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 $\boxed{\mathrm{(B) \ } 9}$

2011 AMC 10B (Problems • Answer Key • Resources)
Preceded by Problem 9	Followed by Problem 11
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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2011 AMC 10B Problems/Problem 10

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