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  4. A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100, Physics 70, Chemistry 40; Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. How many students have offered Mathematics alone?

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Q. A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone?

BITSATBITSAT 2013

Solution:

$n (M$ alone)
$=n(M)-n(M \cap C)-n(M \cap P)+n(M \cap C \cap P)$
$=100-28-30+18=60$

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