A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as belowA. 48 like PizzaB. 45 like HoagiesC. 58 like tacosD. 28 like pizza and hoagiesE. 37 like hoagies and tacosF. 40 like pizza and tacosG. 25 like all three food

A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are 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?

ANS: 20

Step-by-step explanation:

The best formula in this case, one in which we know how many like two items but in which we don't know how many like exactly two items, is this one.

In order to reduce the complexity of these types of problems, a formula has been devised for the case when we know the no of people who like two items but we are not known about the no of people who like exactly two items. Now for this case, the formula goes as follows:

Total = A + B + C - (The Total Of Those Who Like Two) + (1 x Those Who Like All Three) + (Those Who Like None)

here

Total = 75

A (Those who like pizza) = 48

B (Those who like hoagies) = 45

C (Those who like tacos) = 58

The Total Of Those Who Like Two = 28+37+40 = 105

Those Who Like All Three = 25

now those who like none can be determined by the above formula:

Those Who Like None = Total - A - B - C + (The Total Of Those Who Like Two) - (1 x Those Who Like All Three)

Those Who Like None = 75 - 48 - 45 - 58 + 105 - 25 = 4

Now we can find those who like only one:

Only Pizza = P - (P and H + P and T - All 3) = 48 - (28 + 40 - 25) = 5;

Only Hoagies = H - (P and H + H and T - All 3) = 45 - (28 + 37 - 25) = 5;

Only Tacos = T - (P and T + H and T - All 3) = 58 - (40 + 37 - 25) = 6.

hence the number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20.