CAT 2025 Slot 3 DILR Set 4 Q14–Q17

A DILR caselet from the Data Interpretation & Logical Reasoning (DILR) section of CAT 2025 Slot 3, with 4 questions (Arrangements). Answers are CAT's official key.

The set

Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of 'Passing the Buck'.

The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:

• Immediately to the left;
• Immediate to the right;
• Second to the left; or
• Second to the right.

The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as '?'.
Round Position Name
1 Immediately to the left Aarav
2 Second to the right ?
3 Immediately to the right Diya
4 ? ?
5 ? Aarav
6 Second to the left ?
7 Immediately to the left Gaurav
8 Immediately to the left ?
9 ? Farhan
10 ? Chirag

Question 14

Who is sitting immediately to the right of Bina?
  1. A
    Chirag
  2. B
    Aarav
  3. C
    Farhan
  4. D
    Eshan

Answer: (D) Eshan Arrangements MCQ

Solution

  1. Number seats in the 'left' direction from Bina (seat 0). Round 1: Aarav at seat 1. Round 2: second right of Aarav, seat 6. Round 3: Diya at seat 5.
  2. Round 5 Aarav (seat 1), round 6 second left gives seat 3, round 7 gives Gaurav at seat 4, round 8 goes to seat 5 = Diya.
  3. Round 9 Diya passes to Farhan (seat 3 or 6); round 10 Farhan passes to Chirag, who must be at most 2 seats away among seats 2, 3, 6. Only Farhan at 3 with Chirag at 2 works, so Eshan is at 6.
  4. Order going left: Bina, Aarav, Chirag, Farhan, Gaurav, Diya, Eshan. Round 4 receiver (within 2 of Diya and of Aarav) can be Farhan, Eshan or Bina.
  5. Bina passed left to Aarav, so the seat on her other side, seat 6, is to her right: Eshan.

Question 15

Who is sitting third to the left of Eshan?
  1. A
    Aarav
  2. B
    Chirag
  3. C
    Gaurav
  4. D
    Divya

Answer: (B) Chirag Arrangements MCQ

Solution

  1. Number seats in the 'left' direction from Bina (seat 0). Round 1: Aarav at seat 1. Round 2: second right of Aarav, seat 6. Round 3: Diya at seat 5.
  2. Round 5 Aarav (seat 1), round 6 second left gives seat 3, round 7 gives Gaurav at seat 4, round 8 goes to seat 5 = Diya.
  3. Round 9 Diya passes to Farhan (seat 3 or 6); round 10 Farhan passes to Chirag, who must be at most 2 seats away among seats 2, 3, 6. Only Farhan at 3 with Chirag at 2 works, so Eshan is at 6.
  4. Order going left: Bina, Aarav, Chirag, Farhan, Gaurav, Diya, Eshan. Round 4 receiver (within 2 of Diya and of Aarav) can be Farhan, Eshan or Bina.
  5. Three seats left of Eshan (seat 6) is seat \(6 + 3 = 9 \equiv 2\): Chirag.

Question 16

For which of the following pass types can the total number of occurrences be uniquely determined?
  1. A
    Second to the right
  2. B
    Second to the left
  3. C
    Immediately to the left
  4. D
    Immediately to the right

Answer: (D) Immediately to the right Arrangements MCQ

Solution

  1. Number seats in the 'left' direction from Bina (seat 0). Round 1: Aarav at seat 1. Round 2: second right of Aarav, seat 6. Round 3: Diya at seat 5.
  2. Round 5 Aarav (seat 1), round 6 second left gives seat 3, round 7 gives Gaurav at seat 4, round 8 goes to seat 5 = Diya.
  3. Round 9 Diya passes to Farhan (seat 3 or 6); round 10 Farhan passes to Chirag, who must be at most 2 seats away among seats 2, 3, 6. Only Farhan at 3 with Chirag at 2 works, so Eshan is at 6.
  4. Order going left: Bina, Aarav, Chirag, Farhan, Gaurav, Diya, Eshan. Round 4 receiver (within 2 of Diya and of Aarav) can be Farhan, Eshan or Bina.
  5. Rounds 9 (second right) and 10 (immediately right) are now fixed. Rounds 4-5 are second right twice (via Farhan), or immediately left plus second left (via Eshan or Bina).
  6. 'Immediately to the right' occurs only in rounds 3 and 10 in every case: exactly 2. The other three counts change with the round-4 choice.

Question 17

For which of the following children is it possible to determine how many times they received the Buck?
  1. A
    Bina
  2. B
    Gaurav
  3. C
    Farhan
  4. D
    Eshan

Answer: (B) Gaurav Arrangements MCQ

Solution

  1. Number seats in the 'left' direction from Bina (seat 0). Round 1: Aarav at seat 1. Round 2: second right of Aarav, seat 6. Round 3: Diya at seat 5.
  2. Round 5 Aarav (seat 1), round 6 second left gives seat 3, round 7 gives Gaurav at seat 4, round 8 goes to seat 5 = Diya.
  3. Round 9 Diya passes to Farhan (seat 3 or 6); round 10 Farhan passes to Chirag, who must be at most 2 seats away among seats 2, 3, 6. Only Farhan at 3 with Chirag at 2 works, so Eshan is at 6.
  4. Order going left: Bina, Aarav, Chirag, Farhan, Gaurav, Diya, Eshan. Round 4 receiver (within 2 of Diya and of Aarav) can be Farhan, Eshan or Bina.
  5. Receivers: Aarav, Eshan, Diya, ?, Aarav, Farhan, Gaurav, Diya, Farhan, Chirag. The unknown round-4 receiver is Farhan, Eshan or Bina.
  6. So Bina's, Farhan's and Eshan's counts are uncertain, while Gaurav received exactly once.

Same concept in other years

See every question on Circular seating with players moving or passing around the circle.

More Arrangements questions from CAT

All 40 Arrangements questions asked since 2017.