2001 AMC 8 Problem 21

The mean of a set of five different positive integers is 15. The median is 18. The maximum possible value of the largest of these five integers is

\text{(A)}\ 19 \qquad \text{(B)}\ 24 \qquad \text{(C)}\ 32 \qquad \text{(D)}\ 35 \qquad \text{(E)}\ 40

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.