The 120 consumers were asked about their buying preferences concerning another product that is sold in the market under three labels. The results were
12 buy only those sold under label A.

24 buy only those sold under label B.

27 buy only those sold under label C.

14 buy only those sold under labels A and B.

9 buy only those sold under labels A and C.

11 buy only those sold under labels B and C.

7 buy the product sold under all three labels.

How many of the consumers surveyed buy the product sold under none of these labels?

A) 81
B) 16
C) 12
D) 32
E) 104

Question

The 120 consumers were asked about their buying preferences concerning another product that is sold in the market under three labels. The results were ​
12 buy only those sold under label A.
​
24 buy only those sold under label B.
​
27 buy only those sold under label C.
​
14 buy only those sold under labels A and B.
​
9 buy only those sold under labels A and C.
​
11 buy only those sold under labels B and C.
​
7 buy the product sold under all three labels.
​
How many of the consumers surveyed buy the product sold under none of these labels?
​
A) 81
B) 16
C) 12
D) 32
E) 104

Quizplus · Accepted Answer

To find the number of consumers who buy the product sold under none of these labels, we can use the formula:

Total consumers = Only A + Only B + Only C + A and B + A and C + B and C + All three + None

We know that:
Only A = 12
Only B = 24
Only C = 27
A and B = 14
A and C = 9
B and C = 11
All three = 7
Total consumers = 120

Substituting these values in the formula, we get:

120 = 12 + 24 + 27 + 14 + 9 + 11 + 7 + None
None = 16

Therefore, 16 of the consumers surveyed buy the product sold under none of these labels. The answer is option B.

The 120 Consumers Were Asked About Their Buying Preferences Concerning