Question

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1^st round, the 4^th student behind P leaves the game.
After the 2^nd round, the 5^th student behind Q leaves the game.
After the 3^rd round, the 3^rd student behind V leaves the game.
After the 4^th round, the 4^th student behind U leaves the game.

Who all are left in the game after the 4^th round?

• A. P; T; Q; S
• B. V; P; T; Q
• C. W; R; Q; V
• D. Q; T; V; W

Hint:

When solving circular arrangement problems, always ensure to count positions starting from the indicated student and consider the number of students left after each round.

Answer 1

The Correct Option is A

Step 1: Initial Setup
The students are initially arranged in the following order:
$$P, Q, R, S, T, U, V, W$$
Step 2: After the 1^st Round
The 4^th student behind P leaves the game.
Starting from P and counting clockwise: Q (1), R (2), S (3), T (4). So, T leaves the game.
The new arrangement is:
$$P, Q, R, S, U, V, W$$
Step 3: After the 2^nd Round
The 5^th student behind Q leaves the game.
Starting from Q: R (1), S (2), U (3), V (4), W (5). So, W leaves the game.
The new arrangement is:
$$P, Q, R, S, U, V$$
Step 4: After the 3^rd Round
The 3^rd student behind V leaves the game.
Starting from V: P (1), Q (2), R (3). So, R leaves the game.
The new arrangement is:
$$P, Q, S, U, V$$
Step 5: After the 4^th Round
The 4^th student behind U leaves the game.
Starting from U: V (1), P (2), Q (3), S (4). So, S leaves the game.
The final arrangement is:
$$P, Q, U, V$$
Step 6: Conclusion
The students left in the game after the 4^th round are: P, Q, U, and V.