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NDA 2018 Maths · Mathematics · Sets, Relations and Functions · easy

In a group of 100 students, 40 study Physics, 35 study Chemistry and 15 study both. How many study neither subject?

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In a group of 100 students, 40 study Physics, 35 study Chemistry and 15 study both. How many study neither subject?
  1. A. 40
  2. B. 25
  3. C. 35
  4. D. 60
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Answer: (A) 40

By inclusion-exclusion, n(P∪C)=40+35−15=60n(P\cup C)=40+35-15=60. Students studying neither =100−60=40=100-60=40. Answering 60 gives the number studying at least one subject, and 25 comes from forgetting to subtract the overlap before taking the complement.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake