Given the following survey results, how many people like C only?
- 21 people like Product A
- 14 people like Products A and B
- 12 people like Products A and C
- 8 people like Products A, B and C
- 26 people like Product B
- 14 people like Products B and C
- 39 people like Product C
- 21 people like Product A
- 14 people like Products A and B
- 12 people like Products A and C
- 8 people like Products A, B and C
- 26 people like Product B
- 14 people like Products B and C
- 39 people like Product C
1 Answer
21
Explanation:
For each product, there will be people who like it only (ex. A only), people who like it and one other (ex. A and B only) and those who like all three. Let's work through this.
I'll note that this question appears to be a more fleshed-out version of this one posted earlier in the week: https://socratic.org/questions/in-a-survey-it-was-found-that-21-people-liked-product-a-26-liked-product-b-and-3 where the total number of likes for C was 39. I'll use that figure in here.
For product A, 21 people in total like it. 14 people like A and B (and might like C), 12 like C and A (and might like B), and 8 like A, B and C. This means that we need to subtract the 8 (those who like all three) from the numbers listed for people liking two products. This will give us:
People who like A and B only
People who like A and C only
For Product B, 26 people like it. 14 like A and B (and might like C), 14 people like B and C (and might like A), and 8 like all three. We can do the same sort of math for this that we did for A:
People who like A and B only
People who like B and C only
We can now do C. 39 people like C. 4 people like C and A only. 6 people like B and C only. And 8 like A, B, and C. Therefore:
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I want to note that when I first started working with A that if we take the numbers given as "only", we'd end up with something that made no sense:
A total likes = 21
A, B likes = 14
A, C likes = 12
which puts us at 26 likes, which is more than the 21 given. And so I realized we needed to subtract out from the A, B likes, for instance, those people who also liked C.