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 integers 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>? | |
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| − | and 1+3+667=671 | + | <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 == | ||
| + | The sum is the highest if two factors are the lowest! | ||
| + | So, <math>1 \cdot 3 \cdot 667 = 2001</math> and <math>1+3+667=671</math>, (E). | ||
Revision as of 15:59, 28 July 2006
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 
, (E).
