Brain Teasers
TV shows
95 people were asked what type of TV programs they liked out of news, movies and documentaries.
64 like news
80 like movies
2 like only documentaries
23 like movies and documentaries
51 like movies and news
34 like only movies and news
10 like only news and documentaries
How many people like all three types of TV shows?
64 like news
80 like movies
2 like only documentaries
23 like movies and documentaries
51 like movies and news
34 like only movies and news
10 like only news and documentaries
How many people like all three types of TV shows?
Answer
17 like all three typesThe breakdown of the results is as follows:
2 like only documentaries
23 like only movies
3 like only news
6 like only movies and documentaries
34 like only movies and news
10 like only news and documentaries
17 like all three types
---
95 total viewers
The following equations satisfy the given conditions:
3 like only news + 34 like only movies and news + 10 like only news and documentaries + 17 like all three types = 64 like news
23 like only movies + 6 like only movies and documentaries + 34 like only movies and news + 17 like all three types = 80 like movies
2 like only documentaries
6 like only movies and documentaries + 17 like all three types = 23 like movies and documentaries
34 like only movies and news + 17 like all three types = 51 like movies and news
34 like only movies and news
10 like only movies and documentaries
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Comments
exactly how did you come to that answer?!
Use a Venn Diagram
because
51 like movies and news
34 like only movies and news
17/51 like all three. The rest of the info can be ignored
51 like movies and news
34 like only movies and news
17/51 like all three. The rest of the info can be ignored
Easy with a ven diagram. 51-34=17
If you finish the venn diagram, there are only 95 people, not 100! 23 only m, 34 only m and n, 6 only m and d, and 17 m and n and d. Altogether 80 m. Also 34 + 17 = m and n, and 17 + 6 = 23 m and d. It says 10 only n and d which is 10 + 17 = 27 n and d. n = 64 means 64 - 10 - 17 - 34 = 3 only n.
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