Question #N60
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. 20
B. 30
C. 50
D. 70
Correct Answer is: A
Let P represent the set of students who prefer pizza and B represent the set of students who prefer burgers. We are given that |P| = 120, |B| = 80, and |P \cap B| = 50. We want to find |P' \cap B'|, the number of students who prefer neither. We can use the following formula: |P' \cap B'| = |U| - |P \cup B| = |U| - (|P| + |B| - |P \cap B|). Since there are 200 students surveyed, we know |U| = 200. Substituting the given values into the formula, we get |P' \cap B'| = 200 - (120 + 80 - 50) = 200 - 150 = 50. Therefore, the number of students who prefer neither pizza nor burgers is 50.