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Average of Consecutive Integers

CAT 2000 Slot 1 · Quantitative Ability · Easy · Arithmetic

This is an easy Quantitative Ability question from the CAT 2000 Slot 1 paper. It tests Arithmetic. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Consider a sequence of seven consecutive integers. The average of the first five integers is nn. The average of all the seven integers is:

  1. A.

    nn

  2. B.

    n+1n + 1

  3. C.

    k×nk \times n, where kk is a function of nn

  4. D.

    n+(27)n + \left(\frac{2}{7}\right)

Answer

B

Explanation

Let the 7 consecutive integers be x−3,x−2,x−1,x,x+1,x+2,x+3x-3, x-2, x-1, x, x+1, x+2, x+3. The average of the first 5 integers is x−1=n  ⟹  x=n+1x-1 = n \implies x = n+1. The average of all 7 integers is x=n+1x = n+1.

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