CMO 2009 Problem 6

Given an integer $n > 3.$ Prove that there exists a set $S$ consisting of $n$ pairwisely distinct positive integers such that for any two different non-empty subset of $S$ : $A,B, \frac {\sum_{x\in A}x}{|A|}$ and $\frac {\sum_{x\in B}x}{|B|}$ are two composites which share no common divisors.