Read the given information carefully and answer the questions that follow.…
2024
Read the given information carefully and answer the questions that follow.
Eleven friends X, Y, Z, A, B, C, D, E, F, G, and H are sitting in the first row of the stadium watching a cricket match.
E is to the immediate left of A and third to the right of F.
G is the immediate neighbour of X and Y and third to the left of D.
X is the second to the right of B, who is at one of the ends.
C is sitting next to the right of A and A is second to the right of Z.
If B and A, Z and Y, X and E, and H and C interchange their positions then which of the following pairs of friends is sitting at the ends?
- A.
A and B
- B.
B and C
- C.
A and H
- D.
H and C
Attempted by 5 students.
Show answer & explanation
Correct answer: C
Concept
In a single-row seating puzzle, first anchor the clues that fix an exact position — an occupant placed "at one of the ends", and clues stated as a fixed count from another person (e.g. second/third to the right or left of X). Once a few positions are pinned this way, relative clues ("immediate left of", "neighbour of") fix the remaining people one at a time, because each such clue only has one open slot left to satisfy it. The completed row is then just a list of position numbers 1 to 11; applying any stated interchange of two people means swapping the two numbers those people hold.
Application
B sits at one of the two ends, and X is second to the right of B. Only B = position 1 keeps X's position (3) within the row of 11, so B = 1 and X = 3.
G is the immediate neighbour of both X and Y, so G sits between X and Y. Testing G = 2 forces Y = 1, which is already B's seat, so G = 4 and Y = 5.
G is third to the left of D, so D = G + 3 = 7.
E is immediate left of A (A = E + 1), C is next to the right of A (C = A + 1), A is second to the right of Z (Z = A − 2), and E is third to the right of F (E = F + 3), so Z, E, A, C sit at F + 2, F + 3, F + 4, F + 5 respectively.
The only unused positions are 2, 6, 8, 9, 10, 11. Setting F = 6 places Z = 8, E = 9, A = 10, C = 11 — all inside that set — leaving position 2 for H, the one person left over.
The completed row (positions 1 to 11) is: B, H, X, G, Y, F, D, Z, E, A, C.
Apply the four stated interchanges to this row: B (1) swaps with A (10); Z (8) swaps with Y (5); X (3) swaps with E (9); H (2) swaps with C (11).
The row after the interchanges becomes: A, C, E, G, Z, F, D, Y, X, B, H — so position 1 is A and position 11 is H.
Cross-check
Re-tracing each of the four swaps independently against the original row confirms the same result: the person originally at position 1 (B) and the person originally at position 10 (A) exchange seats, so A now occupies position 1; the person originally at position 2 (H) and the person originally at position 11 (C) exchange seats, so H now occupies position 11. Both end seats are therefore held by A and H.
Hence, A and H are the pair of friends sitting at the ends after the interchanges.