Eight friends, A, H, I, K, M, N, S and T are sitting around a circle facing the center, but not necessarily in the same order. A is between H and K. N is not an immediate neighbor of H and I. T is an immediate neighbor of I and K. A is second to the left of S. Which of the following must be true?

(A) M is seated second next to T.
(B) K is seated opposite to I.
(C) S is not seated next to N.
(D) H is seated next to S.

Choose the correct answer from the options given below:

(A) and (D) only

The correct answer is Option (2) → (A) and (D) only

Step-by-Step Logical Deduction:

To solve circular arrangement problems, we place the participants based on fixed constraints and then fill in the variables.

1. A is second to the left of S: Let’s place S at a position. Moving two spots clockwise (left for those facing the center), we place A.
2. A is between H and K: This means H and K are the immediate neighbors of A. We have two possible configurations: (H-A-K) or (K-A-H).
3. T is an immediate neighbor of I and K: This means the sequence must be I-T-K.
4. Combining the clues: Since K must be next to both A and T, the sequence becomes I-T-K-A-H.
5. Refining the circle: * We know A is second to the left of S. Counting from S: S $\rightarrow$ (Empty) $\rightarrow$ A.
• Looking at our sequence I-T-K-A-H, we can see that H must be the person sitting next to S to satisfy the "second to the left" rule.
• Positions so far: S - H - A - K - T - I. (6 positions filled).
6. Placing N and M: Two spots remain.
• Constraint: N is not an immediate neighbor of H or I.
• The spots available are between I and S, and between H and S. However, the spot between H and S is already occupied by the "empty" space we noted.
• If we place N between I and S, it is next to I (which is forbidden).
• Therefore, the only way to satisfy "N is not next to H or I" is to place M next to I, and N between M and S.
• Final sequence (Clockwise): S - H - A - K - T - I - M - N (back to S).

Evaluating the Statements:

• (A) M is seated second next to T: From T, moving two spots we find M (T $\rightarrow$ I $\rightarrow$ M). True.
• (B) K is seated opposite to I: In a circle of 8, the opposite of the 4th position is the 8th. Counting from I (1), T (2), K (3), A (4), H (5), S (6), N (7), M (8). K is opposite N, not I. False.
• (C) S is not seated next to N: In our deduction, N ended up between M and S. So S is seated next to N. False.
• (D) H is seated next to S: As shown in the layout, H and S are immediate neighbors. True.

Conclusion: Only (A) and (D) are true.