Question #N56

A survey of 200 students found that 120 students prefer pizza, 80 students prefer burgers, and 50 students prefer both. How many students prefer neither pizza nor burgers?
A. 30
B. 50
C. 70
D. 100

Correct Answer is: A

Let P represent the set of students who prefer pizza, B represent the set of students who prefer burgers, and represent the set of students who prefer both. We know that | = 120, | = 80, and | = 50. We are asked to find | , which represents the set of students who prefer neither pizza nor burgers. Using the principle of inclusion-exclusion, we have: | = | + | - | = 120 + 80 - 50 = 150. Since there are 200 students in the survey, the number who prefer neither pizza nor burgers is 200 - 150 = 50.