Common Residue Systems, and Significance

Petya gave Vasya a number puzzle. Petya chose a digit $X$ and said, "I am thinking of a three digit number that is divisible by 11. The hundreds digit is $X$ and the tens digit is 3. Find the units digit." Vasya was excited because he knew how to solve this problem, but then realized that the problem Petya gave did not have an answer. What digit $X$ did Petya chose?

Source: 2012-2013 Fall Online Math Open