32) In a school, 100 students were interviewed 28 took PE, 31 took BIO, 42 took ENG, 9 took PE and BIO, 10 took PE and ENG, 6 took BIO and ENG, 4 took all three subjects, then
a) How many students took none of the three subjects?
b) How many students took PE but not BIO or ENG?
c) How many students took BIO and PE but not ENG?
Answers
Given:
Total students = 100
Students who took PE = 28
Students who took Bio = 31
Students who took Eng = 42
Students who took both PE and Biology = 9
Students who took both PE and Eng = 10
Students who took both Bio and Eng = 6
Students who took all = 4
To Find:
a) How many students took none of the three subjects?
b) How many students took PE but not BIO or ENG?
c) How many students took BIO and PE but not ENG?
Solution:
Students taking only PE and not Bio and Eng
= 28 – (5+6+4)
= 28 - 15
= 13
Students taking only Bio and not PE and Eng
= 31 – (5+4+2)
= 31 - 11
= 20
Students taking only Eng and not PE and Bio
= 42 – (6+4+2)
= 42 - 12
= 30
Now,
Students who took three subjects
= 100 - ( 13 + 5 + 4 + 20 + 2 + 30 + 6 )
= 100 - 80
= 20
Students who took BIO and PE but not ENG will be = 5