U = {1, 2, 3, ..., 90}, A is the set of numbers divisible by 2, B by 3, and C by 5. What is n(A ∩ B ∩ C)?
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Answer and explanation
Correct answer: 3
A number in A ∩ B ∩ C must be divisible by 2, 3, and 5 simultaneously. Since these numbers are pairwise coprime, their least common multiple is 2 × 3 × 5 = 30. The multiples of 30 in U are 30, 60, and 90. Therefore the triple intersection has 3 elements, so option B is correct.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
A number in A ∩ B ∩ C must be divisible by 2, 3, and 5 simultaneously. Since these numbers are pairwise coprime, their least common multiple is 2 × 3 × 5 = 30. The multiples of 30 in U are 30, 60, and 90. Therefore the triple intersection has 3 elements, so option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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