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Arithmetic Sequence Terms Divisibility

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Algebra

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x,17,3x−y2−2x, 17, 3x - y^2 - 2, and 3x+y2−303x + y^2 - 30, are four consecutive terms of an increasing arithmetic sequence.

The sum of the four number is divisible by:

  1. A.

    2

  2. B.

    3

  3. C.

    5

  4. D.

    7

  5. E.

    11

Answer

A

Explanation

Let common difference be dd. d=17−x=(3x−y2−2)−17=(3x+y2−30)−(3x−y2−2)d = 17 - x = (3x - y^2 - 2) - 17 = (3x + y^2 - 30) - (3x - y^2 - 2). Solving these equations yields x=13x = 13 and y2=16y^2 = 16. The terms are 13,17,21,2513, 17, 21, 25. Sum =13+17+21+25=76= 13 + 17 + 21 + 25 = 76, which is divisible by 2.

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