Difference between revisions of "2010 AMC 12B Problems/Problem 6"
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Revision as of 01:48, 26 September 2020
- The following problem is from both the 2010 AMC 12B #6 and 2010 AMC 10B #12, so both problems redirect to this page.
Contents
Problem 6
At the beginning of the school year, 
of all students in Mr. Well's class answered "Yes" to the question "Do you love math", and answered "No." At the end of the school year, 
answered "Yes" and 
answered "No." Altogether, 
of the students gave a different answer at the beginning and end of the school year. What is the difference between the maximum and the minimum possible values of 
?
Solution
Clearly, the minimum possible value would be 
. The maximum possible value would be 
. The difference is 
.
Video Solution
https://youtu.be/vYXz4wStBUU?t=160
~IceMatrix
See also
| 2010 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. 
