2011 AMC 10B Problems/Problem 10

Problem

Consider the set of numbers $\{1, 10, 10^2, 10^3, \ldots, 10^{10}\}$. 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?

$\textbf{(A)}\ 1 \qquad\textbf{(B)}\ 9 \qquad\textbf{(C)}\ 10 \qquad\textbf{(D)}\ 11 \qquad\textbf{(E)} 101$

Solution

The sum of the other ten elements is the same as ten $1$s. $10^{10}$ is the same as $1$ followed by ten $0$s. If you subtract one, it is equal to ten $9$s. Therefore if you divide the sum of the other ten elements by the largest element, it is closest to $\boxed{\mathrm{(B) \ } 9}$

See Also

2011 AMC 10B (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
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All AMC 10 Problems and Solutions

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