Difference between revisions of "2012 AMC 12B Problems/Problem 6"
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| − | The original expression <math>x-y</math> now becomes <math>(x+k) - (y-k)=(x-y)+2k> | + | The original expression <math>x-y</math> now becomes <math>(x+k) - (y-k)=(x-y)+2k>x-y</math>, where <math>k</math> is a positive constant, hence the answer is '''(A)'''. |
Revision as of 23:50, 27 February 2012
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).
