Difference between revisions of "2012 AMC 12B Problems/Problem 6"
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== Problem== | == Problem== | ||
| − | In order to estimate the value of x-y where x and y are real numbers with x | + | In order to estimate the value of x-y where x and y are real numbers with x>y>0. Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted. Which statement is always true? |
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| + | ==Solution== | ||
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| + | Since the original equation x-y now becomes (x+k) - (y-k), where k is a constant. so simplified, the equation becomes: x-y+2k, which is greater than x-y, hence the answer is: A. | ||
Revision as of 21:26, 23 February 2012
Problem
In order to estimate the value of x-y where x and y are real numbers with x>y>0. Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted. Which statement is always true?
Solution
Since the original equation x-y now becomes (x+k) - (y-k), where k is a constant. so simplified, the equation becomes: x-y+2k, which is greater than x-y, hence the answer is: A.
