1994 AHSME Problems/Problem 24

Problem

A sample consisting of five observations has an arithmetic mean of $10$ and a median of $12$. The smallest value that the range (largest observation minus smallest) can assume for such a sample is

$\textbf{(A)}\ 2 \qquad\textbf{(B)}\ 3 \qquad\textbf{(C)}\ 5 \qquad\textbf{(D)}\ 7 \qquad\textbf{(E)}\ 10$

Solution

The minimum range occurs in the set $\{7,7,12,12,12\}$, so the answer is $\boxed{\textbf{(C)}\ 5}$

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