2007 AMC 8 Problem 18

The product of the two 99-digit numbers

303,\!030,\!303,\!...,\!030,\!303 and 505,\!050,\!505,\!...,\!050,\!505

has thousands digit A and units digit B. What is the sum of A and B?

\textbf{(A)}\ 3 \qquad \textbf{(B)}\ 5 \qquad \textbf{(C)}\ 6 \qquad \textbf{(D)}\ 8 \qquad \textbf{(E)}\ 10

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