Difference between revisions of "2000 AMC 10 Problems/Problem 1"
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In the year 2001, the United States will host the International Mathematical Olympiad. Let <math>I</math>, <math>M</math>, and <math>O</math> be distinct positive integers such that the product <math>I\cdot M\cdot O=2001</math>. What is the largest possible value of the sum <math>I+M+O</math>? | In the year 2001, the United States will host the International Mathematical Olympiad. Let <math>I</math>, <math>M</math>, and <math>O</math> be distinct positive integers such that the product <math>I\cdot M\cdot O=2001</math>. What is the largest possible value of the sum <math>I+M+O</math>? | ||
| + | |||
| + | <math>\mathrm{(A)}\ 23 \qquad\mathrm{(B)}\ 55 \qquad\mathrm{(C)}\ 99 \qquad\mathrm{(D)}\ 111 \qquad\mathrm{(E)}\ 671</math> | ||
==Solution== | ==Solution== | ||
Revision as of 18:44, 8 January 2009
Problem
In the year 2001, the United States will host the International Mathematical Olympiad. Let 
, 
, and 
be distinct positive integers such that the product 
. What is the largest possible value of the sum 
?
Solution
Clearly, 
, or 
is the largest.
See Also
| 2000 AMC 10 (Problems • Answer Key • Resources) | ||
| 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 | ||
| All AMC 10 Problems and Solutions | ||
