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GATE 2025 EC GA Q.8: solution and answer

GATE 2025 · ECGA Q.8 · 2 marks · MCQ

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 round, 4 student behind P leaves the game. After 2 round, 5 student behind Q leaves the game. After 3 round, 3 student behind V leaves the game. After 4 round, 4 student behind U leaves the game. Who all are left in the game after the 4 round?

Note: The figure shown is representative.

GATE 2025 EC GA question 8: A single circle with eight equally spaced positions on it, each marked with a bold cross and labelled with a letter…Tap to open full size
Figure from the GATE 2025 EC paper. It is part of the question.
Figure description

A single circle with eight equally spaced positions on it, each marked with a bold cross and labelled with a letter outside the circle. Going clockwise from the top: P at the top (12 o'clock), R at upper right (about 1:30), T at the right (3 o'clock), Q at lower right (about 4:30), S at the bottom (6 o'clock), V at lower left (about 7:30), U at the left (9 o'clock), W at upper left (about 10:30). So the clockwise order is P, R, T, Q, S, V, U, W and back to P. No arrows or other markings.

  1. (A)

    P; T; Q; S

  2. (B)

    V; P; T; Q

  3. (C)

    W; R; Q; V

  4. (D)

    Q; T; V; W

Answer and solution

ANSWER

(D) Q; T; V; W. This counts round 4 from the place U left, because U had already gone in round 2. That flaw is why the official key is MTA (marks to all).

Official answer: marks to all candidatesSource: Official answer key, GATE 2025 EC (IIT Roorkee)

  1. Read the circle. Going clockwise from the top, the order is P, R, T, Q, S, V, U, W, then back to P. The students move clockwise, so the student behind someone is the next one anticlockwise from them. For example, W is directly behind P. In musical chairs everyone walks round the circle together, so the students' order never changes. Only who is still playing matters, not which chair they are in.

  2. Round 1: the 4th student behind P. Counting anticlockwise from P: W (1), U (2), V (3), S (4). S leaves. Still playing, in clockwise order: P, R, T, Q, V, U, W.

  3. Round 2: the 5th student behind Q. Counting anticlockwise from Q: T (1), R (2), P (3), W (4), U (5). U leaves. Still playing: P, R, T, Q, V, W.

  4. Round 3: the 3rd student behind V. Counting anticlockwise from V (S has gone, so the next student is Q): Q (1), T (2), R (3). R leaves. Still playing: P, T, Q, V, W.

  5. Check the options after three rounds. The final four must come from . Option (A) contains S and option (C) contains R, so both are out. That leaves (B) and (D). Round 4 decides between them, because it must remove either W or P.

  6. Round 4: the question is defective as printed. It asks for the 4th student behind U, but U left in round 2, so there is no U to count from. This flaw is why the official key gave marks to every candidate (MTA). The most natural repair is to count from the place where U was standing, between V and W. Counting anticlockwise from there, over the students still playing: V (1), Q (2), T (3), P (4). P leaves. Counting from W, the student just ahead of U's old place, gives the same result: V (1), Q (2), T (3), P (4).

  7. Check the direction. If 'behind' meant clockwise instead, round 1 would remove S, round 2 R and round 3 P. U would still be playing in round 4, which would remove V. That leaves T, Q, U, W, which matches no option, so the anticlockwise reading is the intended one.

  8. Left after the 4th round: Q, T, V, W. This is option (D). It rests on counting round 4 from U's vacated place. The official key is MTA.

KEY IDEA

The students move clockwise, so 'behind' means counting anticlockwise. Musical chairs never changes the students' order round the circle, so each round just removes one name from a cyclic list, and you count only the students still playing. Rounds 1 to 3 remove S, U and R. Once U and R are gone, options (A) and (C) are ruled out before round 4.

WATCH OUT FOR

The first common mistake is counting 'behind' clockwise, in the direction of motion. That removes S, R, P, V and leaves T, Q, U, W, which is not an option. The second is counting the empty chairs of students who have left as if someone were still sitting there. A third is not noticing that U has already left when round 4 asks for the student behind U. The question is flawed as printed, and that is why the official key is MTA.

From the GATE 2025 EC paper. Every question of this paper · Download the full paper · All 41 Reasoning questions, with notes

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