2002 AMC 10A Problems/Problem 1

Problem

The ratio $\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ is closest to which of the following numbers?

$\textbf{(A)}\ 0.1 \qquad \textbf{(B)}\ 0.2 \qquad \textbf{(C)}\ 1 \qquad \textbf{(D)}\ 5 \qquad \textbf{(E)}\ 10$

Solution

We factor $\frac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}$ as $\frac{10^{2000}(1+100)}{10^{2001}(1+1)}=\frac{101}{20}$ . As $\frac{101}{20}=5.05$ , our answer is $\boxed{\textbf{(D)}\ 5 }$ .

2002 AMC 10A (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

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2002 AMC 10A Problems/Problem 1

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