CAT 2026 · Slot 1 · Expected paper

CAT 2026 › Slot 1 paper › DILR › Set 1

CAT 2026 Slot 1 DILR Q2: Games & Tournaments

The set

PairUp, a dating app, divides six users — Anaya, Raghav, Mehul, Tara, Ishaan and Zoya — into two groups of three: Priority Matches, managed by Cupid, and Discovery Matches, managed by Matchmaker.

At the end of each month, each user receives a compatibility rating. Within each group, the three users receive distinct ratings of 1, 2 and 3.

A user's score at the end of a month is the cumulative sum of their ratings from the beginning of the year. At the end of each month, the Discovery Matches user with the highest score is promoted to Priority Matches, while the Priority Matches user with the lowest score moves to Discovery Matches. In case of a tie, the user with the higher rating in the latest month ranks higher.

The following information is known:

  1. Anaya, Raghav and Mehul were in Priority Matches at the beginning of Month 1. All three were in Discovery Matches at the beginning of Month 4.
  2. Tara and Zoya were the only users who received the same rating in all four months.
  3. Raghav received a rating of 1 in Month 2.
  4. Anaya and Tara received ratings of 1 and 2, respectively, in Month 3.

TITA (type the answer) · +3 / 0

How many users changed groups more than once up to the beginning of Month 4?
Answer and solution

Correct answer: 0

Solution

Priority starts as {Anaya, Raghav, Mehul} and is {Tara, Ishaan, Zoya} at the start of Month 4. With only three swaps (one per month-end), each swap must send out one of Anaya/Raghav/Mehul and bring in one of Tara/Ishaan/Zoya. So each user changes group exactly once (or the swap order fails). Answer: $0$.

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

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