1995 AHSME Problems/Problem 25
Problem
A list of five positive integers has mean and range . The mode and median are both . How many different values are possible for the second largest element of the list?
Solution
Let be the smallest element, so is the largest element. Since the mode is , at least two of the five numbers must be . The last number we denote as .
Then their average is . Clearly . Also we have . Thus there are a maximum of values of which corresponds to values of ; listing shows that all such values work. The answer is .
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
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Followed by Problem 26 | |
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