In an examination group of 120 students, 72 study Mathematics, 64 study Physics, and 38 study both subjects. How many study exactly one subject?
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Answer and explanation
Correct answer: 60
The students studying exactly Mathematics are 72 − 38 = 34, because those studying both subjects must be removed. The students studying exactly Physics are 64 − 38 = 26. Adding these non-overlapping groups gives 34 + 26 = 60. Equivalently, n(A △ B) = n(A) + n(B) − 2n(A ∩ B) = 60. Thus, option A is correct.
Frequently asked questions
What is the correct answer to this question?
60
Why is this the correct answer?
The students studying exactly Mathematics are 72 − 38 = 34, because those studying both subjects must be removed. The students studying exactly Physics are 64 − 38 = 26. Adding these non-overlapping groups gives 34 + 26 = 60. Equivalently, n(A △ B) = n(A) + n(B) − 2n(A ∩ B) = 60. Thus, 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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