2002 AMC 10A Problem 1

Attempt Problem 1 of the 2002 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2002 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

The ratio

\dfrac{10^{2000}+10^{2002}}{10^{2001}+10^{2001}}

is closest to which of the following numbers?

0.1

0.2

1

5

10

Factor

10^{2000}

out of the numerator

The denominator equals

2\cdot 10^{2001}

Factoring gives

\dfrac{10^{2000}(1+100)}{2\cdot 10^{2001}}=\dfrac{101}{20}=5.05,

which is closest to

5.

Thus, the correct answer is D.

Problem 1 in other years