2018 AMC 12B 第 15 题

Choose the hundreds digit (not $0$ or $3$) and the units digit (odd, not $3$) first

For each such pair, the allowed tens digits split evenly into three residue classes mod $3$

Write the number as $\overline{abc}.$ The hundreds digit $a$ has $8$ choices ($1,2,4,5,6,7,8,9$), and the units digit $c$ has $4$ choices ($1,5,7,9$).

The tens digit $b$ may be any of $\{0,1,2,4,5,6,7,8,9\}.$ These split into three residue classes mod $3$ of equal size $\{0,6,9\},\{1,4,7\},\{2,5,8\},$ so exactly $3$ choices of $b$ make $a+b+c$ divisible by $3.$

The count is $8\cdot4\cdot3=96.$

Thus, the correct answer is A.