A survey of 540 adults aged 18-24 year olds was conducted in which they were asked what they did last friday night it found:

Question

171 watch tv

150 hung out with friends

200 ate pizza but did not hang out with friends

28 watched Tv and ate pizza but did not hang out with friends

44 watched Tv and hung out with friends, but did not eat pizza

31 hung out with friends and ate pizza but did not watch TV

33 watched TV hung out with friends and ate pizza

how many 18-24 yearolds did not do any of these three activities last friday night?

Answer 1

This was a fun little puzzle.

If we number the statements (and reorder their contents so they all have the same information in the same order), we get the following:

1) 171 watched TV

2) 150 hung out with friends

3) 200 did not hang out with friends, ate pizza

4) 28 watched TV, did not hang out with friends, ate pizza

5) 44 watched TV, hung out with friends, did not eat pizza

6) 31 did not watch TV, hung out with friends, ate pizza

7) 33 watched TV, hung out with friends, ate pizza

Combing 3) and 4) you get 8) as follows:

8) 172 did not watch TV, did not hang out with friends, ate pizza

Combing 5) and 7) you get 9) as follows:

9) 77 watched TV hung out with friends

Combing 2) and 9) you get 10) as follows:

10) 73 did not watch TV, hung out with friends

By negating 1) you get 11 as follows:

11) 369 did not watch TV

Combing 10) and 11) you get 12) as follows:

12) 296 did not watch TV did not hang out with friends

Combining 8) and 12) you get the final conclusion 13) as follows:

13) 124 did not watch TV, did not hang out with friends, did not eat pizza