CAT 2026 Slot 1 DILR Q9: 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.

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 $= 150$.

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