If 60% of students are in A, 50% are in B, and 25% are in both A and B, what percentage are in exactly one of the two sets?
Answer and explanation
Correct answer: 60%
Exactly one means belonging to A only or B only, but not to both. The A-only percentage is 60% − 25% = 35%, and the B-only percentage is 50% − 25% = 25%. Adding these disjoint parts gives 35% + 25% = 60%. Equivalently, exactly one = A + B − 2(A ∩ B) = 60 + 50 − 2(25) = 60%. The 85% option is the union and incorrectly includes the common group once.
Frequently asked questions
What is the correct answer to this question?
60%
Why is this the correct answer?
Exactly one means belonging to A only or B only, but not to both. The A-only percentage is 60% − 25% = 35%, and the B-only percentage is 50% − 25% = 25%. Adding these disjoint parts gives 35% + 25% = 60%. Equivalently, exactly one = A + B − 2(A ∩ B) = 60 + 50 − 2(25) = 60%. The 85% option is the union and incorrectly includes the common group once.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
