Direction: Study the following information carefully and answer the question…

2019

Direction: Study the following information carefully and answer the question given below.

Eleven seats are placed in a single row in which three seats are vacant. Persons sitting in these seats face North. No two vacant seats are adjacent to each other. Persons are of different ages. Seats are numbered 1 to 11 from West to East.

Note: "Two persons sitting between P and Q" does not mean only two seats lie between them; there may be vacant seats between them.

Three persons sit between A and B. The person who is 32 years old sits immediate left of B. D and E are immediate neighbours of A, whose seat number is less than 6. B is as many years older than H as he is younger than D. C sits 3rd to the left of A. One person sits between G and F, who is 40 years old. The sum of the ages of D and G is 82. H sits immediate left of one of the vacant seats. The age of H is half the age of the person who sits at seat number 11. The persons whose ages are 26 and 28 years sit at odd-numbered seats. D sits to the left of the person whose age is 22 years and to the right of the person whose age is 28 years. No vacant seat is between H and the person whose age is 22 years.

Which of the following is true regarding C?

  1. A.

    C does not sit at seat number 1

  2. B.

    One of the vacant seats is not adjacent to C

  3. C.

    C's age is 22 years

  4. D.

    Two persons are sitting between A and C

  5. E.

    None is true

Show answer & explanation

Correct answer: B

Concept

In a linear arrangement, fix the strongest position clues first (a fixed person, a fixed gap, a 'between' count), then layer the relative clues and finally the numeric (age) clues. Because all persons face North, a person's LEFT is the lower-numbered (West) seat and RIGHT is the higher-numbered (East) seat. 'Persons between' counts only occupied seats; vacant seats are skipped.

Solving the arrangement

  1. A's seat is less than 6 and D, E are its immediate neighbours, so position alone allows A = 4 (giving C = 1) or A = 5 (giving C = 2). We carry both forward; the age clues below will eliminate A = 5, leaving A = 4 and C = 1 with D, E flanking A.

  2. Three persons sit between A (seat 4) and B; counting only occupied seats to the right places B at seat 9. The person 32 years old sits immediate left of B (seat 8), and one person sits between G and F (F = 40), which fixes G at seat 8 with age 32 and F at seat 11.

  3. H sits immediate left of a vacant seat and the age of H is half of the seat-11 person (F = 40), so H = 20 and H takes seat 6 with seat 7 vacant. The remaining vacant seats are 2 and 10 (no two vacant adjacent).

  4. Ages: F = 40, G = 32, H = 20. D + G = 82 gives D = 50; 2B = D + H gives B = 35. The 22- and 28-year-olds must sit so that D is right of the 28-year-old and left of the 22-year-old, and no vacant seat lies between H and the 22-year-old; only A = 4 satisfies all of these, fixing C = 28 (seat 1), A = 22 (seat 4) and E = 26 (seat 5), which also meets the odd-seat rule for 26 and 28. The A = 5 branch fails these age and adjacency conditions and is rejected, so the arrangement is unique.

Cross-check & result

Final row: 1 C(28), 2 vacant, 3 D(50), 4 A(22), 5 E(26), 6 H(20), 7 vacant, 8 G(32), 9 B(35), 10 vacant, 11 F(40). Every clue checks out. Now test the statements about C (seat 1, age 28): C does sit at seat 1, so 'C does not sit at seat 1' is false; C is 28, not 22; between A (4) and C (1) only seat 3 is occupied, so only one person sits between them, not two. But vacant seats 7 and 10 are not adjacent to C, so 'one of the vacant seats is not adjacent to C' is true. Hence the true statement is that one of the vacant seats is not adjacent to C.

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