2014 AMC 12A Problems/Problem 5

Problem

On an algebra quiz, of the students scored points, scored points, scored points, and the rest scored points. What is the difference between the mean and median score of the students' scores on this quiz?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}}\ 4\qquad\textbf{(E)}\ 5$ (Error compiling LaTeX. Unknown error_msg)

Solution

The mean can solved by the following. 10% of 70 is 7, 35% of 80 is 28, 30% of 90 is 27, and (100% - 10% - 35% - 30%) = 25%. 25% of 100 is 25. 7 + 28 + 27 + 25 = 87.
The median can be solved by finding the score present at the 50% mark, which is 90.
90-87 equals 3, which is (C) 3.