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

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. – Ar Agarwal · 2 years, 9 months ago

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– Rohit Nair · 2 years, 9 months ago

HOW ????????????????????Log in to reply

ans is 4. – Kishan Chaudhary · 1 year, 9 months ago

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4 – Sahil Nare · 2 years, 2 months ago

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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 – Ärnäv Mändäl · 2 years, 8 months ago

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