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Set S and Set T both contain x elements. The average of Set

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Set S and Set T both contain x elements. The average of Set [#permalink] New post 16 Oct 2017, 08:30
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Set S and Set T both contain x elements. The average of Set S is 40. If the average of Set S and Set T combined is 50, which of the following must be true?

I. The average of Set T is 60.

II. The range of Set T is greater than that of Set S.

III. x is an even number

(A) I only

(B) I & II

(C) II only

(D) I & III

(E) All of the above


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Re: Set S and Set T both contain x elements. The average of Set [#permalink] New post 16 Oct 2017, 09:42
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We can rewrite the information we have in formulas, i.e. given the mean of set S being 40, the combined mean is computed as \(\frac{40x+?x}{2x}=50\), where ? is the mean of set T.
Doing computations, we get \(40x+?x = 100x\), thus \(?=60\). The mean of set T is 60 ans I is true.

Then, moving to the other statements, knowing the mean of the sets does not give any information about the members of the set so that we cannot infer anything about the range, so II is false. Finally, there is no reason why x should be even to get the results we have because the mean does not depend on the elements being an odd or even number, thus II is false too.

Answer A
Re: Set S and Set T both contain x elements. The average of Set   [#permalink] 16 Oct 2017, 09:42
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Set S and Set T both contain x elements. The average of Set

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