In a class of 100 students, 72 chose at least one of A or B. If only A has 28 students and only B has 34 students, how many students are in both?
Answer and explanation
Correct answer: 10
The union A ∪ B consists of three disjoint parts: students who chose only A, students who chose only B, and students who chose both. Therefore, 72 = 28 + 34 + n(A ∩ B). Solving gives n(A ∩ B) = 72 − 28 − 34 = 10. The 100-student total is not needed for this calculation because the question already gives the number choosing at least one option, that is, the union size.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The union A ∪ B consists of three disjoint parts: students who chose only A, students who chose only B, and students who chose both. Therefore, 72 = 28 + 34 + n(A ∩ B). Solving gives n(A ∩ B) = 72 − 28 − 34 = 10. The 100-student total is not needed for this calculation because the question already gives the number choosing at least one option, that is, the union size.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
