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Ratio of elements in a set

Source: AMC 10 2011 b Problem 10

February 24, 2011
ratioAMC

Problem Statement

Consider the set of numbers {1,10,102,103,...1010}\{1,10,10^2,10^3, ... 10^{10} \}. The ratio of the largest element of the set to the sum of the other ten elements of the set is closest to which integer?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 9<spanclass=′latex−bold′>(C)</span> 10<spanclass=′latex−bold′>(D)</span> 11<spanclass=′latex−bold′>(E)</span> 101 <span class='latex-bold'>(A)</span>\ 1 \qquad <span class='latex-bold'>(B)</span>\ 9 \qquad <span class='latex-bold'>(C)</span>\ 10 \qquad <span class='latex-bold'>(D)</span>\ 11 \qquad <span class='latex-bold'>(E)</span>\ 101
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