10.1. What two digits need to be appended to the right of the number 2013 so that the resulting six-digit number is divisible by 101? Find all possible solutions.
Answer: 94, the obtained number will be equal to 201394.

Solution: The remainder of dividing the number $\overline{2013 x y}$ by 101 is $\overline{x y}+7$ and this must be divisible by 101. This is greater than 0 but less than 202, so $\overline{x y}+7=101, \overline{x y}=94, x=9, y=4$.

Grading: Just the answer with verification: 1 point. Failure to justify $\overline{x y}+7=101$ minus points.