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2002 AMC 10A Problem 1

Problem 1 of 25EasierArithmetic

The ratio 102000+102002102001+102001\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}} is closest to which of the following numbers?

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Solution

Factoring gives 102000(1+100)2⋅102001=10120=5.05,\dfrac{10^{2000}(1+100)}{2\cdot 10^{2001}}=\dfrac{101}{20}=5.05, which is closest to 5.5. Thus, the correct answer is D.
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