Difference between revisions of "2010 AMC 10B Problems/Problem 12"
| Line 11: | Line 11: | ||
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 students who originally answered "No." answer "Yes." In this case, <math>x=50+30=80</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 students 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{\mathrm{(D)} 60}</math> | + | Subtract <math>80-20</math> to obtain an answer of <math>\boxed{\mathrm{(D)}\ 60}</math> |
Revision as of 19:57, 24 January 2011
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 who originally answered "No." answer "Yes." In this case, 
Subtract 
to obtain an answer of 
