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 .

• A. Pavan
• B. Rishi
• C. Swathi
• D. Tanvi

Hint:

Think of the three games as a knockout ladder; only the final winner never loses. Use clue (i) to fix Game 1, then clues (ii) and (iii) to pin down who wins each later game.

Answer 1

The Correct Option is D

Step 1: Set up the players and the game format.
Rishi and Swathi are in Class 5; Pavan and Tanvi are in Class 4. Rishi and Pavan are boys; Swathi and Tanvi are girls. Four students play three games total, and a player who loses a game is out for good. This is a knockout ladder: whoever wins the third game is the only student left who has never lost.

Step 2: Use clue (i) to fix Game 1.
Clue (i) says Game 1 is the only game between two students of the same class. Only two same-class pairs exist: (Rishi, Swathi) from Class 5, or (Pavan, Tanvi) from Class 4. So Game 1 must be one of these two pairs.

Step 3: Test Game 1 = Rishi vs Swathi.
Say Rishi beats Swathi in Game 1. Swathi is out. The remaining three players are Rishi, Pavan, and Tanvi. Game 2 must now pair Rishi with either Pavan or Tanvi, since a second same-class game is not allowed by clue (i).

Step 4: Apply clue (ii) to fix who wins Game 2.
Clue (ii) says Class 5 wins more games than Class 4 out of 3 games, so Class 5 must win at least 2 of the 3 games. Game 1 is already a Class 5 win (Rishi). If Rishi lost Game 2 to a Class 4 player, that Class 4 winner would then face the last remaining Class 4 student in Game 3, a Class4-vs-Class4 game, which guarantees a second Class 4 win. That would give Class 4 two wins and Class 5 only one, breaking clue (ii). So Rishi must win Game 2 as well.

Step 5: Work out Game 3 using clue (iii).
Clue (iii) says boys win two games and girls win one game overall. Game 1 (Rishi) and Game 2 (Rishi) are both boy wins already, so boys already have 2 wins. That means Game 3 must be a girl's win: a girl must beat Rishi in Game 3. Since Rishi already played one of Pavan or Tanvi in Game 2, the only student left for Game 3 is the other Class 4 student, and she must be the girl, Tanvi. So Game 2 was Rishi vs Pavan (Rishi wins), and Game 3 is Rishi vs Tanvi, with Tanvi winning.

Step 6: Check the class win count.
Class 5 wins Game 1 and Game 2 (2 wins), Class 4 (Tanvi) wins Game 3 (1 win), so Class 5 (2) beats Class 4 (1), matching clue (ii). Boys win Game 1 and Game 2 (2 wins), the girl Tanvi wins Game 3 (1 win), matching clue (iii) too.

Final Answer:
Swathi lost Game 1, Pavan lost Game 2, and Rishi lost Game 3. Only Tanvi, who entered the ladder in Game 3 and won it, never lost a single game. \[ \boxed{\text{Tanvi}} \]