Problem #1740

 1740 In order to estimate the value of $x-y$ where $x$ and $y$ are real numbers with $x > y > 0$, Xiaoli rounded $x$ up by a small amount, rounded $y$ down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct? $\textbf{(A)}$ Her estimate is larger than $x-y$ $\textbf{(B)}$ Her estimate is smaller than $x-y$ $\textbf{(C)}$ Her estimate equals $x-y$ $\textbf{(D)}$ Her estimate equals $y - x$ $\textbf{(E)}$ Her estimate is $0$ This problem is copyrighted by the American Mathematics Competitions.
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