Seven people, A, L, M, I, R, H and S, are sitting in a row, facing north.
Only A sits to the left of S. Only four people sit between A and H. Only I sits between L and R and L is not an immediate neighbor of H.
Who sits at the extreme right of the line?
Correct Answer :
M
Solution :
The correct option is M.
Let's find the arrangement of the seven people (A, L, M, I, R, H, and S) sitting in a row facing north step-by-step:
We have 7 positions from left to right: _ _ _ _ _ _ _
1. "Only A sits to the left of S."
This means S has exactly one person to his left, who is A. Therefore, A must be in the 1st position (extreme left) and S must be in the 2nd position.
Arrangement: A, S, _, _, _, _, _
2. "Only four people sit between A and H."
Since A is in the 1st position, counting 4 positions between A and H (positions 2, 3, 4, and 5), H must sit in the 6th position.
Arrangement: A, S, _, _, _, H, _
3. "Only I sits between L and R and L is not an immediate neighbor of H."
The group of L, I, and R must sit together in 3 consecutive seats: either as (L, I, R) or (R, I, L).
Looking at our remaining empty positions (3rd, 4th, and 7th), the only way to fit 3 consecutive people is in positions 3, 4, and 5.
Since L cannot be an immediate neighbor of H (who is in the 6th position), L cannot be in the 5th position. Thus, L must be in the 3rd position, I in the 4th position, and R in the 5th position.
Arrangement: A, S, L, I, R, H, _
4. Remaining Person:
The only person left to place is M. The only remaining empty seat is the 7th position (extreme right).
Final Arrangement: A, S, L, I, R, H, M
Therefore, M sits at the extreme right of the line.
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