CATSprint

CAT 2025Slot 3DILRQues & Sol

Logical ReasoningHard

Data 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 '?'.

Question 1

Who is sitting immediately to the right of Bina?

Solution

Setup: Fix Bina at position 1 and number positions 1–7 clockwise. Use each round's pass direction to deduce the positions of all seven children step by step.

Steps:

  1. Round 1: Bina (pos 1) passes immediately to the left → pos 2 receives. Receiver = Aarav ∴ Aarav is at pos 2.
  2. Round 2: Aarav (pos 2) passes second to the right → pos 2 − 2 = pos 7 (clockwise numbering means 'right' goes toward lower positions in this setup; second to the right from 2 lands on 7). Receiver unknown → someone sits at pos 7.
  3. Round 3: Holder at pos 7 passes immediately to the right → pos 6 receives. Receiver = Diya ∴ Diya is at pos 6.
  4. Rounds 4 & 5: Buck starts at pos 6 (Diya). Pass types unknown, but buck ends at pos 2 (Aarav) after round 5. Three combinations work: (2R, 2R), (2L, L), or (L, 2L). All are valid — we cannot determine which occurred yet.
  5. Round 6: Aarav (pos 2) passes second to the left → pos 4 receives. Receiver unknown → someone at pos 4.
  6. Round 7: Holder at pos 4 passes immediately to the left → pos 5 receives. Receiver = Gaurav ∴ Gaurav is at pos 5.
  7. Round 8: Gaurav (pos 5) passes immediately to the left → pos 6 receives. Pos 6 = Diya (confirmed).
  8. Rounds 9 & 10: From pos 6, buck must reach Farhan (round 9) then Chirag (round 10). Remaining unplaced positions: 3, 4, 7. From pos 6, a single pass can reach pos 4 or pos 7. Testing pos 7 for Farhan: from pos 7, a single pass cannot reach pos 3 or pos 4 (neither is within 1 or 2 steps). Testing pos 4 for Farhan: from pos 4, a single pass can reach pos 3 → Chirag at pos 3. ✓ This works. ∴ Farhan = pos 4, Chirag = pos 3, Eshan = pos 7 (only one left).
  9. Final circle (clockwise): Pos 1 = Bina, Pos 2 = Aarav, Pos 3 = Chirag, Pos 4 = Farhan, Pos 5 = Gaurav, Pos 6 = Diya, Pos 7 = Eshan. Immediately to the right of Bina (pos 1) is pos 7 = Eshan.

Final Answer: Eshan (Option B)

Question 2

Who is sitting third to the left of Eshan?

Solution

Setup: Use the fully determined seating arrangement derived from all 10 rounds to answer this positional question. The complete arrangement (clockwise): Pos 1 = Bina, Pos 2 = Aarav, Pos 3 = Chirag, Pos 4 = Farhan, Pos 5 = Gaurav, Pos 6 = Diya, Pos 7 = Eshan.

Steps:

  1. From the set solution: Eshan sits at position 7 in the clockwise arrangement.
  2. 'Third to the left' means moving 3 positions in the leftward (counter-clockwise) direction from Eshan's seat.
  3. Moving left (counter-clockwise) from pos 7: one step → pos 1 (Bina), two steps → pos 2 (Aarav)... wait — 'left' in a circle of people facing inward means clockwise movement along the circle. Third to the left of pos 7 = pos 7 + 3 = pos 10 → mod 7 = pos 3.
  4. Pos 3 = Chirag.

Final Answer: Chirag (Option C)

Question 3

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

Solution

Setup: After establishing the full seating arrangement, examine which rounds have known pass types and which are ambiguous (rounds 4, 5, 9, 10). Determine which pass type's total count is fixed regardless of which valid scenario plays out in the ambiguous rounds.

Steps:

  1. Known pass types from the table: Round 1 = Immediately Left, Round 2 = Second Right, Round 3 = Immediately Right, Round 6 = Second Left, Round 7 = Immediately Left, Round 8 = Immediately Left. These 6 rounds are fixed.
  2. Ambiguous rounds: Rounds 4 & 5 have three valid combinations — (2R, 2R), (2L, L), or (L, 2L). Rounds 9 & 10 have unknown pass types (though positions are determined: pos 6→4 and pos 4→3).
  3. Rounds 9 & 10 pass types: From pos 6 to pos 4 is a shift of 2 positions leftward → Second to the Left. From pos 4 to pos 3 is a shift of 1 position leftward → Immediately to the Left. These are now fixed.
  4. Count analysis for each pass type across scenarios:
    • Immediately Left (IL): Fixed in rounds 1, 7, 8, 10 = 4 occurrences. In rounds 4&5: scenario (2L,L) adds 1 IL, scenario (L,2L) adds 1 IL, scenario (2R,2R) adds 0 IL. Total can be 4 or 5 — NOT unique.
    • Second Right (2R): Fixed in round 2 = 1. Scenario (2R,2R) adds 2, others add 0. Total = 1 or 3 — NOT unique.
    • Immediately Right (IR): Fixed only in round 3 = 1. None of the three ambiguous scenarios for rounds 4&5 include IR. Rounds 9&10 also don't use IR. Total = exactly 1 in all scenarios — UNIQUE ✓.
    • Second Left (2L): Fixed in rounds 6, 9 = 2. Scenario (2R,2R) adds 0, (2L,L) adds 1, (L,2L) adds 1. Total = 2 or 3 — NOT unique.
  5. Only 'Immediately to the right' has a uniquely determinable count of 1.

Final Answer: Immediately to the right (Option C)

Question 4

For which of the following children is it possible to determine how many times they received the Buck?

Solution

Setup: After establishing the full seating arrangement and the three possible scenarios for rounds 4 & 5, track how many times each of the four named children (Farhan, Eshan, Bina, Gaurav) received the Buck across all rounds, checking whether the count is scenario-dependent.

Steps:

  1. Confirmed Buck receptions from fixed rounds:
    • Round 1: Aarav receives
    • Round 2: Eshan (pos 7) receives
    • Round 3: Diya receives
    • Round 6: Farhan (pos 4) receives
    • Round 7: Gaurav receives
    • Round 8: Diya receives
    • Round 9: Farhan receives
    • Round 10: Chirag receives
  2. Ambiguous rounds 4 & 5 — three scenarios:
    • Scenario A (2R, 2R): From pos 6, 2R → pos 4 (Farhan), then 2R → pos 2 (Aarav). Farhan receives in round 4.
    • Scenario B (2L, L): From pos 6, 2L → pos 1 (Bina), then L → pos 2 (Aarav). Bina receives in round 4.
    • Scenario C (L, 2L): From pos 6, L → pos 7 (Eshan), then 2L → pos 2 (Aarav). Eshan receives in round 4.
  3. Total receptions per child:
    • Farhan: Gets buck in round 6 (fixed) + round 9 (fixed) + round 4 only in Scenario A. Total = 2 (Scenarios B & C) or 3 (Scenario A) — NOT uniquely determinable.
    • Eshan: Gets buck in round 2 (fixed) + round 4 only in Scenario C. Total = 1 (Scenarios A & B) or 2 (Scenario C) — NOT uniquely determinable.
    • Bina: Gets buck in round 4 only in Scenario B. Total = 0 (Scenarios A & C) or 1 (Scenario B) — NOT uniquely determinable.
    • Gaurav: Gets buck only in round 7 (fixed). Gaurav does NOT appear in any of the three ambiguous scenarios (rounds 4 & 5 route Bina/Eshan/Farhan, not Gaurav). Total = exactly 1 in all scenarios — UNIQUE ✓.
  4. Gaurav is the only child among the options whose reception count is fixed at 1, regardless of which scenario unfolds in rounds 4 & 5.

Final Answer: Gaurav (Option D)