2000 AMC 10 Problems/Problem 1

Problem

In the year 2001, the United States will host the International Mathematical Olympiad. Let $I$ , $M$ , and $O$ be distinct positive integers such that the product $I\cdot M\cdot O=2001$ . What is the largest possible value of the sum $I+M+O$ ?

$\mathrm{(A)}\ 23 \qquad\mathrm{(B)}\ 55 \qquad\mathrm{(C)}\ 99 \qquad\mathrm{(D)}\ 111 \qquad\mathrm{(E)}\ 671$

Solution

$2001=1\cdot 3\cdot 667=3\cdot 23\cdot 29$

$1+3+667=671$

$3+23+29=55$

$1+29+69=99$

$1+23+87=111$

Clearly, $671$ , or $\boxed{E}$ is the largest.

2000 AMC 10 (Problems • Answer Key • Resources)
Preceded by First question	Followed by Problem 2
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2000 AMC 10 Problems/Problem 1

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