1995 AHSME Problem 25

A list of five positive integers has mean 12 and range 18. The mode and median are both 8. How many different values are possible for the second- largest element of the list?

\mathrm{(A) \ 4 } \qquad \mathrm{(B) \ 6 } \qquad \mathrm{(C) \ 8 } \qquad \mathrm{(D) \ 10 } \qquad \mathrm{(E) \ 12 }

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