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| − | == Problem ==
| + | #redirect [[2010 AMC 12B Problems/Problem 6]] |
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| − | At the beginning of the school year, <math>50\%</math> of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and <math>50\%</math> answered "No." At the end of the school year, <math>70\%</math> answered "Yes" and <math>30\%</math> answered "No." Altogether, <math>x\%</math> 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 <math>x</math>?
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| − | <math>\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 60 \qquad \textbf{(E)}\ 80</math>
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| − | == Solution ==
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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>
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| − | The maximum possible value occurs when <math>60\%</math> of the students (which accounts for <math>30\%</math> of the overall student population) 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>
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| − | Subtract <math>80-20</math> to obtain an answer of <math>\boxed{\textbf{(Z)}\ 60}</math>
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| − | ==See Also==
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| − | {{AMC10 box|year=2010|ab=B|num-b=11|num-a=13}}
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| − | {{MAA Notice}}
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