The Venn diagram consists of 3 interlocking regions, represented by 3 interlocking circles. Surrounding the interlocking regions is one large region representating the class of 70. The capital letters represent the total numbers of students offering the subjects: E=economics; M=mathematics; G=geography. There are 8 regions: a to g, where these are numbers of students in each region (draw the Venn diagram labelling the regions, and entering numbers when the value of a region is found; then it is much easier to see what regions have to be added together):-
a. Economics only = 6
b. Mathematics only
c. Geography only
d. Economics and mathematics only
e. Economics and geography only
f. Mathematics and geography only
g. All subjects
h. No subjects (0)
From the data we can write:
E=a+d+e+g=53
M=b+d+f+g
G=c+e+f+g=50
70=a+b+c+d+e+f+g
a=6
a+e=18, so e=12
36=e+g, so, since e=12, g=24
34=f+g, so since g=24, f=10
So f=mathematics and geography only=10 students.
a=6, so d+e+g=53-6=47 and d+36=47, so d=11
a+b+c+d+e+f+g=a+(c+e+f+g)+b+d=6+50+b+11=70 and b=3,
so the number of mathematics students=3+11+34=48.