Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west.…

2014

Ten students A, B, C, D, E, F, G, H, I and J are sitting in a row facing west. B and F are not sitting on either of the edges; G is sitting to the left of D and H is sitting to the right of J; There are four persons between E and A; I is to the north of B and F is to the South of D; J is between A and D and G is between E and F. There are two persons between H and C.

If G and A interchange their positions then who become immediate neighbours of E?

  1. A.

    G & F

  2. B.

    F only

  3. C.

    A only

  4. D.

    F & A

Attempted by 7 students.

Show answer & explanation

Correct answer: C

Concept

In a linear seating arrangement where everyone faces the same direction, a clue given in compass terms (north/south) must first be converted into the same left/right frame as the other clues, using the shared facing direction: turning 90 degrees clockwise from the direction everyone faces gives everyone's shared right hand. Once every clue speaks the same left-right language, the 'between' and 'edge' clues fix the row order, and any interchange of two seats is resolved by finding who newly occupies the seat next to the person being asked about.

Application

  1. Since every student faces west, each one's right hand points north and left hand points south (turning 90 degrees clockwise from facing west lands on north). So 'I is to the north of B' becomes 'I is to the right of B', and 'F is to the South of D' becomes 'F is to the left of D'.

  2. G is between E and F, and both G (given directly) and F (translated above) sit to the left of D -- so E, G and F form one ordered block, entirely to the left of D, with G sandwiched between the other two.

  3. B and F can never occupy an edge seat, but E carries no such restriction -- so within the E/G/F block, E (not F) must be the one touching the row's edge; the block reads E, then G, then F from that edge inward.

  4. J sits between A and D, and H sits to the right of J -- so D, J, A and H form a chain to the right of the E-G-F block, in that relative order from left to right.

  5. The 'four persons between E and A' clue fixes the gap: with E anchored at the row's left edge, A must sit exactly five seats to its right.

  6. Filling in D (to the right of both G and F) and J (between A and D) gives the order E, G, F, D, J, A for the first six seats.

  7. The remaining clues -- 'two persons between H and C' together with 'I to the right of B' -- place B and I next to each other in seats 8 and 9 (with I to the right of B), and put C and H three seats apart at the two ends of what remains (seats 7 and 10); the given clues do not further distinguish which of C or H takes which end, but neither placement disturbs the seats already fixed for G and A, so it does not affect the answer to this question.

Cross-check

  • Edge check: B sits eighth and F sits third from the left -- neither occupies seat 1 or seat 10, matching the first clue.

  • Between-count check: E (seat 1) and A (seat 6) have G, F, D and J sitting between them -- exactly four people, as required.

  • Gap check: H (seat 10) and C (seat 7) have B and I sitting between them -- exactly two people, as required.

With every clue satisfied, one fully consistent row (left to right) is E, G, F, D, J, A, C, B, I, H (swapping the positions of C and H also satisfies every clue and does not change what follows). Now interchange G (seat 2) and A (seat 6): the row becomes E, A, F, D, J, G, C, B, I, H. E still sits at the extreme left end, so it has only one neighbouring seat -- the one immediately to its right, now occupied by A.

Therefore, after G and A exchange seats, A alone becomes the immediate neighbour of E.

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