Difference between revisions of "2011 AMC 10B Problems/Problem 10"

Revision as of 16:12, 4 June 2011

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
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All AMC 10 Problems and Solutions

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−	== Problem 10 ==	+	== Problem==

	Consider the set of numbers <math>\{1, 10, 10^2, 10^3, \ldots, 10^{10}\}</math>. 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?		Consider the set of numbers <math>\{1, 10, 10^2, 10^3, \ldots, 10^{10}\}</math>. 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?

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Difference between revisions of "2011 AMC 10B Problems/Problem 10"

Revision as of 16:12, 4 June 2011

Problem

Solution

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