In the addition shown below $A$, $B$, $C$, and $D$ are distinct digits. How many different values are possible for $D$?
\[\begin{tabular}{cccccc}&A&B&B&C&B\\ +&B&C&A&D&A\\ \hline &D&B&D&D&D\end{tabular}\]
$\textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 8\qquad\textbf{(E)}\ 9$
From the first column, we see $A+B < 10$ because it yields a single digit answer.  From the fourth column, we see that $C+D$ equals $D$ and therefore $C = 0$.  We know that $A+B = D$.  Therefore, the number of values $D$ can take is equal to the number of possible sums less than $10$ that can be formed by adding two distinct natural numbers.  Letting $A=1$, and letting $B=2,3,4,5,6,7,8$, we have 
\[D = 3,4,5,6,7,8,9 \implies \boxed{\textbf{(C)}\ 7}\]