CAT 2026 Slot 1 DILR: Set 2: University survey — Initiatives M, N and candidates Devansh, Ishita with Solutions

5 questions: Q6, Q7, Q8, Q9, Q10. Solve each one here: tap the answer, press Check, then open the solution.

Venn / Survey

The set

A university think tank recently conducted a comprehensive survey among 720 respondents to understand their views on two progressive initiatives and two candidates running for the post of General Secretary of the student council. The initiatives included:

Initiative M, a faculty-supported plan to make research internships mandatory in undergraduate programs.
Initiative N, a student-led proposal to build mental health infrastructure on campus, including therapy pods and weekly wellness seminars.

Each respondent had the option to support neither, either, or both initiatives. Additionally, every individual expressed support for only one candidate — either Devansh or Ishita. 450 students supported initiative M and 360 students supported initiative N. While 300 students supported Devansh, 50% of those who supported Ishita supported N. $\tfrac{5}{12}$ of the students who supported N supported Devansh. $\tfrac{5}{12}$ of those who did not support N supported Devansh. Every student who supported Devansh and N also supported initiative M. Among those who supported Ishita, $\tfrac{1}{7}$ did not support any of the initiatives. $\tfrac{1}{3}$ of those who supported N supported Ishita but did not support M.

These results allowed the university to observe clear trends in how policy preferences aligned with leadership choices among the student body.

Question 6Venn / Survey

MCQ · +3 / −1

What % of surveyed respondents who supported Devansh supported initiative M but not N?

Answer and solution

Correct answer: C

Solution

Full breakdown (shared by Q6–Q10):
Devansh $= 300$, Ishita $= 720 - 300 = 420$.
Devansh & N $= \tfrac{5}{12} \times 360 = 150$ — all of them also support M (both).
Devansh & not N $= \tfrac{5}{12} \times 360 = 150$ (M-only + neither).
Ishita & N $= 50\% \times 420 = 210$; Ishita N-not-M $= \tfrac{1}{3} \times 360 = 120$, so Ishita both $= 90$.
Ishita neither $= \tfrac{1}{7} \times 420 = 60$; Ishita & not N $= 210$, so Ishita M-only $= 150$.
M total $450 = $ Devansh M $+ (90 + 150) \Rightarrow$ Devansh M $= 210$, Devansh M-only $= 60$, Devansh neither $= 90$.
Q6: $\dfrac{60}{300} \times 100 = 20\%$
Venn diagrams for Devansh and Ishita supporters of initiatives M and N

Venn diagrams for Devansh and Ishita supporters of initiatives M and N

Question 7Venn / Survey

MCQ · +3 / −1

How many students who supported Ishita supported N but not M?

Answer and solution

Correct answer: B

Solution

Ishita & N $= 210$, of which both $= 90$. Ishita N-not-M $= \tfrac{1}{3} \times 360 = 120$.

Question 8Venn / Survey

TITA (type the answer) · +3 / 0

What % of people who supported Devansh did not support any of the initiatives?

Your answer

Answer and solution

Correct answer: 30

Solution

Devansh & not N $= 150$; Devansh M-only $= 60$ (from M total 450), so Devansh neither $= 90$.
$\dfrac{90}{300} \times 100 = 30\%$

Question 9Venn / Survey

MCQ · +3 / −1

How many respondents are there who supported either Devansh or Ishita but did not support any of the initiatives?

Answer and solution

Correct answer: A

Solution

Ishita neither $= \tfrac{1}{7} \times 420 = 60$; Devansh neither $= 90$. Total $= 150$.

Question 10Venn / Survey

MCQ · +3 / −1

What is the ratio of the number of respondents who supported Devansh but did not support any of the initiatives to those who supported Ishita and M but did not support N?

Answer and solution

Correct answer: D

Solution

Devansh neither $= 90$. Ishita M-not-N $= (420 - 210) - 60 = 150$.
Ratio $= 90 : 150 = 3 : 5$

An expected paper by Cetking, not the actual CAT paper. CAT is conducted by the IIMs.