In a survey, n(A)=96, n(B)=88, n(C)=82, 69 people are in exactly two sets, and 21 are in all three sets. How many people are in exactly one set?
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Answer and explanation
Correct answer: 65
The total of the three set sizes counts each person according to the number of sets to which that person belongs. If x people belong to exactly one set, then 96+88+82 = x + 2(69) + 3(21). Thus 266 = x + 138 + 63, so x = 266 − 201 = 65. The required number of people in exactly one set is therefore 65.
Frequently asked questions
What is the correct answer to this question?
65
Why is this the correct answer?
The total of the three set sizes counts each person according to the number of sets to which that person belongs. If x people belong to exactly one set, then 96+88+82 = x + 2(69) + 3(21). Thus 266 = x + 138 + 63, so x = 266 − 201 = 65. The required number of people in exactly one set is therefore 65.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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