In a survey of the dining preferences of 36 dormitory students at the end of the spring semester, the following facts were discovered about Adam's Lunch AL, Pizza Tower PT, and the Dining Hall DH.
13 liked AL but not PT
1 liked AL only
21 liked AL
20 liked PT
25 liked DH
7 liked PT and AL but not DH
10 liked PT and DH

How many liked PT or DH?

A)15
B)16
C)99
D)6
E)35

Question

In a survey of the dining preferences of 36 dormitory students at the end of the spring semester, the following facts were discovered about Adam's Lunch AL, Pizza Tower PT, and the Dining Hall DH. ​
13 liked AL but not PT
1 liked AL only
21 liked AL
20 liked PT
25 liked DH
7 liked PT and AL but not DH
10 liked PT and DH
​
How many liked PT or DH?
​
A)15
B)16
C)99
D)6
E)35

Quizplus · Accepted Answer

To find the number of students who liked PT or DH, we need to add the number of students who liked PT and the number of students who liked DH, but we also need to subtract the number of students who liked both PT and DH to avoid counting them twice. Using the given information:

Number who liked PT or DH = Number who liked PT + Number who liked DH - Number who liked both PT and DH
Number who liked PT or DH = 20 + 25 - 10
Number who liked PT or DH = 35

Therefore, 35 students liked PT or DH. The answer is E.

In a Survey of the Dining Preferences of 36 Dormitory