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Subsets and Means

Source: 2015 AMC 8 #13

November 25, 2015

Problem Statement

How many subsets of two elements can be removed from the set {1,2,3,4,5,6,7,8,9,10,11}\{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} so that the mean (average) of the remaining numbers is 6?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 6<span class='latex-bold'>(A)</span>\text{ 1}\qquad<span class='latex-bold'>(B)</span>\text{ 2}\qquad<span class='latex-bold'>(C)</span>\text{ 3}\qquad<span class='latex-bold'>(D)</span>\text{ 5}\qquad<span class='latex-bold'>(E)</span>\text{ 6}
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