Tuesday, June 2, 2020

06/02/2020 (2019: AMC 8, Problem 11)

Q: The eighth grade class at Lincoln Middle School has 93 students. Each student takes a math class or a foreign language class or both. There are 70 eighth graders taking a math class, and there are 54 eight graders taking a foreign language class. How many eight graders take only a math class and not a foreign language class?

$\textbf{(A) }16\qquad\textbf{(B) }23\qquad\textbf{(C) }31\qquad\textbf{(D) }39\qquad\textbf{(E) }70$

The overlap between the two activities can be calculated by doing a + b - c, where a is math, b is foreign language, and c is the number of students.
This means that you do 70 + 54 - 93 = 124 - 93 = 31. The answer is C.

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