1994 AHSME Problems/Problem 24

Revision as of 03:36, 28 May 2021 by Logsobolev (talk | contribs) (See Also)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

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 $\boxed{\textbf{(C)}\ 5}$

See Also

1994 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 23
Followed by
Problem 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS