{"status": "success", "data": {"description_md": "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 $x$?\n\n$\\textbf{(A)}\\ 0 \\qquad \\textbf{(B)}\\ 20 \\qquad \\textbf{(C)}\\ 40 \\qquad \\textbf{(D)}\\ 60 \\qquad \\textbf{(E)}\\ 80$", "description_html": "

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 ?

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

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

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2010 AMC 10B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/10_amc10B_p13", "prev": "/problem/10_amc10B_p11"}}