(3) 50
(4) Cannot be determined from the data

Show solution

(1) 20. In 1997 the number of Purana replaced (disposed off) = 10, so 20 Purana were newly introduced from 1996 to 1997. Working forward, the total number of Purana replaced in 1999 = 14, and Purana purchased in 1999 = 14 + 30 ÷ 5 = 20.

ModerateCAT 2003

32. How many Purana mixer-grinders were disposed off in 2000?

(1) 0
(2) 5
(3) 6
(4) Cannot be determined from the data

Show solution

(4) Cannot be determined from the data. The number disposed off depends on how many Purana were bought in 1998, but the year-on-year breakup of new purchases versus disposals cannot be separated from the net stock shown, so it cannot be determined.

Pie Charts

CAT 2001. Directions (Q. 10 to 12): Answer the questions on the basis of following information. The questions are based on the pie charts given below. Chart 1 shows the distribution of twelve million tons of crude oil transported through different modes over a specific period of time. Chart 2 shows the distribution of the cost of transporting this crude oil. The total cost was ₹30 million.

Data from the chart, Chart 1: Volume Transported
Mode	Share of volume
Pipeline	49%
Road	22%
Airfreight	11%
Ship	9%
Rail	9%

Data from the chart, Chart 2: Cost of Transportation
Mode	Share of cost
Pipeline	65%
Rail	12%
Ship	10%
Airfreight	7%
Road	6%

ModerateCAT 2001

10. The cost in rupees per ton of oil moved by rail and road happens to be roughly

(1) 3
(2) 1.5
(3) 4.5
(4) 8

Show solution

(2) 1.5. Volume by rail and road together = (9% + 22%) of 12 million = 12 × 31 ÷ 100 = 3.72 million tons. Cost by rail and road together = (12% + 6%) of ₹30 million = 18 × 30 ÷ 100 = ₹5.4 million. Cost per ton = 5.4 ÷ 3.72 ≈ 1.5.

EasyCAT 2001

11. From the charts given, it appears that the cheapest mode of transport is

(1) Road
(2) Rail
(3) Pipeline
(4) Ship

Show solution

(1) Road. The cheapest mode has the lowest cost per ton, i.e. the smallest (cost share ÷ volume share): Road = 6/22 ≈ 0.27; Rail = 12/9 ≈ 1.33; Pipeline = 65/49 ≈ 1.33; Ship = 10/9 ≈ 1.11. Road has the lowest value, so it is the cheapest.

ModerateCAT 2001

12. If the costs per ton of transport by ship, air and road are represented by P, Q and R respectively, which of the following is true?

(1) R > Q > P
(2) P > R > Q
(3) P > Q > R
(4) R > P > Q

Show solution

(3) P > Q > R. Cost per ton ∝ (cost share ÷ volume share): Ship P = 10/9 ≈ 1.11; Air Q = 7/11 ≈ 0.64; Road R = 6/22 ≈ 0.27. Therefore P > Q > R.