Question

a class has 75 students. the data shows the number of students offering one or more subjects mathematics 100; physics 70; chemistry 40; maths and physics 30; maths and chemistry 28; physics and chemistry 23; physics chemistry and maths 18. how many students have offered mathematics?

Answer 1

Answer:

M-Mathematics

P-Physics

C-Chemistry

Let n(M∩P−C)=x refer the venn diagram

Given n(M∪P∪C)=147

n(M)=100,n(P)=70,n(C)=40

n(M∩P)=28,n(M∩P)=18+x,n(P∩C)=23,n(M∩P∩C)=18

n(M∪P∪C)=n(M)+n(P)+n(C)−n(M∩P)−n(P∩C)−n(M∩C)+n(M∩P∩C)

147=100+70+40−28−23−(18+x)+18

147=210−51−x

⇒147=159−x

⇒x=12

Hence, the number of students offered mathematics alone are 72−x which is 60.