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

BTGmoderatorLU wrote: ↑

Thu Mar 12, 2020 3:13 pm

Source: GMAT Prep

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 food?

A. 4
B. 16
C. 17
D. 20
E. 23

The OA is D

Say

# students who like Pizza = P = 48;
# students who like Hoagies = H = 45;
# students who like Tacos = T = 58;

# students who like Pizza & Hoagies = PH = 28;
# students who like Pizza & Tacos = PT = 40;
# students who like Tacos & Hoagies = TH = 37;

# students who like all = A = 25;

# students who like none = N

Thus,

75 = P + H + T – (PH + HT + HT) + A + N
75 = 48 + 45 + 58 – (28 + 40 + 37) + 25 + N

N = 4

Only Pizza = P – (PH + PT) + A = 48 – (28 + 40 – 25) = 5;
Only Hoagies = H – (PH + HT) + A = 45 – (28 + 37 – 25) = 5;
Only Tacos = T – (PT + HT) + A = 58 – (40 + 37 – 25) = 6.

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

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorLU wrote: ↑

Thu Mar 12, 2020 3:13 pm

Source: GMAT Prep

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 food?

A. 4
B. 16
C. 17
D. 20
E. 23

The OA is D

Notice that we have:

Total = #P + #H + #T - #(P and H) - #(P and T) - #(T and H) + #(P and H and T) + #None

We have Total = 75, #P = 48, #H = 45, #T = 58, #(P and H) = 28, #(P and T) = 40, #(T and H) = 37 and #(P and H and T) = 25. Let’s substitute these values in the equation above:

75 = 48 + 45 + 58 - 28 - 40 - 37 + 25 + #None

75 = 151 - 105 + 25 + #None

#None = 75 - 71 = 4

So, there are 4 students who like none of the three kinds of food.

Next, we have the formula:

Total = #(Exactly one) + #(Exactly two) + #(All three) + #None

Notice that all of the values #(P and H) = 28, #(P and T) = 40, #(T and H) = 37 include the 25 students who like all three kinds of food; therefore, we have:

#(only P and H) = 28 - 25 = 3
#(only P and T) = 40 - 25 = 15
#(only T and H) = 37 - 25 = 12

Thus, #(Exactly two) = 3 + 15 + 12 = 30. Let’s substitute Total = 75, #(Exactly two) = 30, #(All three) = 25 and #None = 4 in the formula above:

75 = #(Exactly one) + 30 + 25 + 4

75 = #(Exactly one) + 59

#(Exactly one) = 75 - 69 = 16

Finally, the number of students who like zero or one kind of food is 16 + 4 = 20.

Answer: D