30-36 If the square of a two-digit number is subtracted from the square of the number obtained by reversing its digits, the difference is usually not divisible by
(A) 9.
(B) the product of the two digits.
(C) the sum of the two digits.
(D) the difference of the two digits.
(E) 11.
(8th American High School Mathematics Examination, 1957)
［Solution］Let this two-digit number be $10 m+n$. Notice that
$$
\begin{aligned}
& (10 m+n)^{2}-(10 n+m)^{2} \\
= & {[(10 m+n)+(10 n+m)][(10 m+n)-(10 n+m)] } \\
= & 99(m+n)(m-n) .
\end{aligned}
$$

Therefore, the correct choice is $(B)$.