2011 AMC 10A Problem 13

Since the hundreds digit can only be a $2$ or $5,$ we can case on this value. Case $1:$ hundreds digit is $2$ The only option for the units digit is $8,$ since the number must be even. This leaves $4$ options for the tens digit. This gives us $1 \cdot 4 = 4$ numbers for this case. Case $2:$ hundreds digit is $5$ Similarly to above, $2$ and $8$ are the only options for the units digit, leaving $4$ options for the tens digit. This gives us $2 \cdot 4 = 8$ numbers for this case. The total number of integers is then $4 + 8 = 12.$ Thus, A is the correct answer.