AMC 8 1988 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: $\boxed{1:01}$, $\boxed{4:44}$, and $\boxed{12:21}$. How many times during a $12$-hour period will be palindromes? $\text{(A)}\ 57 \text{(B)}\ 60 \text{(C)}\ 63 \text{(D)}\ 90 \text{(E)}\ 93$