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2000 AMC 12 Problems/Problem 1

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The following problem is from both the 2000 AMC 12 #1 and 2000 AMC 10 #1, so both problems redirect to this page.

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?

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

Solution

The sum is the highest if two factors are the lowest.

So, 1 \cdot 3 \cdot 667 = 2001 and 1+3+667=671 \Longrightarrow \boxed{\text{(E)}}.

See Also

2000 AMC 12 (ProblemsResources)
Preceded by
First
Question
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
2000 AMC 10 (ProblemsResources)
Preceded by
First
Question
Followed by
Problem 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Want to learn how to tackle those tough MATHCOUNTS and AMC counting and probability problems? Check out Art of Problem Solving's Introduction to Counting & Probability by David Patrick.
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