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Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte
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Bunuel
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Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte [#permalink] New post  01 Jan 2020, 02:08
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Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

(A) 0
(B) 1
(C) 2008
(D) n/2
(E) (n + 1)/(2n)
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Re: Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte [#permalink] New post  01 Jan 2020, 05:23
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Take smaller values of n, such as n=5 or n=6.

Notice that n=5 => X=7,Y=6
n=6 => X=8, Y=7.

As we can see, X=n+2 and Y=n+1.

Hence, X-Y = 1.

Option B
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Re: Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte [#permalink] New post  01 Jan 2020, 05:41
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Even set = {2,4,6,8,...2n}
Odd set = {3,5,7,9,...2n+1}

By property, if a certain number x is added to all elements of a set, the average of the set increases by x

By this property, since the odd set is just the even set with 1 added to all elements, the average of the odd set must be 1 greater than the average of the even set

So X-Y=1

Answer is (B)

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Re: Consider the set S = {2, 3, 4, ...., 2n+1), where n is a positive inte [#permalink]
01 Jan 2020, 05:41
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