2003 AMC 10B Problem 25

How many distinct four-digit numbers are divisible by $3$ and have $23$ as their last two digits?

$\textbf{(A) } 27 \qquad\textbf{(B) } 30 \qquad\textbf{(C) } 33 \qquad\textbf{(D) } 81 \qquad\textbf{(E) } 90$

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