GATE DA 2026 Set 1 — Question 8
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Question
Rishi and Swathi are students of Class 5. Pavan and Tanvi are students of Class 4. Rishi and Pavan are boys. Swathi and Tanvi are girls. The four students played a total of three games of chess. The games were played one after another. A player who lost a game did not participate in any more games. It was observed that:(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.The student who did not lose any game is __________.
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.The student who did not lose any game is __________.
Correct answer
(D) Tanvi
Solution
Let's analyze the tournament structure. There are 4 players and 3 games with "loser out". This implies a sequential "king of the hill" or ladder structure because a standard bracket (semis + final) would require two initial pairs, but condition (i) says only the first game had students of the same class.Players:
Winner is Class 4. Game 2 must be Winner(G1) vs Class 5. If Class 4 wins G2, they have 2 wins. Game 3 is Winner(G2) vs Class 5. Even if Class 5 wins G3, Class 4 has 2 wins, Class 5 has 1. This violates condition (ii) "Class 5 won more games". If Class 5 wins G2, then G3 is Class 5 vs Class 5 (remaining), which violates condition (i) "first game was the only game... same class". Thus, Game 1 cannot be Class 4 vs Class 4.Case 2: Game 1 is Class 5 vs Class 5 (Rishi vs Swathi).
- Class 5: Rishi (Boy), Swathi (Girl)
- Class 4: Pavan (Boy), Tanvi (Girl)
Winner is Class 4. Game 2 must be Winner(G1) vs Class 5. If Class 4 wins G2, they have 2 wins. Game 3 is Winner(G2) vs Class 5. Even if Class 5 wins G3, Class 4 has 2 wins, Class 5 has 1. This violates condition (ii) "Class 5 won more games". If Class 5 wins G2, then G3 is Class 5 vs Class 5 (remaining), which violates condition (i) "first game was the only game... same class". Thus, Game 1 cannot be Class 4 vs Class 4.Case 2: Game 1 is Class 5 vs Class 5 (Rishi vs Swathi).
- Winner is Class 5 (1 win).
- Game 2: Winner(G1) vs Class 4 (Pavan or Tanvi).
- If Class 4 wins G2: Class 4 has 1 win. Game 3 is Class 4 vs Class 4 (remaining). Violation of (i).
- So, Class 5 must win Game 2. (Class 5 wins: 2).
- Game 3: Winner(G2) [Class 5] vs Remaining Class 4.
- Current wins: Class 5 = 2, Class 4 = 0.
- Condition (ii) is satisfied ( or ).
- Condition (iii): Boys won 2, Girls won 1.
- G1: Rishi (B) vs Swathi (G). Rishi must win to contribute to Boy wins? Or Swathi wins?
- G2: Winner(G1) vs Pavan (B) or Tanvi (G).
- G3: Winner(G2) vs Tanvi (G) or Pavan (B).
- If Rishi wins G1 (1 Boy win) and G2 (vs Pavan, 2 Boy wins), then in G3 Rishi plays Tanvi. If Rishi wins G3, total 3 Boy wins (Violation). So Tanvi must win G3 (1 Girl win).
- Result: Boys 2 wins (Rishi x2), Girls 1 win (Tanvi). Total wins: Class 5 (2), Class 4 (1). All conditions met.
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