AMC 10 Mock Exam 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?
$\mathbf{(A)}$ Her estimate is larger than $x-y$
$\mathbf{(B)}$ Her estimate is smaller than $x-y$
$\mathbf{(C)}$ Her estimate equals $x-y$
$\mathbf{(D)}$ Her estimate equals $y - x$
$\mathbf{(E)}$ Her estimate is $0$
Submit your answer and solution and explanation below! Solutions will be accepted for 48 hours until 9/7 at 2pm Pacific Time.
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Note: The question above is a past AMC problem. Solutions submitted must be written by students. Copied solutions will be disqualified.