2012 AMC 12B Problems/Problem 6

Problem

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. Which statement is always true?

Solution

Since the original equation x-y now becomes (x+k) - (y-k), where k is a constant. so simplified, the equation becomes: x-y+2k, which is greater than x-y, hence the answer is: A.