Subsets of numbers

I am coping with a rather stupid-sounding problem of which I can somehow not see whether it is obviously true or obviously false. My suspicion is that this problem is actually well-known. Maybe you know more about this.

This is the problem:
We are given a finite set S of positive reals that sum to at least 1. Is there a constant c, such that for any such set S, there exists a j and a subset S', |S'| = |S|/j such that every number in S' is at least c * 1/(j|S|)?

Any thoughts, anyone?

Try it with j = |S|, I think that simplifies the problem.

Correct. Wrong formulation of the problem. I believe I meant to ask the following:

We are given a finite set S of positive reals that sum to at least 1. Is there a constant c, such that for any such set S, there exists a j in (0,1] and a subset S', |S'| >= j|S| such that every number in S' is at least c * 1/(j|S|)?

good lord, why was anyone curious about such a byzantine supposition in the first place