2012 AMC 12B Problems/Problem 6
Problem
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 .
Solution
The original expression now becomes
, where
is a positive constant, hence the answer is (A).