Let \(S\) be the set of real numbers with mean \(M\). If the means of the set \(S \cup \{ 15\}\) and \(S \cup \{ 15, 1\}\) are \(M + 2\) and \(M + 1\) respectively, then how many elements does \(S\) have?

This note is part of the set Pre-RMO 2014

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TopNewestAnswer is 4.

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HOW ????????????????????

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ans is 4.

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4

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the answer is 4 . equations are y/x=m y+15/x+1=m+2 y+16/x+2=m+1 where y is the sum of numbers and x is the number of elements. thus solving them , we get x=4

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