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2012 AMC 10B Question 6

AMC10 · 2012 AMC 10B

Question 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?
  1. Her estimate is larger than $x-y$
  2. Her estimate is smaller than $ x-y $
  3. Her estimate equals $x-y $
  4. Her estimate equals $ y-x $
  5. Her estimate is $ 0 $