Question

Five people-A, B, C, D, and E-are seated in a row. A is not next to B. C is next to D. E is not at the ends. Who is in the middle?

• A. A
• B. B
• C. C
• D. E
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Hint:

In seating arrangements, start with constraints that limit positions (e.g., not at ends) and test the middle position first for questions asking about it.

Answer 1

The Correct Option is D

- Step 1: List the constraints. Five seats (1 to 5). A not next to B. C next to D. E not at ends (so E in positions 2, 3, or 4).
- Step 2: Identify middle position. With five seats, position 3 is the middle.
- Step 3: Assign E. Since E cannot be at ends (1 or 5), E can be in 2, 3, or 4. Test E in position 3 (middle).
- Step 4: Assign C and D. C and D are next to each other. Possible pairs around E (position 3): (1,2), (2,3), (3,4), or (4,5).
- Step 5: Assign A and B. A and B cannot be next to each other. If E is in 3, try C and D in 4 and 5. Positions 1 and 2 get A and B.
- Step 6: Test arrangement. Example: 1-A, 2-B, 3-E, 4-C, 5-D. Check: A not next to B (satisfied), C next to D (4,5), E not at ends (position 3).
- Step 7: Verify middle. E is in position 3 (middle) in valid arrangements. Other positions for E (2 or 4) are possible but don’t consistently place E in the middle.
- Step 8: Final conclusion. Option (4) E is the correct answer, as E can be in the middle.
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