AMC 12 2012b Problem 6

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}