◆ DILR · Data Interpretation

Venn / Special / Mixed DI, approach + real CAT sets

Logic-driven DI where the data is a puzzle: machine-scheduling, signal-coded routes, ranked-list construction and college cut-off logic. Learn the set, sufficiency and logic-table methods, then drill actual CAT sets reproduced faithfully from the book, with the book's own answers.

3approach cards

4CAT sets

10questions

↩ All DI Approach Sheet CAT Sets

Approach & Concept Sheet

Method cards for set-based, sufficiency and logic-driven DI.

1Venn / set-based DI

Use overlapping regions for "only", "exactly two", "all three", "at least one".
|A∪B∪C| = ΣA − Σ(pairs) + |A∩B∩C|
Fill the innermost region first, then work outward subtracting overlaps.
"At least"/"at most" wording ⇒ extremes: push counts to one side to bound the answer.

2Data sufficiency in DI

Ask: do the given facts uniquely determine the asked value, or is "Cannot be determined" the answer?
If a needed quantity (e.g. GDP, count of a sub-group) is never given, you cannot compute absolutes, only ratios.
Don't assume; many CAT options reward spotting that the data is insufficient.

3Logic-based DI

You're given an incomplete table; each question's conditions complete it differently.
Read the rules and exceptions below the data carefully, they constrain the grid.
Treat conditions as a puzzle: each new clue resets/extends the table; don't carry one question's assumptions into the next.
Look for an invariant (a row/column sum that stays fixed) to anchor the logic.

CAT Previous-Year Sets

Real CAT logic-based / special DI sets, reproduced from the book with data tables intact. Difficulty: Easy Moderate Hard. Click any question to reveal the book's solution.

Logic-Based & Special DI

Directions (Q. 1 to 5): Answer the questions on the basis of following information. Machine M1 as well as machine M2 can independently produce either product P or product Q. The time taken by machines M1 and M2 (in minutes) to produce one unit of product P and product Q are given in the table below (Each machine works 8 hour per day):

Product	M1	M2
P	10	8
Q	6	6

ModerateCAT 1995

1. What is the maximum number of units that can be manufactured in one day?

(1) 140
(2) 160
(3) 120
(4) 180

Show solution

(2) 160. Q takes the least time on both machines (6 min on each), so produce only Q to maximise output. Units of Q on M1 = (8 × 60)/6 = 80; units of Q on M2 = (8 × 60)/6 = 80. Maximum number of units = 80 + 80 = 160.

HardCAT 1995

2. If M1 works at half its normal efficiency, what is the maximum number of units produced, if atleast one unit of each must be produced?

(1) 96
(2) 89
(3) 100
(4) 119

Show solution

(4) 119. At half efficiency M1 takes P: 20 min, Q: 12 min (M2 unchanged at P: 8, Q: 6). To maximise output on M1, make Q: (8 × 60)/12 = 40 units. On M2 make 3 units of P (to satisfy "atleast one of each"), taking 24 min; remaining Q on M2 = (480 − 24)/6 = 456/6 = 76. Total products = 40 + 3 + 76 = 119.

ModerateCAT 1995

3. What is the least number of machine hours required to produce 30 pieces of P and 25 pieces of Q respectively?

(1) 6 hr 30 min
(2) 7 hr 24 min
(3) 6 hr 48 min
(4) 4 hr 6 min

Show solution

(1) 6 hr 30 min. To minimise time, make P on M2 (faster for P at 8 min) and Q on M1 (6 min). 30 units of P on M2 = 30 × 8 = 240 min = 4 hr; 25 units of Q on M1 = 25 × 6 = 150 min = 2.5 hr. Total time = 4 + 2.5 = 6 hr 30 min.

Directions (Q. 6 to 8): Answer the questions on the basis of following information. In a country, the following signals are applicable:

Signal	Meaning
3 Red Lights	Stop
2 Red Lights	Turn Left
1 Red Light	Turn Right
3 Green Lights	Go @ 100 kmph
2 Green Lights	Go @ 40 kmph
1 Green Light	Go @ 20 kmph

A man headed towards north and follows the given signals as:

Point	Signal
Starting Point	-
After half-an-hour, 1st Signal	1 Green Light
After 15 minutes, 2nd Signal	2 Red and 2 Green Lights
After half-an-hour, 3rd Signal	1 Red and 3 Green Lights
After 24 minutes, 4th Signal	2 Red and 2 Green Lights
After 15 minutes, 5th & Last Signal	3 Red Lights

ModerateCAT 2002

6. What is the total distance covered by the man till the last signal?

(1) 90 km
(2) 120 km
(3) 110 km
(4) 84 km

Show solution

(1) 90 km. Each leg's distance = speed × time, where each signal sets the speed for the next leg: 20 × ½ + 40 × ¼ + 40 × ½ + 100 × ⅖ + 40 × ¼ = 10 + 10 + 20 + 40 + 10 = 90 km.

EasyCAT 2002

7. If the first signal after the starting point, is 1 Red and 2 Green lights, then what is the total distance covered by the man till the last signal?

(1) 90 km
(2) 50 km
(3) 40 km
(4) 80 km

Show solution

(1) 90 km. Since only the direction of the man has changed (the turn), and the speeds and times of every leg are unchanged, the total distance covered remains 90 km.

Directions (Q. 9 to 12): Answer the questions on the basis of the following information. Below is a table that lists countries region-wise. Each region-wise list is sorted, first by birth rate and then alphabetically by the name of the country. We now wish to merge the region-wise list into one consolidated list and provide overall rankings to each country based first on birth rate and then on death rate. Thus, if some countries have the same birth rate, then the country with a lower death rate will be ranked higher. Further, countries having identical birth and death rates will get the same rank. For example, if two countries are tied for the third position, then both will be given rank 3, while the next country (in the ordered list) will be ranked 5.

Rank	Country	Birth Rate	Death Rate	Region
1	South Africa	36	12	Africa
2	Egypt	39	13	Africa
3	Cameroon	42	22	Africa
4	Mozambique	45	18	Africa
5	Zaire	45	18	Africa
6	Ghana	46	14	Africa
7	Angola	47	23	Africa
8	Madagascar	47	22	Africa
9	Morocco	47	16	Africa
10	Tanzania	47	17	Africa
11	Ethiopia	45	23	Africa
12	Ivory Coast	43	23	Africa
13	Rhodesia	48	14	Africa
14	Uganda	48	17	Africa
15	Nigeria	49	22	Africa
16	Saudi Arabia	49	19	Africa
17	Sudan	49	17	Africa
18	Algeria	50	16	Africa
19	Kenya	50	14	Africa
20	Upper Volta	50	28	Africa
1	Germany (FRG)	10	12	Europe
2	Austria	12	13	Europe
3	Belgium	12	12	Europe
4	Germany (DRG)	12	14	Europe
5	Sweden	12	11	Europe
6	Switzerland	12	9	Europe
7	U.K.	12	12	Europe
8	Netherlands	13	8	Europe
9	France	14	11	Europe
10	Italy	14	10	Europe
11	Greece	16	9	Europe
12	Bulgaria	16	10	Europe
13	Hungary	18	12	Europe
14	Spain	18	8	Europe
15	USSR	18	9	Europe
16	Yugoslavia	18	8	Europe
17	Czech Republic	19	11	Europe
18	Portugal	19	10	Europe
19	Romania	19	10	Europe
20	Poland	20	9	Europe
1	Japan	16	6	Asia
2	Korea (ROK)	26	6	Asia
3	Sri Lanka	26	9	Asia
4	Taiwan	26	5	Asia
5	Malaysia	30	6	Asia
6	China	31	11	Asia
7	Thailand	34	10	Asia
8	Turkey	34	12	Asia
9	India	36	15	Asia
10	Burma	38	15	Asia
11	Iran	42	12	Asia
12	Vietnam	42	17	Asia
13	Korea (DPRK)	43	12	Asia
14	Pakistan	44	14	Asia
15	Nepal	46	20	Asia
16	Bangladesh	47	19	Asia
17	Syria	47	14	Asia
18	Iraq	48	14	Asia
19	Afghanistan	52	30	Asia
1	U.S.A.	15	9	N. America
2	Canada	16	7	N. America
3	Cuba	20	6	N. America
4	Mexico	40	7	N. America
1	Australia	16	8	Pacific
2	Philippines	34	10	Pacific
3	Indonesia	38	16	Pacific
1	Argentina	22	10	S. America
2	Chile	22	7	S. America
3	Colombo	34	10	S. America
4	Brazil	36	10	S. America
5	Venezuela	36	6	S. America
6	Guatemala	40	14	S. America
7	Peru	40	13	S. America
8	Ecuador	42	11	S. America

ModerateCAT 2003

9. In the consolidated list, what would be the overall rank of the Philippines?

(1) 32
(2) 33
(3) 34
(4) 35

Show solution

(2) 33. Number of countries with birth rate less than 34 = 32. Number of countries with birth rate equal to 34 = 4. Among these 4, three have equal death rate (10), Thailand, Philippines and Colombo, so all three get the same rank of 33.

HardCAT 2003

11. In the consolidated list, which country ranks 37th?

(1) South Africa
(2) Brazil
(3) Turkey
(4) Venezuela

Show solution

(4) Venezuela. The three countries at birth rate 34, death rate 10 share rank 33. Turkey (birth rate 34, death rate 12) then has rank 36. Among countries with a birth rate of 36, Venezuela has the lowest death rate (6) and hence ranks 37th.

HardCAT 2003

12. In the consolidated list, how many countries in Asia will rank lower than every country in South America, but higher than atleast one country in Africa?

(1) 8
(2) 7
(3) 6
(4) 5

Show solution

(1) 8. The Asian countries must be ranked above atleast Upper Volta in Africa, so Afghanistan is excluded. They must also be ranked below Ecuador (the lowest-ranked South-American country), so the countries from Japan to Burma are excluded. Only 8 countries from Iran to Iraq in the Asia list meet both requirements.

Directions (Q. 22 to 24): Answer the questions on the basis of following information. For admission to various affiliated colleges, a university conducts a written test with four different sections, each with a maximum of 50 marks. The following table gives the aggregate as well as the sectional cut-off marks fixed by six different colleges affiliated to the university. A student will get admission only if he/she gets marks greater than or equal to the cut-off marks in each of the section and his/her aggregate marks are atleast equal to the aggregate cut-off marks as specified by the college.

College	Section A	Section B	Section C	Section D	Aggregate Cut-off Marks
College 1	42	42	42		176
College 2		45	45		175
College 3			46		171
College 4	43			45	178
College 5	45		43		180
College 6		41		44	176

HardCAT 2008

22. Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?

(1) 181
(2) 176
(3) 184
(4) 196

Show solution

(3) 184. For each college he must miss a sectional or aggregate cut-off. To miss a sectional cut-off in a section he must score less than the least cut-off in that section across colleges. Section C has cut-offs 42, 45, 46, 43 (least 42) and Section D has cut-offs 45, 44 (least 44). Failing Section C (score < 42) blocks colleges 1, 2, 3, 5; failing Section D (score < 44) blocks colleges 4 and 6, together covering all six colleges. To maximise the total, take full marks in A and B and the highest failing scores in C and D: 50 + 50 + 41 + 43 = 184.

HardCAT 2008

23. Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her?

(1) 180
(2) 181
(3) 196
(4) 176

Show solution

(2) 181. To get calls from all colleges she must clear every sectional cut-off (the maximum cut-off in each section): Section A = max(42, 43, 45) = 45; Section B = max(42, 45, 41) = 45; Section C = max(42, 45, 46, 43) = 46; Section D = max(45, 44) = 45. Minimum aggregate = 45 + 45 + 46 + 45 = 181, which is also more than the aggregate cut-off of all six colleges.