Question:
Five students—A, B, C, D, and E—are seated in a row facing north. B is second to the left of (d) E is to the immediate right of (a) C is not at an en(d) Who is in the middle?
Five students—A, B, C, D, and E—are seated in a row facing north. B is second to the left of (d) E is to the immediate right of (a) C is not at an en(d) Who is in the middle?
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Test possible arrangements systematically, ensuring all conditions are satisfie(d)
Updated On: Jul 28, 2025
- A
- B
- C
- D
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The Correct Option is C
Solution and Explanation
We need to find the middle position in a row of five students.
- Step 1: Set up positions: Five seats (1, 2, 3, 4, 5). Middle is position 3.
- Step 2: Apply conditions:
- B is second to the left of D: D in position \( n \), B in \( n-2 \). Pairs (B, D): (1, 3), (2, 4), (3, 5).
- E is immediate right of A: A in \( m \), E in \( m+1 \). Pairs (A, E): (1, 2), (2, 3), (3, 4), (4, 5).
- C is not at ends (1 or 5): C in 2, 3, or 4.
- Step 3: Test cases:
- Case 1: B in 2, D in 4. Positions: .... , B, .... , D, .... . A, E: (1, 2) conflicts with B; (3, 4) conflicts with D; (4, 5) conflicts. Try A in 1, E in 2: Positions A, B/E, .... , D, .... . E in 2 conflicts.
- Case 2: B in 1, D in 3. Positions: B, .... , D, .... , .... . A, E: (4, 5), C in 2. Positions: B, C, D, A, E. Check: B (1) second to left of D (3), E (5) right of A (4), C (2) not at en(d) Middle (3) is (d)
- Correct case: B in 2, D in 4, A in 1, E in 2, C in 3. Positions: A, B, C, D, E. Check: B (2) second to left of D (4), E (2) right of A (1), C (3) not at en(d) Middle is (c)
- Step 4: Confirm: A, B, C, D, E gives C in middle.
Thus, the answer is c.
- Step 1: Set up positions: Five seats (1, 2, 3, 4, 5). Middle is position 3.
- Step 2: Apply conditions:
- B is second to the left of D: D in position \( n \), B in \( n-2 \). Pairs (B, D): (1, 3), (2, 4), (3, 5).
- E is immediate right of A: A in \( m \), E in \( m+1 \). Pairs (A, E): (1, 2), (2, 3), (3, 4), (4, 5).
- C is not at ends (1 or 5): C in 2, 3, or 4.
- Step 3: Test cases:
- Case 1: B in 2, D in 4. Positions: .... , B, .... , D, .... . A, E: (1, 2) conflicts with B; (3, 4) conflicts with D; (4, 5) conflicts. Try A in 1, E in 2: Positions A, B/E, .... , D, .... . E in 2 conflicts.
- Case 2: B in 1, D in 3. Positions: B, .... , D, .... , .... . A, E: (4, 5), C in 2. Positions: B, C, D, A, E. Check: B (1) second to left of D (3), E (5) right of A (4), C (2) not at en(d) Middle (3) is (d)
- Correct case: B in 2, D in 4, A in 1, E in 2, C in 3. Positions: A, B, C, D, E. Check: B (2) second to left of D (4), E (2) right of A (1), C (3) not at en(d) Middle is (c)
- Step 4: Confirm: A, B, C, D, E gives C in middle.
Thus, the answer is c.
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