2003 AMC 10B Problem 22

A clock chimes once at 30 minutes past each hour and chimes on the hour according to the hour. For example, at 1 \text{PM} there is one chime and at noon and midnight there are twelve chimes. Starting at 11:15 \text{AM} on \text{February 26, 2003}, on what date will the 2003\text{rd} chime occur?

\textbf{(A) } \text{March 8} \qquad\textbf{(B) } \text{March 9} \qquad\textbf{(C) } \text{March 10} \qquad\textbf{(D) } \text{March 20} \qquad\textbf{(E) } \text{March 21}

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