1988 AJHSME Problem 25

A palindrome is a whole number that reads the same forwards and backwards. If one neglects the colon, certain times displayed on a digital watch are palindromes. Three examples are: \underline{\,1:01\,}, \underline{\,4:44\,}, and \underline{\,12:21\,}. How many times during a 12-hour period will be palindromes?

\text{(A)}\ 57 \qquad \text{(B)}\ 60 \qquad \text{(C)}\ 63 \qquad \text{(D)}\ 90 \qquad \text{(E)}\ 93

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