imc

Question

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?

Accepted Answer

Let'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+2z We can see that x-y+2z is greater than x-y, and so the answer is Her estimate is larger than x-y.