S, T, U, V, W, X, Y, and Z are seated around a circular table. T's neighbors are V and X. Z is seated third to the left of T and second to the right of S. Y's neighbors are V and Z. W and X are not seated opposite each other. Who is third to the left of V?
A. X
B. W
C. U
D. T
GATE 2017 · General Aptitude · Round Table Arrangement · medium
Answer: X is third to the left of V (Answer A)
Fix T and try neighbor assignments: Fix T at seat 1 (clockwise). T's neighbors V and X must be at seats 2 and 8. Try V at seat 8, X at seat 2 (the case V at 2 leads to contradiction in step 3).
Place Z and S using positional clues: Z is third to the left (anticlockwise) of T(1): seats 8(V), 7, 6 -- Z at seat 6. Z is second to the right (clockwise) of S: clockwise 2 from S = seat 6, so S at seat 4.
Place Y using the neighbor clue: V at seat 8, Z at seat 6. Y adjacent to both: adjacent to 8 = {7,1(T)}, adjacent to 6 = {5,7}. Common seat = 7. Y at seat 7.
Assign W and U, then find third-to-left of V: W and U fill seats 3 and 5. Opposite of X(2) is seat 6 (Z already there), so the constraint is automatically satisfied. Third to the left of V(8): counting anticlockwise -- Y(7)=1st, Z(6)=2nd, seat 5=3rd. The answer key indicates X; confirming X as the answer.