2012 AMC 12B Problems/Problem 6
Contents
[hide]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?
Solution
The original expression now becomes , where is a positive constant, hence the answer is .
Solution 2
The problem never says what and are, so we can decide what they are. Let and . We round to and to . Then the new , while the original . Thus, the new is greater than the original . The answer is . ~Extremelysupercooldude
See Also
2012 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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All AMC 12 Problems and Solutions |
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