ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics
CAT 2019 Slot 2 DILR · Set 3 of 8Data InterpretationModerate DifficultyQ9–Q12 · 2 MCQ + 2 TITA

CAT 2019 Slot 2 DILR Set 3: Venn Diagrams (4 Questions) with Solutions

The Venn Diagrams set from the official CAT 2019 Slot 2 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2019 Slot 2 DILR · Questions 9–12
Students in a college are discussing two proposals -
A: a proposal by the authorities to introduce dress code on campus, and
B: a proposal by the students to allow multinational food franchises to set up outlets on college campus.
A student does not necessarily support either of the two proposals. In an upcoming election for student union president, there are two candidates in fray: Sunita and Ragini. Every student prefers one of the two candidates.
A survey was conducted among the students by picking a sample of 500students. The following information was noted from this survey.
1
250students supported proposal A and 250students supported proposal B.
2
Among the 200students who preferred Sunita as student union president, 80%80 \% supported proposal A.
3
Among those who preferred Ragini, 30\% supported proposal A.
4
20\% of those who supported proposal B preferred Sunita.
5
40%40 \% of those who did not support proposal B preferred Ragini.
6
Every student who preferred Sunita and supported proposal B also supported proposal A.
7
Among those who preferred Ragini, 20\% did not support any of the proposals.

In the exam this set competed with 7 others for 60 minutes. Budget about 8 minutes if you attempt it.

Q9. Venn Diagrams

TITA · +3 / 0
Among the students surveyed who supported proposal A, what percentage preferred Sunita for student union president?
Correct Answer
64
Step-by-step solution
📌 Core Concept
Split the 500 students into a Sunita/Ragini by A/B table using the percentages, then read off the required ratio.
🔢 Step-by-Step Solution
1
Sunita supporters = 200, so Ragini supporters = 500−200=300500 - 200 = 300.
2
Clue 2: Sunita and A = 0.8×200=1600.8 \times 200 = 160. Clue 3: Ragini and A = 0.3×300=900.3 \times 300 = 90. Total A = 160+90=250160 + 90 = 250, which matches clue 1.
3
Students supporting A number 250, and 160 of them preferred Sunita.
4
Percentage = 160250×100=64\frac{160}{250} \times 100 = 64.
Quick Check
The two A groups add to 250, as clue 1 requires, so the split is consistent.
Correct Answer: 64

Q10. Venn Diagrams

TITA · +3 / 0
What percentage of the students surveyed who did not support proposal A preferred Ragini as student union president?
Correct Answer
84
Step-by-step solution
📌 Core Concept
Build the full Sunita/Ragini table across the four A/B regions, then count Ragini supporters outside A.
🔢 Step-by-Step Solution
1
Sunita = 200 and Ragini = 300. Sunita and A = 160, Ragini and A = 90 (clues 2 and 3).
2
Clue 4: Sunita and B = 0.2×250=500.2 \times 250 = 50, so Ragini and B = 250−50=200250 - 50 = 200.
3
Clue 5: Students not supporting B = 500−250=250500 - 250 = 250, and 40% of them, which is 100, preferred Ragini. So Sunita and not B = 150.
4
Clue 7: Ragini supporting neither proposal = 0.2×300=600.2 \times 300 = 60. Ragini and not B = 100, so Ragini with A only = 100−60=40100 - 60 = 40.
5
Ragini and both = 90−40=5090 - 40 = 50, so Ragini with B only = 200−50=150200 - 50 = 150.
6
Students not supporting A = 500−250=250500 - 250 = 250. Among them Ragini supporters are B only plus neither, which is 150+60=210150 + 60 = 210.
7
Percentage = 210250×100=84\frac{210}{250} \times 100 = 84.
Quick Check
Ragini: 40+50+150+60=30040 + 50 + 150 + 60 = 300, as required.
Correct Answer: 84

Q11. Venn Diagrams

MCQ · +3 / −1
What percentage of the students surveyed who supported both proposals A and B preferred Sunita for student union president?
  1. A) 25
  2. B) 50
  3. C) 20
  4. D) 40
Correct Answer
B) 50
Step-by-step solution
📌 Core Concept
Count the students in A∩BA \cap B for each candidate, using the table of regions, and take Sunita's share.
🔢 Step-by-Step Solution
1
Sunita = 200, Ragini = 300. Sunita and A = 160, Ragini and A = 90.
2
Clue 4: Sunita and B = 0.2×250=500.2 \times 250 = 50. Clue 6 says every such student also supports A, so Sunita and both = 50.
3
Clue 5: Students not supporting B = 250, and 40% of them, which is 100, preferred Ragini. Clue 7: Ragini with neither = 0.2×300=600.2 \times 300 = 60. So Ragini with A only = 100−60=40100 - 60 = 40.
4
Ragini and both = 90−40=5090 - 40 = 50.
5
Students supporting both A and B = 50+50=10050 + 50 = 100, of whom 50 preferred Sunita.
6
Percentage = 50100×100=50\frac{50}{100} \times 100 = 50.
Why Not the Others
25: this would need only 25 Sunita supporters among the 100 in both.
20: this does not match any ratio from the table.
40: this does not match any ratio from the table.
Correct Answer: B

Q12. Venn Diagrams

MCQ · +3 / −1
How many of the students surveyed who supported proposal B, did not support proposal A and preferred Ragini as student union president?
  1. A) 150
  2. B) 210
  3. C) 200
  4. D) 40
Correct Answer
A) 150
Step-by-step solution
📌 Core Concept
Find Ragini's supporters who back B only, which means B but not A, by working through the clues region by region.
🔢 Step-by-Step Solution
1
Ragini = 500−200=300500 - 200 = 300. Ragini and A = 0.3×300=900.3 \times 300 = 90.
2
Clue 4: Sunita and B = 0.2×250=500.2 \times 250 = 50, so Ragini and B = 250−50=200250 - 50 = 200.
3
Clue 5: Students not supporting B = 250, and 40% of them, which is 100, preferred Ragini.
4
Clue 7: Ragini with neither proposal = 0.2×300=600.2 \times 300 = 60. So Ragini with A only = 100−60=40100 - 60 = 40.
5
Ragini and both = 90−40=5090 - 40 = 50.
6
Ragini with B only = 200−50=150200 - 50 = 150.
Why Not the Others
210: this is Ragini outside A, which also includes the 60 who support neither.
200: this is all Ragini supporters of B, including the 50 who also support A.
40: this is Ragini with A only.
Correct Answer: A
Timed Practice

Attempt all of CAT 2019 Slot 2 DILR under the clock

The whole section, 60 minutes, in the TCS iON-style simulator. Free, no sign-up.

Start Free Test

CAT 2019 Slot 2 DILR at a Glance

Sets in this section8
Questions in this section32
Section time60 minutes
Convenor IIMIIM Kozhikode

More CAT DILR Sets with Solutions