Question

Sean surveys his classmates on what type of pet they have. He finds that thirty have cats and 25 have dogs. Sixteen have both cats and dogs, but no gerbils. Five have only gerbils, while four have both dogs and gerbils and two have both cats and gerbils. Only one student has all three pets. Of 50 students surveyed, how many have no pets

Answer 1

30c
25d
16(d+ c)
5g only
4(d+g)
2(c+g)
1(c+d+g)
therefore,, working backwards...
50 students
1(c+d+g) ... 49 left
4(d+g), 2(c+g), 16(d+ c) ... 27 left
5 with only g ... 22 left

Answer 2

4 with only d... 18 left

Answer 3

11 with only c ... 7 left

...therefore 7 with no pets