In one semster 120 students did commerce. 38 did Ins 111,36 did Eng 111, 100 did math 111,26 did ins 111 and eng 111,22 did eng 111and math 111,26 did ins 111 and math111,18 did all 3

Question

a) none of the 3 b) only math 111 c) ins 111 and eng 111 and not math 111 d) only one course e) only 2 courses

Answer 1

(a)

The Venn diagram helps to solve this type of problem. Here's the key:

A=Commerce students who didn't take any of the 3 subjects.

B=Ins only students

C=Math only

D=Eng only

E=Ins+Eng only

F=Math+Eng only

G=Ins+Math only

H=All 3

Now some figures:

A+B+C+D+E+F+G+H=120

B+E+G+H=38

D+E+F+H=36

C+F+G+H=100

E+H=26

F+H=22

G+H=26

H=18

So, E=8, F=4, G=8.

C=100-(4+8+18)=70

D=36-(8+4+18)=6

B=38-(8+8+18)=4

A=120-(4+70+6+8+4+8+18)=2

(a) A=2 students took none of the 3

(b) C=70 students took math only

(c) E=8 students took ins and eng only

(d) B+C+D=80 students took only one course

(e) E+F+G=20 students took only two courses