If n(A) = 3x + 8, n(B) = 2x + 17, n(A ∩ B) = x + 5, and n(A ∪ B) = 60, what is x?
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Answer and explanation
Correct answer: 10
For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B), because the common elements are counted twice in n(A) + n(B). Substitution gives (3x + 8) + (2x + 17) − (x + 5) = 60. Thus 4x + 20 = 60, so 4x = 40 and x = 10. Checking gives n(A) = 38, n(B) = 37, intersection = 15, and union = 38 + 37 − 15 = 60.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
For two finite sets, n(A ∪ B) = n(A) + n(B) − n(A ∩ B), because the common elements are counted twice in n(A) + n(B). Substitution gives (3x + 8) + (2x + 17) − (x + 5) = 60. Thus 4x + 20 = 60, so 4x = 40 and x = 10. Checking gives n(A) = 38, n(B) = 37, intersection = 15, and union = 38 + 37 − 15 = 60.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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