2012 AMC 12B Problems/Problem 6
In order to estimate the value of where and are real numbers with , Xiaoli rounded up by a small amount, rounded down by the same amount, and then subtracted her rounded values. Which of the following statements is necessarily correct?
(A) Her estimate is larger than .
(B) Her estimate is smaller than .
(C) Her estimate equals .
(D) Her estimate equals .
(E) Her estimate is .
The original expression now becomes , where is a positive constant, hence the answer is (A).