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:
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:
Solution
Looking at the constraints, let me systematically determine the seating arrangement.
Given information:
- 8 friends sitting in a circle facing center: A, H, I, K, M, N, S, T
- 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
Let's place A at position 3 in the circle.
Since A is second to the left of S, moving clockwise (to the right) from A:
Position 3 → Position 4 → Position 5
Therefore, S is at position 5.
A is between H and K means either H-A-K or K-A-H in sequence.
T is an immediate neighbor of both I and K.
Testing K-A-H arrangement:
- K at position 2, A at position 3, H at position 4
Since T must be adjacent to K (at position 2):
- T can be at position 1 or position 3
- Position 3 has A, so T must be at position 1
Since T must also be adjacent to I:
- I can be at position 2 or position 8
- Position 2 has K, so I must be at position 8
Current arrangement: T(1), K(2), A(3), H(4), S(5), ?, ?, I(8)
Remaining people: M and N for positions 6 and 7.
N is not an immediate neighbor of H or I:
- H at position 4 has neighbors at positions 3 and 5 (A and S)
- I at position 8 has neighbors at positions 7 and 1 (? and T)
Therefore, N cannot be at position 7, so:
- N at position 6
- M at position 7
Final arrangement: T(1), K(2), A(3), H(4), S(5), N(6), M(7), I(8)
Checking each statement:
(A) M is seated second next to T:
From T(1), moving two positions: 1→8→7 (counterclockwise) or 1→2→3 (clockwise)
M is at position 7. This is TRUE ✓
(B) K is seated opposite to I:
K is at position 2, I is at position 8
Opposite position to 2 in an 8-person circle is 2+4=6 (N's position)
This is FALSE ✗
(C) S is not seated next to N:
S at position 5, N at position 6
They are immediate neighbors. This is FALSE ✗
(D) H is seated next to S:
H at position 4, S at position 5
They are immediate neighbors. This is TRUE ✓
Statements (A) and (D) only must be true.
The correct answer is Option 2.