In a complex linear arrangement, seven people A, B, C, D, E, F, and G sit in a straight line facing north. B sits third to the left of G. D sits second to the right of C. A is neither at an end nor adjacent to D. If F sits to the immediate left of B, who sits at the extreme right end?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → D
Note: The given answer is as per the official NTA Answer Key. However, the question has two possible answers, i.e. both Option (1) and Option (2), as explained below.
All seven face North, so left and right are the same for everyone, and the seats can be numbered 1 to 7 from the left.
Placing F, B and G:
F is to the immediate left of B, and B is third to the left of G, so F, B and G sit in seats \(n\), \(n+1\) and \(n+4\)
G needs a seat from 5 to 7, so G can be in seat 5, 6 or 7
Placing C, D and A in each case (D is second to the right of C; A is at neither end and not next to D):
G in seat 7: F, B and G take seats 3, 4 and 7; the free seats 1, 2, 5 and 6 have no pair two apart, so C and D cannot be placed
G in seat 6: F, B and G take seats 2, 3 and 6:
The free seats are 1, 4, 5 and 7, and the only pair two apart is 5 and 7, so C is in seat 5 and D in seat 7
A, not at an end, takes seat 4 (not next to D), and E takes seat 1
The person at the right end is D (Option 1)
G in seat 5: F, B and G take seats 1, 2 and 5:
The free seats are 3, 4, 6 and 7, and the only pair two apart is 4 and 6, so C is in seat 4 and D in seat 6
A, not at an end, takes seat 3 (not next to D), and E takes seat 7
The person at the right end is E (Option 2)
Tip for students: When a question has two possible answers, mark the one you worked out yourself. If NTA’s answer key gives a different answer, challenge it when NTA opens the window for challenges.