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).
