Let U = {1, 2, ..., 50}. If A is the set of multiples of 4 in U and B is the set of multiples of 6 in U, what is n(A ∩ B)?
Answer and explanation
Correct answer: 4
The governing concept is intersection together with the least common multiple. A number in A ∩ B must be divisible by both 4 and 6, so it must be a multiple of lcm(4,6) = 12. The positive multiples of 12 not exceeding 50 are 12, 24, 36, and 48. There are exactly four such numbers, hence n(A ∩ B) = 4. Therefore option A is correct; the larger choices incorrectly count separate multiples rather than common ones.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is intersection together with the least common multiple. A number in A ∩ B must be divisible by both 4 and 6, so it must be a multiple of lcm(4,6) = 12. The positive multiples of 12 not exceeding 50 are 12, 24, 36, and 48. There are exactly four such numbers, hence n(A ∩ B) = 4. Therefore option A is correct; the larger choices incorrectly count separate multiples rather than common ones.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
