# Problem #2269

 2269 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? $\textbf{(A)}\ \text{Her estimate is larger than }x-y$ $\textbf{(B)}\ \text{Her estimate is smaller than }x-y$ $\textbf{(C)}\ \text{Her estimate equals }x-y$ $\textbf{(D)}\ \text{Her estimate equals }y - x$ $\textbf{(E)}\ \text{Her estimate is 0}$ This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
• Numbers involving pi should be written as 7pi or 7pi/3 as appropriate.
• Square roots should be written as sqrt(3), 5sqrt(5), sqrt(3)/2, or 7sqrt(2)/3 as appropriate.
• Exponents should be entered in the form 10^10.
• If the problem is multiple choice, enter the appropriate (capital) letter.
• Enter points with parentheses, like so: (4,5)
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