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P20 [Algebra] - Turkish NMO 1st Round - 2001

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April 20, 2014

Problem Statement

If the sum of any 1010 of 2121 real numbers is less than the sum of remaining 1111 of them, at least how many of these 2121 numbers are positive?
<spanclass=′latex−bold′>(A)</span> 18<spanclass=′latex−bold′>(B)</span> 19<spanclass=′latex−bold′>(C)</span> 20<spanclass=′latex−bold′>(D)</span> 21<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 18 \qquad<span class='latex-bold'>(B)</span>\ 19 \qquad<span class='latex-bold'>(C)</span>\ 20 \qquad<span class='latex-bold'>(D)</span>\ 21 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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