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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
In a survey where 100 students reported which subject they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover, 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business. 8 students like both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is
Solution
Given totals: \(|M|=32,\ |B|=38,\ |L|=30\)
Intersections (inclusive): \(|M\cap L|=7,\ |M\cap B|=10,\ |B\cap L|=8,\ |M\cap B\cap L|=5\).
Compute “only” counts:
\(\displaystyle |M\ \text{only}|=|M|-|M\cap B|-|M\cap L|+|M\cap B\cap L|=32-10-7+5=20\)
\(\displaystyle |B\ \text{only}|=|B|-|M\cap B|-|B\cap L|+|M\cap B\cap L|=38-10-8+5=25\)
\(\displaystyle |L\ \text{only}|=|L|-|M\cap L|-|B\cap L|+|M\cap B\cap L|=30-7-8+5=20\)
Exactly one subject: \(20+25+20=\boxed{65}\).
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