Let U = {1, 2, ..., 72}. If A is the set of multiples of 6 and B is the set of multiples of 8, what is n(A ∩ B)?
Answer and explanation
Correct answer: 3
An element of A ∩ B must be divisible by both 6 and 8. Therefore all common elements are multiples of lcm(6,8) = 24. Within U = {1,2,...,72}, the relevant multiples are 24, 48, and 72. Equivalently, their number is floor(72/24) = 3. Hence n(A ∩ B) = 3 and option A is correct; counting all multiples of either number would incorrectly produce a larger value.
Frequently asked questions
What is the correct answer to this question?
3
Why is this the correct answer?
An element of A ∩ B must be divisible by both 6 and 8. Therefore all common elements are multiples of lcm(6,8) = 24. Within U = {1,2,...,72}, the relevant multiples are 24, 48, and 72. Equivalently, their number is floor(72/24) = 3. Hence n(A ∩ B) = 3 and option A is correct; counting all multiples of either number would incorrectly produce a larger value.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
