2010 AMC 12B Problems/Problem 14
Contents
Problem 14
Let , , , , and be positive integers with and let be the largest of the sum , , and . What is the smallest possible value of ?
Solution 1
We want to try make , , , and as close as possible so that , the maximum of these, is smallest.
Notice that . In order to express as a sum of numbers, we must split up some of these numbers. There are two ways to do this (while keeping the sum of two numbers as close as possible): or . We see that in both cases, the value of is , so the answer is .
Solution 2
Since , , and , we have that . Hence, , or .
For the values , , so the smallest possible value of is . The answer is (B).
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See also
2010 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 13 |
Followed by Problem 15 |
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