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# Pre-RMO 2014/8

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

Note by Pranshu Gaba
3 years ago

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- 3 years ago

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

- 2 years, 11 months ago

ans is 4.

- 2 years ago

4

- 2 years, 5 months ago

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

- 2 years, 10 months ago