Question

A, B, C, D and E sit on a long bench. C does not sit next to A or E. A and E have three persons sitting between them.
Who is sitting in the middle of the bench?

• A. B
• B. C
• C. D
• D. None of these

Hint:

Three people between A and E forces them to the two ends of the bench, then use the no-neighbour clue to place C.

Answer 1

The Correct Option is B

Instead of numbering seats first, this method eliminates each option in turn to see which one survives every clue.

1. A bench seats five people in a single row, and the clue says three people sit between A and E. On a row of exactly five seats, the only way to fit three people strictly between two others is to place those two at the two extreme ends, so A and E must be the end occupants, leaving three middle seats for B, C and D.
2. Test option B as the middle occupant. If B sits in the middle, then C and D fill the two seats next to the ends, meaning one of C or D sits right next to A and the other sits right next to E. Since C cannot sit next to either A or E, this placement forces C into one of the forbidden seats no matter how B, C and D are arranged. So B in the middle cannot satisfy the clue about C.
3. Test option D as the middle occupant. By the same reasoning, B and C would then fill the two seats next to the ends, again forcing C to sit next to either A or E, which is not allowed. So D in the middle also fails.
4. Test option C as the middle occupant. Then B and D fill the two seats next to the ends, which means C, sitting in the middle, is not adjacent to either end seat. Since A and E are the end occupants, C ends up with no shared border with A or E at all, fully satisfying the clue that C does not sit next to A or E.
5. Since placing B or D in the middle always forces C into a forbidden position, and only placing C in the middle avoids that problem, C must be the one sitting in the middle of the bench, and None of these does not apply since a valid, consistent placement exists with C in the centre.