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

This question is a constraint-satisfaction puzzle: four students, three knockout games, and three clues about class and gender. Instead of building the bracket forward, we can check each candidate "never lost" student against the three clues and see which one survives.

1. Pavan: For Pavan to never lose, he must win every game he plays. But clue (i) forces Game 1 to be a same-class pair, so Game 1 is either Rishi-Swathi or Pavan-Tanvi. If Game 1 were Pavan-Tanvi, Pavan (Class 4, boy) would already need two more wins over Class 5 players to stay undefeated, which would give Class 4 more wins than Class 5, breaking clue (ii). So Pavan cannot be the undefeated student.
2. Rishi: If Rishi is undefeated, he must win every game he enters. Suppose Game 1 is Rishi vs Swathi (Rishi wins), Game 2 is Rishi vs one Class 4 student (Rishi wins again), and Game 3 is Rishi vs the last Class 4 student (Rishi wins a third time). That gives boys 3 wins and girls 0 wins, which does not match clue (iii) (boys 2, girls 1). So Rishi winning all three games is impossible; Rishi is not the answer.
3. Swathi: For Swathi to be undefeated she must win Game 1 (against Rishi, the only slot where a Class 5 student meets another Class 5 student), then beat both Class 4 students in Games 2 and 3. That gives the girl Swathi three wins and the boys zero wins, directly breaking clue (iii), which needs boys to win two games. So Swathi is not the answer.
4. Tanvi: Suppose Game 1 is Rishi vs Swathi and Rishi (boy) wins, Game 2 is Rishi vs Pavan and Rishi (boy) wins again, and Game 3 is Rishi vs Tanvi and Tanvi (girl) wins. Check the clues: Game 1 is the only same-class game (Rishi and Swathi both Class 5), satisfying clue (i). Class 5 wins Games 1 and 2, Class 4 (Tanvi) wins Game 3, so Class 5 has 2 wins to Class 4's 1, satisfying clue (ii). Boys win Games 1 and 2, the girl Tanvi wins Game 3, so boys have 2 wins and girls have 1, satisfying clue (iii). Every clue checks out, and Tanvi is the only player who entered the bracket and won every game she played.

Since Pavan, Rishi, and Swathi each fail at least one clue when assumed undefeated, only Tanvi's scenario satisfies all three clues at once.

Let's summarize:

• Game 1 must be Rishi vs Swathi because that is the only same-class pairing that keeps Class 5 ahead on wins.
• Rishi wins Games 1 and 2 to give boys their two wins, then loses Game 3 to Tanvi, who supplies the girls' one win and stays undefeated.

So the student who did not lose any game is Tanvi.