$33 \cdot 60$ denotes $25_{b}$ as a two-digit number in base $b$. If $52_{b}$ is twice $25_{b}$, then $b$ equals
(A) 7.
(B) 8.
(C) 9.
(D) 11.
(E) 12.
(16th American High School Mathematics Examination, 1965)
[Solution] From the given, $25_{b}=2 b^{1}+5 b^{0}, 52_{b}=5 b^{1}+2 b^{0}$, and by the problem statement $52_{b}=2\left(25_{b}\right)$, which means $5 b+2=2(2 b+5)$, solving this gives $b=8$. Therefore, the answer is $(B)$.