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Difference between revisions of "1997 AHSME Problems/Problem 18"

(Created page with "==Problem== A list of integers has mode <math>32</math> and mean <math>22</math>. The smallest number in the list is <math>10</math>. The median <math>m</math> of the list is a ...")
(No difference)

Revision as of 08:59, 9 August 2011

Problem

A list of integers has mode $32$ and mean $22$. The smallest number in the list is $10$. The median $m$ of the list is a member of the list. If the list member $m$ were replaced by $m+10$, the mean and median of the new list would be $24$ and $m+10$, respectively. If were $m$ instead replaced by $m-8$, the median of the new list would be $m-4$. What is $m$?

$\textbf{(A)}\ 16\qquad\textbf{(B)}\ 17\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 19\qquad\textbf{(E)}\ 20$

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