1991 AJHSME Problems/Problem 19
Problem
The average (arithmetic mean) of different positive whole numbers is . The largest possible value of any of these numbers is
Solution
If the average of the numbers is , then their sum is .
To maximize the largest number of the ten, we minimize the other nine. Since they must be distinct, positive whole numbers, we let them be . Their sum is .
The sum of nine of the numbers is , and the sum of all ten is so the last number must be .
See Also
1991 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 18 |
Followed by Problem 20 | |
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