1994 AHSME Problem 15

For how many n in \{1, 2, 3, ..., 100 \} is the tens digit of n^2 odd?

\textbf{(A)}\ 10 \qquad\textbf{(B)}\ 20 \qquad\textbf{(C)}\ 30 \qquad\textbf{(D)}\ 40 \qquad\textbf{(E)}\ 50

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