CAT 2025 Slot 3 · DILR · Set 1: Passing the Buck

Number the seats around the circle so that moving one seat to the left adds 1 and one seat to the right subtracts 1 (positions taken mod 7). Put Bina at 0.

Round 1: Bina passes immediately left to Aarav, so Aarav = 1.

Round 2: Aarav passes second to the right, to seat 1 − 2 = −1 (seat 6).

Round 3: seat 6 passes immediately right, to seat 5, who is Diya.

Round 6: Aarav (1) passes second to the left, to seat 3.

Round 7: seat 3 passes immediately left, to seat 4, who is Gaurav.

Round 8: Gaurav (4) passes immediately left, to seat 5 – Diya again.

Round 9: Diya (5) passes to Farhan, who must be within two seats: seat 3 or seat 6 (seats 4 and 0 are Gaurav and Bina).

Round 10: Farhan passes to Chirag. The only empty seats are 2, 3 and 6. If Farhan were at 6, Chirag would have to be at 4, 5, 0 or 1 – all taken. So Farhan = 3 and Chirag = 2, leaving Eshan at 6.

Order going left from Bina: Bina (0), Aarav (1), Chirag (2), Farhan (3), Gaurav (4), Diya (5), Eshan (6).

Immediately to the right of Bina is seat −1 = 6, Eshan.

Shortcut: Round 10 decides it – Farhan must have an empty seat next to or two away from him for Chirag, which only happens at seat 3.

Hence, the answer is option 2.

From the arrangement (moving left adds 1): Bina 0, Aarav 1, Chirag 2, Farhan 3, Gaurav 4, Diya 5, Eshan 6.

Third to the left of Eshan is seat 6 + 3 = 9, i.e. seat 2 (mod 7), which is Chirag.

Shortcut: going left from Eshan you pass Bina, then Aarav, then reach Chirag.

Hence, the answer is option 3.

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.

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.