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by GMATGuruNY » Wed Jul 09, 2014 2:58 am
A survey was conducted to determine the popularity of 3 food among students. The data collected from 75 students is summarized as below:

48 like Pizza
45 like Hoagies
58 like tacos
28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
25 like all three food

What is the number of students who like none or only one of the foods?

A. 4
B. 16
C. 17
D. 20
E. 23
Draw a VENN DIAGRAM representing the following:
75 Total
48 like pizza
45 like hoagies
58 like tacos
N = ?
Image

Complete the Venn diagram by working from the INSIDE OUT.

25 like all 3 foods:
Image

28 like pizza and hoagies
37 like hoagies and tacos
40 like pizza and tacos
Subtracting from these figures the 25 who like all 3 foods, we get:
Image

Subtracting the values in the diagram from P=48, H=45, and T=58, we get:
Image

Subtracting the values in the diagram from Total = 75, we get:
Image

Thus:
Only P + Only H + Only T + N = 5 + 5 + 6 + 4 = 20.

The correct answer is D.
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by mcdesty » Thu Jul 10, 2014 11:21 am
Here is another way to think about it.
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