In the addition problem, each digit has been replaced by a letter.  If different letters represent different digits then what is the value of $C$?

$\text{(A)}\ 1 \qquad \text{(B)}\ 3 \qquad \text{(C)}\ 5 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 9$
From this we have 
\[111A+11B+C=300.\]
Clearly, $A 201 \Rightarrow A\geq 2.\]
Thus, $A=2$ and $11B+C=78$.  From here it becomes clear that $B=7$ and $C=1\rightarrow \boxed{\text{A}}$.