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?

Question

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? (A) 35 (B) 48 (C) 60 (D) 22

Tardigrade Admin · Accepted Answer

n (M alone) =n(M)-n(M ∩ C)-n(M ∩ P)+n(M ∩ C ∩ P) =100-28-30+18=60

35

48

60

22

n(M alone) =n(M)−n(M∩C)−n(M∩P)+n(M∩C∩P) =100−28−30+18=60

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