In a survey, n(A) = 82, n(B) = 76, n(C) = 70, 54 people are in exactly two sets, and 18 are in all three sets. How many people are in exactly one set?
Answer and explanation
Correct answer: 66
First count total memberships across the three sets: n(A) + n(B) + n(C) = 82 + 76 + 70 = 228. People in exactly one set contribute one membership each, those in exactly two sets contribute two each, and those in all three contribute three each. If x is the exactly-one count, then 228 = x + 2(54) + 3(18). Hence x = 228 − 108 − 54 = 66. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
66
Why is this the correct answer?
First count total memberships across the three sets: n(A) + n(B) + n(C) = 82 + 76 + 70 = 228. People in exactly one set contribute one membership each, those in exactly two sets contribute two each, and those in all three contribute three each. If x is the exactly-one count, then 228 = x + 2(54) + 3(18). Hence x = 228 − 108 − 54 = 66. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
