2010 AMC 10B Problem 12

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\% answered "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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.