Answer:
891
Step-by-step explanation:
[tex]$1001$ 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$x - y = 1001 - 110 = \boxed{891}$[/tex]
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