In a group, 45 people like tea, 36 like coffee, and 15 like both. How many like only tea?
Answer and explanation
Correct answer: 30
The people who like tea consist of two disjoint parts: those who like only tea and those who like both tea and coffee. Therefore, n(only tea) = n(tea) − n(both) = 45 − 15 = 30. The coffee total is not needed for this calculation. The value 66 is the number who like at least one beverage, since 45 + 36 − 15 = 66, not the number who like only tea. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
30
Why is this the correct answer?
The people who like tea consist of two disjoint parts: those who like only tea and those who like both tea and coffee. Therefore, n(only tea) = n(tea) − n(both) = 45 − 15 = 30. The coffee total is not needed for this calculation. The value 66 is the number who like at least one beverage, since 45 + 36 − 15 = 66, not the number who like only tea. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
