Of 180 people who were asked if they had watched recent

As directed, make a Venn diagram. You will easily get the answer.



The red area is 38 (Only Game 1 Watchers).
The light green region is 20 (people who watched game 2 and game 3 including people who watched all three games)
Orange and Yellow region combined will be 56 - 20 = 36 since the entire game 2 circle has 56 people.
Similarly the brown and dark green region together will be 64 - 20 = 44 since the entire game 3 circle has 64 people.

To get 'None', that is people who watch no games, from the total 180, we need to subtract people who watch at least one game i.e. all the people lying anywhere in the three circles

None = 180 - 38 - 20 - 36 - 44 = 42

NO of people who did not watch any game = 42

Thanks a lot. I did create a Venn diagram, but missed the step highlighted

None = 180 - 38 - 20 - 36 - 44 = 42

Here we are assuming that none has watched games 1 and 2, and 2 and 3. if that is true answer should be 42. Question does not look like a proper gmat style question.

Note that we are not assuming that no one watched games 1 and 2 and games 2 and 3. What we know is that 36 people watched either only game 2 or only games 1 and 2 (not game 3). Similarly, we know that 44 people watched only game 3 or games 1 and 3 (not game 2). We don't need to segregate the numbers i.e. we don't need how many people watched only game 3 and how many watched games 1 and 3. They are all people who watched at least 1 game and hence we remove them from 180. We are interested in people who watched no game.

Go back to the venn diagram given above and read the explanation given below it.