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2002 AMC 10A Problems/Problem 1

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Problem

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

\text{(A)}\ 0.1 \qquad \text{(B)}\ 0.2 \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(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{\text{(D)}\ 5 }.

See Also

2002 AMC 10A (Problems • Resources)
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First question 		Followed by
Problem 2
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