In a group, 35% of people are in A, 48% are in B, and 20% are in both. What percentage is in at least one of the two sets?
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Answer and explanation
Correct answer: 63%
The percentage in at least one set is the percentage of the union. Use the inclusion-exclusion rule: percentage(A ∪ B) = percentage(A) + percentage(B) − percentage(A ∩ B). Therefore, 35% + 48% − 20% = 63%. The common 20% is subtracted once because it was included in both 35% and 48%. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
63%
Why is this the correct answer?
The percentage in at least one set is the percentage of the union. Use the inclusion-exclusion rule: percentage(A ∪ B) = percentage(A) + percentage(B) − percentage(A ∩ B). Therefore, 35% + 48% − 20% = 63%. The common 20% is subtracted once because it was included in both 35% and 48%. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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