Question 18
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 $m$ were instead replaced by $m-8,$ the median of the new list would be $m-4.$ What is $m?$