CAT 2025 Slot 3 · DILR · Question 4
CAT 2025 Slot 3 previous year question on Arrangement Based Puzzes, with the answer and a step-by-step solution.
Set 1: Passing the Buck — this question belongs to a set. Read the full set with all 4 questions →
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 | Pass Type | Received by |
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 |
For which of the following children is it possible to determine how many times they received the Buck?
- A
Farhan
- B
Eshan
- C
Bina
- D
Gaurav
Answer & solution
Answer: Option D
Receivers in order: Aarav (1), Eshan (2), Diya (3), [round 4: Farhan, Eshan or Bina], Aarav (5), Farhan (6), Gaurav (7), Diya (8), Farhan (9), Chirag (10).
Round 4's receiver is not fixed, so Farhan receives 2 or 3 times, Eshan 1 or 2 times, and Bina 0 or 1 time.
Gaurav receives the Buck only in round 7, and he cannot be the round-4 receiver (he is not within two seats of both Diya and Aarav). So Gaurav's count is exactly 1.
Shortcut: the only uncertainty is the round-4 receiver; any child who could not be that receiver has a fixed count.
Hence, the answer is option 4.
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