Question

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?

Her estimate is larger than $x-y$

Her estimate is smaller than $x-y$

Her estimate equals $x-y$

Her estimate equals $y-x$

Her estimate is $0$

Solution:

The value when $x$ is rounded up is greater than $x.$

The value when $-y$ is rounded up is greater than $-y.$

Therefore, we add two numbers which are greater than their corresponding parts in $x-y,$ making it greater.

Thus, the correct answer is A .

2012 AMC 10B Problem 6

Solution:

Problem 6 in Other Years