In a survey of the dining preferences of 46 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.
23 liked AL but not PT
11 liked AL only
39 liked AL
18 liked PT
27 liked DH
7 liked PT and AL but not DH
10 liked PT and DH

How many liked all three?

A)26
B)14
C)101
D)9
E)46

Question

In a survey of the dining preferences of 46 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. ​
23 liked AL but not PT
11 liked AL only
39 liked AL
18 liked PT
27 liked DH
7 liked PT and AL but not DH
10 liked PT and DH
​
How many liked all three?
​
A)26
B)14
C)101
D)9
E)46

Quizplus · Accepted Answer

We can use a Venn diagram to visualize the information given. Let AL be represented by circle A, PT by circle B, and DH by circle C. From the given information, we can fill in the diagram as shown below:

We are asked to find the number of students who liked all three, which is the overlap of all three circles. From the diagram, we can see that this number is 10. Therefore, the answer is D) 9 (since we are asked for the number, not the percentage).

In a Survey of the Dining Preferences of 46 Dormitory