Question

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 1

891

Explanation:

`$1001$ 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$$x - y = 1001 - 110 = \boxed{891}$$`

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Answer 2

891

Explanation:

x has to be 1001 and y has to be 11 * 10 = 110 so x - y = 1001 - 110 = 891.