$33 \cdot 73$ In decimal, the number $526=5 \cdot 10^{2}+2 \cdot 10+6$. In a certain kingdom, counting is based on $r$, i.e., base $r$. A person there buys a car for 440 currency units (abbreviated as m.u.), gives the seller $1000 \mathrm{~m}$. u., and gets back $340 \mathrm{~m} . \mathrm{u}$. Then $r$ is
(A) 2 .
(B) 5 .
(C) 7 .
(D) 8 .
(E) 12 .
(12th American High School Mathematics Examination, 1961)
［Solution］Given in the country 1000m.u. $-440 \mathrm{~m} . \mathrm{u} .=340 \mathrm{~m} . \mathrm{u}$. By the definition of base $r$, we have
$$
1 \cdot r^{3}+0 \cdot r^{2}+0 \cdot r+0-\left(4 r^{2}+4 r+0\right)=3 r^{2}+4 r+0 \text {. }
$$

This simplifies to $r^{3}-7 r^{2}-8 r=0$ or $r^{2}-7 r-8=0$, yielding $r=8$ or -1 (discard -1).
Therefore, the answer is $(D)$.