1998 AHSME Problem 2

Letters A,B,C, and D represent four different digits selected from 0,1,2,\ldots ,9. If (A+B)/(C+D) is an integer that is as large as possible, what is the value of A+B?

\mathrm{(A) \ }13 \qquad \mathrm{(B) \ }14 \qquad \mathrm{(C) \ } 15\qquad \mathrm{(D) \ }16 \qquad \mathrm{(E) \ } 17

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