Six people P, Q, R, S, T and U are seated around a round table. Every chair is spaced equidistant from adjacent chairs. R is seated next to T. S is seated second to the left of T. P is sitting between U and R.

Which of the following must be true?

(A) P is seated opposite to Q.

(B) U is seated adjacent to T.

(C) R is seated third to the left of S.

(D) Q and T are not neighbors.

Choose the correct answer from the options given below:

Let six people be seated at positions 1, 2, 3, 4, 5, 6 around a circular table (clockwise).

Place T at position 1.

Since S is seated second to the left of T:

Going left from position 1: position 6 (first left), position 5 (second left)

So S is at position 5.

Since R is seated next to T:

R is either at position 2 or position 6.

Since P is sitting between U and R (meaning P is adjacent to both):

If R is at position 6, then P must be adjacent to R. But positions adjacent to 6 are 5 (occupied by S) and 1 (occupied by T). This is impossible.

Therefore, R must be at position 2.

With R at position 2, P must be adjacent to both U and R:

P must be at position 3 (next to R at position 2)

Then U must be at position 4 (next to P at position 3)

The remaining position 6 goes to Q.

Final arrangement: T(1), R(2), P(3), U(4), S(5), Q(6)

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Checking statement (A): P is seated opposite to Q

P is at position 3, Q is at position 6

In a 6-person circular arrangement, opposite positions are 3 seats apart.

Positions 3 and 6 are indeed opposite.

Statement (A) is TRUE.

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Checking statement (B): U is seated adjacent to T

U is at position 4, T is at position 1

They are not adjacent (positions 2 and 3 are between them).

Statement (B) is FALSE.

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Checking statement (C): R is seated third to the left of S

S is at position 5. Going left: position 4 (first), position 3 (second), position 2 (third)

R is at position 2, which is third to the left of S.

Statement (C) is TRUE.

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Checking statement (D): Q and T are not neighbors

Q is at position 6, T is at position 1

Positions 6 and 1 are adjacent in a circular arrangement.

Q and T ARE neighbors, so statement (D) is FALSE.

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Only statements (A) and (C) are true.

Therefore, the correct answer is Option 4: (A) and (C) only.