2001 AMC 8 Problems/Problem 21
Problem
The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is
Solution
Since there is an odd number of terms, the median is the number in the middle, specifically, the third largest number is , and there are numbers less than and numbers greater than . The sum of these integers is , since the mean is . To make the largest possible number with a given sum, the other numbers must be as small as possible. The two numbers less than must be positive and distinct, so the smallest possible numbers for these are and . The number right after also needs to be as small as possible, so it must be . This means that the remaining number, the maximum possible value for a number in the set, is .
See Also
2001 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
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