Difference between revisions of "2000 AMC 10 Problems/Problem 1"
(New page: 2001=1*3*667=3*23*29 1+3+667=671 3+23+29=55 1+29+69=99 1+23+87=111 Clearly, 671, or E is the largest.) |
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| − | + | ==Problem== | |
| − | + | 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>? | |
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| − | Clearly, 671, or E is the largest. | + | ==Solution== |
| + | |||
| + | <math>2001=1\cdot 3\cdot 667=3\cdot 23\cdot 29</math> | ||
| + | |||
| + | <math>1+3+667=671</math> | ||
| + | |||
| + | <math>3+23+29=55</math> | ||
| + | |||
| + | <math>1+29+69=99</math> | ||
| + | |||
| + | <math>1+23+87=111</math> | ||
| + | |||
| + | Clearly, <math>671</math>, or <math>\boxed{E}</math> is the largest. | ||
Revision as of 14:07, 7 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.
