Difference between averages of odd and even numbers in a set

CAT 2007 Slot 1 · QA · Easy · Averages

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Consider the set S={2,3,4,…,2n+1}S = \{2, 3, 4, \dots, 2n + 1\}, where 'nn' is a positive integer larger than 20072007. Define XX as the average of the odd integers in SS and YY as the average of the even integers in SS. What is the value of X−YX - Y?

  1. A.

    0

  2. B.

    1

  3. C.

    \frac{1}{2}n

  4. D.

    \frac{n+1}{2n}

  5. E.

    2008

Answer

B

Explanation

Sum of odd integers in set S=n(n+2)S = n(n + 2). Average X=n+2X = n + 2. Sum of even integers in set S=n(n+1)S = n(n + 1). Average Y=n+1Y = n + 1. Therefore, X−Y=(n+2)−(n+1)=1X - Y = (n + 2) - (n + 1) = 1.

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