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CAT 2025 Slot 3 DILR · Set 4 of 5Logical ReasoningHard DifficultyQ14–Q17 · 4 MCQ

CAT 2025 Slot 3 DILR Set 4: Arrangements (4 Questions) with Solutions

The Arrangements set from the official CAT 2025 Slot 3 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 2025 Slot 3 DILR · Questions 14–17
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 '?'.
Official Reference Chart - CAT 2025 Slot 3 Official Reference Chart - CAT 2025 Slot 3

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q14. Arrangements

MCQ · +3 / −1
Who is sitting immediately to the right of Bina?
  1. A) Farhan
  2. B) Aarav
  3. C) Eshan
  4. D) Chirag
Correct Answer
C) Eshan
Step-by-step solution
📌 Core Concept
Number the seats 0 to 6 around the circle, with "right" meaning +1+1 and "left" meaning −1-1 (mod 7). Then follow the Buck from Bina through the pass chain.
🔢 Step-by-Step Solution
1
Put Bina in seat 0. Round 1 is "immediately to the left" to Aarav, so Aarav is in seat −1=6-1 = 6.
2
Round 2 is second to the right from Aarav, which is seat 1. Round 3 is immediately to the right to Diya, so Diya is in seat 2.
3
Round 5 ends with Aarav in seat 6. Round 6 is second to the left, so the receiver is in seat 4. Round 7 is immediately to the left to Gaurav, so Gaurav is in seat 3. Round 8 is immediately to the left to seat 2, which is Diya.
4
Round 9 goes from Diya (seat 2) to Farhan. The free seats are 1, 4 and 5, and Farhan must be 1 or 2 steps from seat 2, so Farhan is in seat 1 or 4.
5
If Farhan were in seat 1, Chirag would be in seat 4 or 5. Each is 3 seats away from seat 1, and no pass covers 3 seats. So Farhan is in seat 4.
6
Chirag is then in seat 5, one step to the right of Farhan, which leaves Eshan in seat 1.
7
The child immediately to the right of Bina (seat 0) is in seat 1, which is Eshan.
Why Not the Others
Farhan is in seat 4, Aarav in seat 6 and Chirag in seat 5, so none of them is next to Bina on the right.
Correct Answer: C

Q15. Arrangements

MCQ · +3 / −1
Who is sitting third to the left of Eshan?
  1. A) Chirag
  2. B) Divya
  3. C) Gaurav
  4. D) Aarav
Correct Answer
A) Chirag
Step-by-step solution
📌 Core Concept
The seat map from the pass chain fixes every child's position. "Third to the left" is then three seats back from Eshan.
🔢 Step-by-Step Solution
1
Number the seats with right as +1+1. Round 1 (left to Aarav) puts Aarav in seat 6 when Bina is in seat 0.
2
Round 3 (immediately to the right to Diya) puts Diya in seat 2.
3
Rounds 6 and 7 put the round 6 receiver in seat 4 and Gaurav in seat 3.
4
Round 9 sends the Buck from Diya in seat 2 to Farhan. Round 10 then sends it from Farhan to Chirag, and no pass covers 3 seats. So Farhan is in seat 4 and Chirag is in seat 5.
5
Eshan takes the one remaining seat, seat 1.
6
Three seats to the left of Eshan is seat 1−3=−2≡51-3 = -2 \equiv 5. Chirag sits there.
Why Not the Others
Diya is in seat 2, Gaurav in seat 3 and Aarav in seat 6, so none of them is in seat 5.
Correct Answer: A

Q16. Arrangements

MCQ · +3 / −1
For which of the following pass types can the total number of occurrences be uniquely determined?
  1. A) Second to the left
  2. B) Immediately to the left
  3. C) Second to the right
  4. D) Immediately to the right
Correct Answer
D) Immediately to the right
Step-by-step solution
📌 Core Concept
The passes in rounds 4 and 5 are unknown. List every way they can be completed, then count each pass type across all the options.
🔢 Step-by-Step Solution
1
Seats (Bina = 0, right = +1+1): Aarav 6, Diya 2, Gaurav 3, Eshan 1, Farhan 4, Chirag 5.
2
The known passes are round 1 left, round 2 second right, round 3 right, round 6 second left, round 7 left and round 8 left.
3
Round 9 goes from seat 2 to seat 4, so it is a second-right pass. Round 10 goes from seat 4 to seat 5, so it is an immediately-right pass.
4
Rounds 4 and 5 take the Buck from seat 2 (Diya) to seat 6 (Aarav), a net shift of −3≡4(mod7)-3 \equiv 4 \pmod 7. The only splits are second right then second right (2 + 2), left then second left (−1−2-1-2), or second left then left (−2−1-2-1).
5
Counts of each type under the three splits:
Second right is 4, 2 or 2.
Immediately left is 3, 4 or 4.
Second left is 1, 2 or 2.
Immediately right is 2 in every case (rounds 3 and 10).
6
Only the immediately-right count is the same in every case.
Why Not the Others
Second to the left, immediately to the left and second to the right each change with the choice made in rounds 4 and 5.
Correct Answer: D

Q17. Arrangements

MCQ · +3 / −1
For which of the following children is it possible to determine how many times they received the Buck?
  1. A) Farhan
  2. B) Gaurav
  3. C) Bina
  4. D) Eshan
Correct Answer
B) Gaurav
Step-by-step solution
📌 Core Concept
With the seats fixed, list who can receive the Buck in the unknown rounds 4 and 5. Then check which child's total does not depend on that choice.
🔢 Step-by-Step Solution
1
Seats (Bina = 0, right = +1+1): Eshan 1, Diya 2, Gaurav 3, Farhan 4, Chirag 5, Aarav 6.
2
Fixed receipts are round 1 Aarav, round 2 Eshan (seat 1), round 3 Diya, round 5 Aarav, round 6 seat 4 (Farhan), round 7 Gaurav, round 8 Diya, round 9 Farhan and round 10 Chirag.
3
Rounds 4 and 5 take the Buck from seat 2 to seat 6. The round 4 receiver is Farhan (seat 4) via 2 + 2, Eshan (seat 1) via −1−2-1-2, or Bina (seat 0) via −2−1-2-1.
4
Round 4 therefore cannot go to Gaurav (seat 3), and round 5 always goes to Aarav. Gaurav receives only in round 7, so the total is exactly 1.
5
Farhan gets 2 or 3 receipts, Eshan gets 1 or 2, and Bina gets 0 or 1, depending on the round 4 choice. Only Gaurav's total is fixed.
Why Not the Others
Farhan, Eshan and Bina each have a count that depends on who receives in round 4.
Correct Answer: B
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CAT 2025 Slot 3 DILR at a Glance

Sets in this section5
Questions in this section22
Section time40 minutes
Convenor IIMIIM Kozhikode

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