Difference between revisions of "2010 AMC 10B Problems/Problem 12"
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The minimum possible value occurs when <math>20\%</math> of the students who originally answered "No." answer "Yes." In this case, <math>x=20</math> | The minimum possible value occurs when <math>20\%</math> of the students who originally answered "No." answer "Yes." In this case, <math>x=20</math> | ||
| − | The maximum possible value occurs when <math>30\%</math> of the students who originally answered "Yes." answer "No." and the <math>50\%</math> of the | + | The maximum possible value occurs when <math>30\%</math> of the students who originally answered "Yes." answer "No." and the <math>100\%</math> of the students (which accounts for <math>50\%</math> of the overall student population) who originally answered "No." answer "Yes." In this case, <math>x=50+30=80</math> |
Subtract <math>80-20</math> to obtain an answer of <math>\boxed{\textbf{(D)}\ 60}</math> | Subtract <math>80-20</math> to obtain an answer of <math>\boxed{\textbf{(D)}\ 60}</math> | ||
Revision as of 21:25, 22 December 2012
Problem
At the beginning of the school year, 
of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and answered "No." At the end of the school year, 
answered "Yes" and 
answerws "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
The minimum possible value occurs when 
of the students who originally answered "No." answer "Yes." In this case, 
The maximum possible value occurs when of the students who originally answered "Yes." answer "No." and the 
of the students (which accounts for of the overall student population) who originally answered "No." answer "Yes." In this case, 
Subtract 
to obtain an answer of 
See Also
| 2010 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 11 |
Followed by Problem 13 | |
| 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 10 Problems and Solutions | ||
