Difference between revisions of "2000 AMC 12 Problems/Problem 1"
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In the year <math>2001</math>, the United States will host the [[International Mathematical Olympiad]]. Let <math> \displaystyle I,M,</math> and <math>\displaystyle O</math> be distinct [[positive integer]]s such that the product <math>I \cdot M \cdot O = 2001 </math>. What is the largest possible value of the sum <math>\displaystyle I + M + O</math>? | In the year <math>2001</math>, the United States will host the [[International Mathematical Olympiad]]. Let <math> \displaystyle I,M,</math> and <math>\displaystyle O</math> be distinct [[positive integer]]s such that the product <math>I \cdot M \cdot O = 2001 </math>. What is the largest possible value of the sum <math>\displaystyle 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> | <math> \mathrm{(A) \ 23 } \qquad \mathrm{(B) \ 55 } \qquad \mathrm{(C) \ 99 } \qquad \mathrm{(D) \ 111 } \qquad \mathrm{(E) \ 671 } </math> | ||
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== Solution == | == Solution == | ||
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==See Also== | ==See Also== | ||
* [[2000 AMC 12]] | * [[2000 AMC 12]] | ||
| − | * [[2000 AMC 12/Problem 2 | Next problem]] | + | * [[2000 AMC 12 Problems/Problem 2 | Next problem]] |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 17:40, 13 November 2006
Problem
In the year 
, 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
The sum is the highest if two factors are the lowest!
So, 
and 
.
