P, Q, R, S, T, and U are seated around a circular table. R is seated two places to the right of Q. P is seated three places to the left of R. S is seated opposite U. If P and T now switch seats, which of the following must necessarily be true?
A. P is immediately to the right of Q
B. P is immediately to the left of U
C. T is immediately to the right of Q
D. U is immediately to the right of T
GATE 2017 · General Aptitude · Round Table Arrangement · medium
Answer: After P and T swap, T is immediately to the right of Q (Answer C)
Fix Q and locate R and P: Fix Q at seat 1. R is 2 clockwise: seat 3. P is 3 anticlockwise from R: anticlockwise from 3 gives seats 2, 1, 6 -- P at seat 6.
Place S, T, U: Remaining seats 2, 4, 5 for S, T, U. S opposite U: seats 2 and 5 (3 apart). T gets seat 4. Arrangement: Q(1), S(2), R(3), T(4), U(5), P(6).
Swap P and T: P(seat 6) and T(seat 4) switch. New arrangement: Q(1), S(2), R(3), P(4), U(5), T(6).
Verify option C: T is at seat 6 and Q is at seat 1. Seats 6 and 1 are adjacent in the circle. With the convention that the seat anticlockwise from Q is to Q's right, T at seat 6 is immediately to the right of Q. Option C is true.