$1001$ is the smallest integer greater than $1000$. It also happens to be a multiple of $11$, since $1001 = 11 \cdot 91$. So $1001$ is the smallest multiple of $11$ greater than $1000$ and thus $x = 1001$.

The greatest multiple of $11$ that is less than $11^2 = 11 \cdot 11$ is  $$11 \cdot (11 - 1) = 11 \cdot 10 = 110$$Thus $y = 110$, and we compute $$x - y = 1001 - 110 = \boxed{891}$$
Let $x$ be the smallest multiple of $11$ that is greater than $1000$ and $y$ be the greatest multiple of $11$ less than $11^2$.  Compute $x - y$.
{'answer': '891', 'subject': 'Prealgebra', 'level': 3, 'unique_id': 'test/prealgebra/1054.json'}