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 $A$. 
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) 

a. Her estimate is larger than $x-y$ 
b. Her estimate is smaller than $x-y$ 
c. Her estimate equals $x-y$ 
d. Her estimate equals $y-x$ 
e. Her estimate is $0$ 