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:

1. the first game was the only game where two students of the same class played against each other,
2. the students of Class 5 won more games than the students of Class 4, and
3. 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:

With four players and three knockout-style games, the win totals split as Class 5 = 2 wins, Class 4 = 1 win; work out who can hold those wins without creating a second same-class game.

Answer 1

The Correct Option is D

Step 1: Understand the tournament structure.
Four students play three games, one after another, and a player who loses a game drops out for good. With four distinct players and three games, the natural structure is: game 1 is between two players, its winner plays a third (new) player in game 2, and the winner of game 2 plays the fourth (last) player in game 3. This way, every player who ever loses is eliminated immediately, and all four players get to play at least once, while whoever keeps winning plays more than once.

Step 2: Use condition (i) to fix game 1.
Condition (i) says only the first game pairs two students of the same class. Class 5 has Rishi and Swathi, Class 4 has Pavan and Tanvi. So game 1 is either 'Rishi vs Swathi' or 'Pavan vs Tanvi', and games 2 and 3 must each be a cross-class matchup.

Step 3: Use the win totals from (ii) and (iii).
There are 3 games in total, so total wins split between Class 5 and Class 4 must add to 3. Condition (ii) says Class 5 won more games than Class 4, so the only way to split 3 wins with Class 5 strictly ahead is Class 5 = 2 wins, Class 4 = 1 win. Condition (iii) says boys won 2 games and girls won 1 game overall.

Step 4: Test game 1 = Rishi vs Swathi.
Say Rishi wins game 1 (the other case is checked in Step 6). The loser, Swathi, is eliminated with 0 wins forever. Rishi (the winner) then plays game 2 against one of the Class 4 students. If Rishi lost game 2, the winner (a Class 4 student) would then face the other Class 4 student in game 3, since only Rishi and one Class 4 student remain unused, but that would make game 3 a same-class match, contradicting condition (i). So Rishi must also win game 2. Rishi then plays game 3 against the last remaining student, the second Class 4 student. If Rishi won all three games, all 3 wins would belong to one student, giving either boys 3 or girls 3, which does not match 'boys 2, girls 1' from condition (iii). So Rishi must lose game 3, meaning the Class 4 student in game 3 wins it.

Step 5: Assign the classes and genders to match the win counts.
So far: Rishi wins games 1 and 2 (2 wins), and the Class 4 student in game 3 wins game 3 (1 win). This matches Class 5 = 2, Class 4 = 1 from Step 3. For boys to total 2 and girls to total 1, Rishi (a boy) contributing 2 wins already satisfies the boys' total on his own, so the girls' 1 win must come from the winner of game 3. That means the Class 4 student who wins game 3 is a girl, so it is Tanvi, not Pavan. This also fixes Pavan as the Class 4 student who lost to Rishi in game 2.

Step 6: Check if Swathi could have won game 1 instead.
If Swathi had won game 1 instead of Rishi, she (a girl) would go on to win games 1 and 2 by the same reasoning as Step 4, giving girls 2 wins, which contradicts 'girls won only 1 game'. So Swathi cannot be the game 1 winner, confirming Rishi wins game 1.

Step 7: Lay out the full sequence and find who never lost.
Game 1: Rishi beats Swathi (Swathi eliminated, played 1 game, lost it).
Game 2: Rishi beats Pavan (Pavan eliminated, played 1 game, lost it).
Game 3: Tanvi beats Rishi (Rishi played 3 games total, won 2 and lost 1).
Tanvi only ever played game 3, and she won it, so she never lost a single game.

Final Answer:
The student who did not lose any game is Tanvi. \[ \boxed{\text{Tanvi}} \]