Problem:
The mean, median, unique mode, and range of a collection of eight integers are all equal to 8 . The largest integer that can be an element of this collection is
Answer Choices:
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Solution:
The values satisfy the requirements of the problem, so the answer is at least 14. If the largest number were 15 , the collection would have the ordered form 7, 8,8, 15. But , and a mean of 8 implies that the sum of all values is 64 . In this case, the four missing values would sum to , and their average value would be 6.5 . This implies that at least one would be less than 7 , which is a contradiction. Therefore, the largest integer that can be in the set is .
The problems on this page are the property of the MAA's American Mathematics Competitions