Question

Directions: 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 are sitting at the extreme ends of the bench?

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

Hint:

Work out how many seats are needed given three people between A and E, then place C using the adjacency restriction.

Answer 1

The Correct Option is A

Step 1: Work out how many seats are needed between A and E.
Five people, A, B, C, D and E, sit in a single row on the bench. The question says three persons sit between A and E. That means, counting from A to E, there is A, then 3 people, then E, a total of 1 + 3 + 1 = 5 seats. Since there are exactly 5 people on the bench, A and E must occupy the two extreme (outermost) seats, with the other three people (B, C, D) filling the three seats in between.
Step 2: Place C using the "not next to A or E" condition.
Number the seats 1 to 5 from left to right. A and E sit in seats 1 and 5 (in some order). The seats next to the ends are seat 2 (next to seat 1) and seat 4 (next to seat 5). Since C cannot sit next to A or next to E, C cannot be in seat 2 or seat 4. The only seat left for C among the middle three is seat 3, so C must be exactly in the middle.
Step 3: Place B and D.
With C fixed in seat 3, only seats 2 and 4 remain, and these must be taken by B and D, in either order. The question does not ask for their exact order, only for the extreme ends, so this does not matter here.
Step 4: Read off the extreme ends.
Seat 1 and seat 5, the extreme ends of the bench, are occupied by A and E.
Step 5: Confirm the answer.
Option (1), "A & E", matches this result. Option (2) "B & D" is wrong because B and D sit in the middle seats, not at the ends. Option (3) "C & E" is wrong because C is forced into the middle seat, never an end. Option (4) is unnecessary since a definite pair, A and E, can be found.