Question

In a class, 22 offer maths, 21 offer English and 25 offer science. 4 students offer all three subjects and 36 offer exactly one subject. If all the students offer at least one of the subject, then how many offer two subjects?

Answer 1

Suppose we let

a = math only
b = English only
c = science only
x = math and science only
y = math and English only
z = English and science only

If you draw the Venn diagram, you see that

a+b+c = 36
a+x+y+4 = 22
b+y+z+4=21
c+x+z+4=25

Solve those equations and you get

x = b-7
y = c-11
z = 28-b-c

x+y+z is the number with exactly two subjects

x+y+z = b-7+c-11+28-b-c = 10