smc

The problem is asking for the sum of all the even digits in the numbers $1$ to $100$. We can remove $100$ from the list, add $00$ to the list, and tack on some leading zeros to the single digit numbers without changing the sum of the even digits. This gives the list: $00,01,02,03,...,10,11,...,98,99$. There are $2\cdot 100=200$ digits on that list, and each digit appears $\frac{200}{10}=20$ times. Thus, each even digit appears $20$ times, and the sum of all the even digits is $0\cdot 20+2\cdot 20+4\cdot 20+6\cdot 20+8\cdot 20=(0+2+4+6+8)\cdot 20=400$, and the correct answer is $\boxed{400}$.