If \(U=\{1,2,\ldots,100\}\), \(A=\{x\in U:4\mid x\}\), and \(B=\{x\in U:10\mid x\}\), what is \(|A\cap B|\)?
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Answer and explanation
Correct answer: 5
An element in \(A\cap B\) must be divisible by both 4 and 10. Such numbers are multiples of \(\operatorname{lcm}(4,10)=20\). The multiples of 20 in \(\{1,\ldots,100\}\) are 20, 40, 60, 80, and 100. There are five numbers, so \(|A\cap B|=5\), making option A correct.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
An element in \(A\cap B\) must be divisible by both 4 and 10. Such numbers are multiples of \(\operatorname{lcm}(4,10)=20\). The multiples of 20 in \(\{1,\ldots,100\}\) are 20, 40, 60, 80, and 100. There are five numbers, so \(|A\cap B|=5\), making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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