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?
Answers
Steve
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
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