其它
In order to estimate the value of $x-y$ where $x$ and $y$ are real numbers with $x\textgreater y\textgreater0$, 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? (2012 AMC 10B Problem, Question \#6) 
Overseas Competition->Knowledge Point->Calculation Modules
Let\textquotesingle s define $z$ as the amount rounded up by and down by.  The problem statement tells us that Xiaoli performed the following computation: $(x+z)-(y-z)=x+z-y+z=x-y+2 z$  We can see that $x-y+2 z$ is greater than $x-y$, and so the answer is $A$. 