Difference between revisions of "2012 AMC 12B Problems/Problem 6"
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Revision as of 15:57, 3 July 2013
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).
See Also
| 2012 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 5 |
Followed by Problem 7 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
