Study the following information carefully to answer the questions.A, B, C, D,…
2023
Study the following information carefully to answer the questions.A, B, C, D, E, F, and G are seated in a straight line facing north but not necessarily in the same order.Only three people sit between F and A. Neither F nor A sits at the extreme ends of the line.Only two people sit between A and G. E is not an immediate neighbor of either A or F.E sits third to the left of B. B is not an immediate neighbor of A. E is not an immediate neighbor of C.Who are the immediate neighbors of F?
- A.
AG
- B.
CD
- C.
DG
- D.
GB
Show answer & explanation
Correct answer: D
Concept: In a single-row seating puzzle, turn every relative clue into a seat-gap number — ‘n people between P and Q’ fixes P and Q exactly (n+1) seats apart, and ‘k-th to the left/right’ fixes an exact seat difference. Resolve the two most restrictive numeric clues first (pruned further by any ‘not at the ends’ condition) to collapse the algebra to one or two candidate layouts, then use the negative (‘not an immediate neighbour’) clues to eliminate every candidate but one.
‘Only three people sit between F and A’ fixes their gap at exactly four seats. Since neither F nor A can sit at either end of the 7-seat row, the only seat-pair four apart that keeps both away from the ends is {2, 6} — so {F, A} occupy seats 2 and 6, in either order.
‘Only two people sit between A and G’ fixes G exactly three seats from A. If A is at seat 2, G must be at seat 5 (seat −1 is invalid). If A is at seat 6, G must be at seat 3 (seat 9 is invalid). Both give two candidate layouts to test.
‘E sits third to the left of B’ gives seat(B) = seat(E) + 3, and E cannot be an immediate neighbour of A or of F. Testing the candidate with A at seat 6 and F at seat 2: the only seat left for E that avoids neighbouring both A and F is seat 4, which forces B to seat 7 — but seat 7 is immediately next to A at seat 6, breaking ‘B is not an immediate neighbour of A.’ This layout is rejected.
Testing the other candidate — A at seat 2, F at seat 6, G at seat 5 — the same reasoning again leaves only seat 4 for E (avoiding neighbours of both A and F), forcing B to seat 7. Here seat 7 is not adjacent to A at seat 2, so every clue used so far holds.
Seats 1 and 3 remain for C and D. ‘E is not an immediate neighbour of C’ rules out C at seat 3 (adjacent to E at seat 4), so C takes seat 1 and D takes seat 3.
Cross-check: The completed left-to-right order is C, A, D, E, G, F, B. Checking every original clue against it — the F–A gap (four seats), the A–G gap (three seats), neither F nor A at an end, E not neighbouring A or F, E third to the left of B, B not neighbouring A, and E not neighbouring C — all hold simultaneously, confirming this is the unique valid arrangement.
In this order, F sits at seat 6, flanked on either side by the people at seats 5 and 7.