MathDB
Estimating x-y

Source: 2012 AMC10B Problem #6

February 23, 2012
AMC

Problem Statement

In order to estimate the value of xyx-y where xx and yy are real numbers with x>y>0x>y>0, Xiaoli rounded xx up by a small amount, rounded yy down by the same amount, and then subtracted her values. Which of the following statements is necessarily correct?
<spanclass=latexbold>(A)</span> Her estimate is larger than xy<spanclass=latexbold>(B)</span> Her estimate is smaller than xy<spanclass=latexbold>(C)</span> Her estimate equals xy<spanclass=latexbold>(D)</span> Her estimate equals yx<spanclass=latexbold>(E)</span> Her estimate is 0 <span class='latex-bold'>(A)</span>\ \text{Her estimate is larger than }x-y\\ <span class='latex-bold'>(B)</span>\ \text{Her estimate is smaller than }x-y\\ <span class='latex-bold'>(C)</span>\ \text{Her estimate equals }x-y\\ <span class='latex-bold'>(D)</span>\ \text{Her estimate equals }y-x\\ <span class='latex-bold'>(E)</span>\ \text{Her estimate is }0