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Seven people, A, K, Q, D, E, F and N, are sitting in a row, facing north. D sits sixth from the right end of the row. Only three people sit between F and D. E is the immediate neighbour of Q and N. K sits second to the left of N. Who sits third to the left of A?
D
Q
E
K
E
Fix the position of the person given from the fixed end (right) first, then place others relative to the constraints provided.
Fix the position of the person given from the fixed end (right) first, then place others relative to the constraints provided.
Establish the row structure
There are 7 positions in a row facing north. D sits 6th from the right end, which means D is at the 2nd position from the left end (7 - 6 + 1 = 2). The positions are 1, D(2), 3, 4, 5, 6, 7.
Place F and identify remaining slots
Only three people sit between F and D. If D is at position 2, counting three spots (3, 4, 5), F must be at position 6 (2+4=6). Row: 1, D, 3, 4, 5, F, 7.
Solve for E, Q, N and K
E is the immediate neighbor of Q and N, meaning they sit as a block (Q-E-N or N-E-Q). K sits 2nd to the left of N. Testing placement: If N is at 5, E is at 4, and Q is at 3, then K sits at position 3 (2nd left of N), which is impossible as Q is there. If N is at 7, E is at 5, Q is at 4, then K sits at position 5, impossible. If N is at 4, E is at 3, Q is at 2(occupied), impossible. Let's re-verify: With D at 2 and F at 6, positions 1, 3, 4, 5, 7 are vacant. If N is at 5, E is 4, Q is 3, and K is 2nd to left of N (pos 3), impossible. If N is at 3, K is at 1. Then E must be 4 and Q is 5. Order: K(1), D(2), N(3), E(4), Q(5), F(6), A(7). Third to the left of A(7) is E(4).
A: D is 2nd from left. B: Q is 5th from left. D: K is 1st from left.
C is correct because placing the sequence K-D-N-E-Q-F-A satisfies all conditions, making E the 3rd person to the left of A.
In seating arrangement problems, always start by placing the person defined relative to an absolute end, then immediately map the 'neighbor' constraints.