Read the given instructions carefully and answer the questions: A certain…

2025

Read the given instructions carefully and answer the questions:

A certain number of persons are sitting in a row facing north. Three persons sit between A and B. C sits second to the right of B. D sits fifth to the left of C. Two persons sit between D and E. The number of persons sit between D and C is one more than the number of persons sit between D and F. No one sits to the left of F. The position of A with respect to F is same as the position of C with respect to G. As many persons sit to the left of F as to the right of C.

Who among the following sits third to the left of G?

  1. A.

    B

  2. B.

    E

  3. C.

    A

  4. D.

    C

  5. E.

    D

Attempted by 6 students.

Show answer & explanation

Correct answer: C

Concept

In a single row facing north, each person's right is toward the higher-numbered (eastern) end and their left is toward the lower-numbered (western) end. Translate every clue into a position relation: "k persons sit between X and Y" means their positions differ by k+1; "X is nth to the right of Y" means X is exactly n seats higher than Y; "no one to the left of F" fixes F at the extreme left.

Application

Number the seats 1 (far left) to 10 (far right) and place each clue in turn:

  1. C sits second to the right of B and D is fifth to the left of C, so the three stay rigidly linked: D = C - 5 and B = C - 2.

  2. D and C are 5 seats apart, so 4 persons sit between them; this is one more than the persons between D and F, giving 3 persons between D and F, i.e. F is 4 seats from D.

  3. "No one sits to the left of F" puts F at seat 1, and "as many persons to the left of F as to the right of C" gives 0 = 0, making C the extreme right. Anchoring F at seat 1 then forces D = 5 and C = 10.

  4. Three persons between A and B fixes A at seat 4 (the placement consistent with F on the far left), and two persons between D and E places E at seat 2.

  5. A is 3 seats to the right of F; the clue "A with respect to F is the same as C with respect to G" means C is 3 seats to the right of G, so G sits at seat 7.

Final row (left to right): F(1), E(2), _(3), A(4), D(5), _(6), G(7), B(8), _(9), C(10).

Cross-check

Counting three seats to the left of G (seat 7) lands on seat 4, which is occupied by A. Re-reading every clue against this row confirms it: A and B differ by 4 (3 between), C = B + 2, D = C - 5, D and E differ by 3, F is at the extreme left, and the F/C symmetry holds. Hence the person third to the left of G is A.

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