CAT 2025 Slot 3 · DILR · Question 3

CAT 2025 Slot 3 previous year question on Arrangement Based Puzzes, with the answer and a step-by-step solution.

Arrangement Based PuzzesLOGICAL REASONING - High LevelMultiple choiceMedium

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 pass types can the total number of occurrences be uniquely determined?

A
Immediately to the left
B
Second to the right
C
Immediately to the right
D
Second to the left

Pick an option, then check.

Answer & solution

Answer: Option C

Fill in the missing pass types using the seating (Bina 0, Aarav 1, Chirag 2, Farhan 3, Gaurav 4, Diya 5, Eshan 6).

Round 9: Diya (5) to Farhan (3) is −2, second to the right.

Round 10: Farhan (3) to Chirag (2) is −1, immediately to the right.

Rounds 4 and 5: Diya (5) passes to someone, who passes to Aarav (1). That person must be within two seats of both, so it is Farhan (3), Eshan (6) or Bina (0):

– via Farhan: second right, then second right;

– via Eshan: immediately left, then second left;

– via Bina: second left, then immediately left.

None of these includes 'immediately to the right'. So 'immediately to the right' occurs exactly twice (rounds 3 and 10), while the counts of the other three pass types depend on rounds 4–5.

Shortcut: list the possible routes for the two unknown rounds and look for a pass type that none of them uses.

Hence, the answer is option 3.

CAT 2025 Slot 3 · DILR · Question 3

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