Is there a video for Data Analysis Foundation Quiz #1? I couldn’t find any via the search bar.
Seriously struggling with question 15. I did not know how to tackle this at all. I tried it via Total = A +B - both approach, but since there is an inequality I did not know how to continue.
It obviously is about overlapping sets, but again, the inequality totally threw me off. Even ChatGPT couldn’t help here…
Appreciate any help, thank you!
I’ll start it off for you and I hope you can finish it (it’s good for your own practice).
|B \cup C| = 100 = |B| + |C| - |B \cap C| and you’re given that |C| - |B \cap C| \leq 34. Using those two, you can have |B| \geq 66 (try to fill in the blanks and work out how i got this).
Now, depending on the values of |B \cap C|, you can obtain a range of values for |C| and |B| which works, so clearly all the provided values can work.
For example, I hope your reasoning for why |B \cap C| = 100 could work revolves around restricting |C| \geq 134 and |B| \geq 66 .
Yeah, maybe I just don’t get inequalities…
Total = B + C - both
Only C = C - both smaller or equal than 34
So if only C is 34, then B can be 66 and both is 0
If only C is zero, then B can be 100 and both is zero
If only C is zero, and B is zero, then both can be 100?
Instead of trying to solve the question (for now), can you try to use my template (with the inequalities) and reason it out? I mean if you want to get better at inequalities then the best way to do that is to utilize them, no?
The key here is the strange at most wording.
For an intuitive explanation, draw a venn diagram. We know at most 34 students take only chemistry, so 0 \leq |C \setminus (B\cap C)| \leq 34.
Can there be 0 students in both classes (|B \cap C| = 0)? Sure. Maybe 0 students take only chemistry and everyone takes only Biology.
Can there be 100 students in both classes? Sure. Maybe 0 students take only chemistry and everyone takes both Biology and Chemistry.
Can there be 50 students in both classes? Sure. Maybe 0 students take only chemistry, 50 take both, and 50 take only Biology.
Not a great question IMO, but at no fault of Gregmat - lots of ETS ones seem similarly bad.
