Question

Venn Diagram:

In a school all of the 120 pupils must choose at least one of Archery, Badminton or Cycling.
63 pupils choose archery
62 pupils choose badminton
69 pupils choose cycling
28 pupils choose archery ad badminton
27 pupils choose archery and cycling
32 pupils choose badminton and cycling

Find the centre value (x)

Answer 1

Cycling = 69 - (32 + 27) = 69 -59 = 10
Badminton = 62 - (32+28) = 62 - 60 =2
Archery = 63 - (27 + 28) = 63 - 55 = 8

Total for 1 sport = 10 + 2 + 8 = 20

Pupils left = 120 - 20 = 100

Pupils that picked two sports = 27 + 28 + 32 = 87
Number of pupils to pick all sports = 100 - 87 = 13

13 pupils picked all three