In a survey of 120 people, 66 read a newspaper, 58 read a magazine, and 24 read neither. How many read both?
Answer and explanation
Correct answer: 28
First find the number reading at least one publication: 120 − 24 = 96. Let N denote newspaper readers and M magazine readers. By inclusion–exclusion, n(N ∪ M) = n(N) + n(M) − n(N ∩ M). Therefore, 96 = 66 + 58 − n(N ∩ M), so n(N ∩ M) = 124 − 96 = 28. Hence 28 people read both; 96 is the union, not the intersection.
Frequently asked questions
What is the correct answer to this question?
28
Why is this the correct answer?
First find the number reading at least one publication: 120 − 24 = 96. Let N denote newspaper readers and M magazine readers. By inclusion–exclusion, n(N ∪ M) = n(N) + n(M) − n(N ∩ M). Therefore, 96 = 66 + 58 − n(N ∩ M), so n(N ∩ M) = 124 − 96 = 28. Hence 28 people read both; 96 is the union, not the intersection.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
