# 1991 AJHSME Problems/Problem 19

## Problem

The average (arithmetic mean) of $10$ different positive whole numbers is $10$. The largest possible value of any of these numbers is

$\text{(A)}\ 10 \qquad \text{(B)}\ 50 \qquad \text{(C)}\ 55 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 91$

## Solution

If the average of the numbers is $10$, then their sum is $10\times 10=100$.

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 $1,2,3,4,5,6,7,8,9$. Their sum is $45$.

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