1998 AIME Problems/Problem 14
Problem
An rectangular box has half the volume of an rectangular box, where and are integers, and What is the largest possible value of ?
Solution
Let’s solve for :
Clearly, we want to minimize the denominator, so we test . The possible pairs of factors of are . These give and respectively. Substituting into the numerator, we see that the first pair gives , while the second pair gives . We now check that is optimal, setting , in order to simplify calculations. Since We have Where we see gives us our maximum value of .
- Note that assumes , but this is clear as and similarly for .
See also
1998 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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