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AMC 10 Mock Exam Discussion for 9/5: Question 6

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AMC 10 Mock Exam Discussion for 9/5: Question 6
by John Lensmire - Tuesday, September 5, 2023, 2:02 PM

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.

Top solutions for all the Mock Exam questions will be collected and shared as part of a full 25 Question Mock AMC 10 Exam.

Note: The question above is a past AMC problem. Solutions submitted must be written by students. Copied solutions will be disqualified.