28-12 Li Ming and Wang Ning are doing the multiplication problem $a \cdot b$ (where $a$ and $b$ are positive integers). Li Ming mistakenly reads the unit digit of $a$ as 1 instead of 7, and gets the product 255. Wang Ning, however, misreads the tens digit of $a$ as 6 instead of 5, and gets the product 335. The correct product should be
(A) 285.
(B) 305.
(C) 375.
(D) 380.
(2nd "Five Sheep Cup" Junior High School Mathematics Competition, 1990)
[Solution 1] The last two digits of $a$ should be 57.
Li Ming mistook 7 for 1, and the product he obtained was 255, so $a=57$, and $b=255 \div 51=5$.
Wang Ning mistook 5 for 6, and the product he obtained was 335, so $a=57, b=335 \div 67=5$.
$\therefore$ The correct product is $57 \cdot 5=285$.
Therefore, the answer is $(A)$.
[Solution 2] The last two digits of $a$ should be 57, now we find $b$.
Obviously, $b$ is a common divisor of 255 and 335, and their greatest common divisor is 5, so $b=5$ or 1.
From the problem, we know $b \neq 1$, so $b=5$.
Since $a$ can only be a two-digit number, which is 57, the correct product should be $57 \cdot 5=285$. Therefore, the answer is $(A)$.