2010 AMC 10B Problem 12
Problem 12 of 25IntermediateAlgebra
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 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
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Solution
To minimize we want to have as many kids as possible maintain their answer.
We then need at least percent of the students to change their answer.
To maximize we can have everybody that answered no change their answer, but some who answered yes must stay yes.
We need percent of the people who said yes to stay yes, which means only percent can switch.
This makes the maximum percent of students that can switch percent. The difference is then
Thus, D is the correct answer.