# 2012 AMC 10B Problems/Problem 6

## 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?

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

## Solutions

Say Z=is the amount rounded up by and down by.

*Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values*.

Which translates to:

==

This is 2Z bigger than the original amount of .

Therefore, her estimate is larger than

or