Difference between revisions of "2012 AMC 10B Problems/Problem 6"
(Created page with "== Problem 6 == 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, an...") |
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<math>(X+Z)-(Y-Z)</math>=<math>X+Z-Y+Z</math>=<math>X+2Z-Y</math> | <math>(X+Z)-(Y-Z)</math>=<math>X+Z-Y+Z</math>=<math>X+2Z-Y</math> | ||
| − | This is 2Z bigger than the original amount of <math>X-Y</math>. | + | This is <math>2Z</math> bigger than the original amount of <math>X-Y</math>. |
Therefore, her estimate is larger than <math>X-Y</math> | Therefore, her estimate is larger than <math>X-Y</math> | ||
| − | |||
or | or | ||
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<math> \textbf{(A)}</math> | <math> \textbf{(A)}</math> | ||
Revision as of 18:07, 25 February 2012
Problem 6
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 her rounded values. Which of the following statements is necessarily correct?
A) Her estimate is larger than x-y B) Her estimate is smaller than x-y C) Her estimate equals x-y D) Her estimate equals y - x E) Her estimate is 0
Solutions
Say Z=is the amount rounded up by and down by.
Xiaoli rounded x up by a small amount, rounded y down by the same amount, and then subtracted her rounded values.
Which translates to:
=
=
This is 
bigger than the original amount of 
.
Therefore, her estimate is larger than
or
