A group of college students were asked about their TV watching habits. Of those surveyed, 30 students watch The Walking Dead, 24 watch The Blacklist, and 22 watch Game of Thrones. Additionally, 13 watch The Walking Dead and The Blacklist, 10 watch The Walking Dead and Game of Thrones, and 16 watch The Blacklist and Game of Thrones. There are 7 students who watch all three shows. How many students surveyed watched at least one of the shows?

Answer: 44 students

Step-by-step explanation:

Let Walking dead be denoted as W

Let Blacklist be denoted as B

Let Game of thrones be denoted as G

Total number of students that watch W = 30

W&G&B = 7

W&B only = 13-7 = 6

W&G only = 10-7 = 3

To get the number of people that watch W ONLY, we subtract those that watch W&B only (6), W&G only (3) and W&B&G (7) from 30. Hence,

W Only = 30 - 6 - 3 - 7 = 14 (14 students watch Walking dead only)

Total number of students that watch B = 24

B&G&W = 7

B&W only = 13-7 = 6

B&G only = 16 - 7 = 9

Hence, those that watch B only = 24-6-9-7 = 2 students.

Total number of students that watch G = 22

G&W&B = 7

G&B only = 9

G&W only = 3

Hence those that watch G only = 22-9-3-7 = 3 students.

Hence number of students that watch at least one show = W only + B only + G only + W&B only + W&G only + B&G only + W&B&G.

= 14+2+3+6+3+9+7 = 44 students.