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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>
  
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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>
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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>
  
 
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 21:26, 22 December 2012

Problem

At the beginning of the school year, $50\%$ of all students in Mr. Wells' math class answered "Yes" to the question "Do you love math", and $50\%$ answered "No." At the end of the school year, $70\%$ answered "Yes" and $30\%$ answerws "No." Altogether, $x\%$ 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 $x$?

$\textbf{(A)}\ 0 \qquad \textbf{(B)}\ 20 \qquad \textbf{(C)}\ 40 \qquad \textbf{(D)}\ 60 \qquad \textbf{(E)}\ 80$

Solution

The minimum possible value occurs when $20\%$ of the students who originally answered "No." answer "Yes." In this case, $x=20$

The maximum possible value occurs when $60\%$ of the students (which accounts for $30\%$ of the overall student population) who originally answered "Yes." answer "No." and the $100\%$ of the students (which accounts for $50\%$ of the overall student population) who originally answered "No." answer "Yes." In this case, $x=50+30=80$

Subtract $80-20$ to obtain an answer of $\boxed{\textbf{(D)}\ 60}$

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
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