Consider the set S={2,3,4......2n+1}, where n is a positive integer larger than 2007. Define X as the average of odd integers in S and Y as the average of the even integers in S. What is the value of X-Y?

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1/2n

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2008

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Solution

The correct option is A
1

The question is independent of n, which is shown below.

Take n=1. Then S= {2,3}. X=3 and Y=2. X-Y=1

Also, the number of odd and even numbers in the set are equal. If we take two consecutive numbers at a time, their difference will be 1.
The sum of all such differences, when divided by the no. of odd or even numbers will yield the result as 1.

Hence you can directly mark the answer as option (a).

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