I have a doubt about this question:

Specifically the 4th and 5th options.

Now, here’s what I think:

4th Option: Students taking the maths class IN A is only the subset of people in A. Now had it just been students taking maths class, then it would’ve made sense. But when it is specifically students taking the class in A, doesn’t it mean that B contains the people only from A which would mean that the radius of B would be equal to the radius of A?

Similarly for the 5th option too.

So a numerical example:

Suppose there are 3 subjects, physics, maths and English, and a total of 150 students. Each subject has 50 students. Suppose students taking both maths class and phy is 18. So by option 4, A is 18 and students taking maths in A are still 18, so B is still 18.

Now, people taking maths and not physics can be at max 32.So, B is 32(max). Students taking maths class in B is still 32, so A is still 32.

Had it not written students in A or students in B then the question and its options would make sense. But as it stands, Im finding it a bit confusing.

I didn’t quite catch onto the logic you used, but based on what I understand - since they’re concentric circles, they have the same center - and one circle is inside the other. you can google images for the concept.

Since the radius of B is greater than that of A , circle A is *completely inside* circle B. This means whatever set A represents should be a subset of B - by which *Option A* makes the most sense amongst the rest of the options.

Option A? But they are completely unrelated no?

I’ll give a clearer view of my logic. Basically, students taking maths class in A are already a subset of A. So by that logic in option 4, B and A should be of the same radius. Similarly, for option 5, students taking maths in B is already a subset of students of B. So A should be the same radius as B.

In both the options students in the other respective class is the entire subset of the other class. Is it clearer now?

I think I’m starting to see your logic - for option 4, yes, the entire set represented by A can be a subset of itself. But as you said - A and B would have to be of the same radius. Since they’re concentric, they then share the same center - in other words, for option 4, they would have to be *the same circle*. And that can’t be because the question has told us that the **radius of B is greater than that of A**.

Since they’re concentric and B is of greater radius, A is going to be a subset of B.

In that sense, Option E makes sense in the first half, but in the second half it says *not in a physics class*. This is where I guess it gets tricky - because mathematics & physics are the only two classes given in all 4 scenarios. If those are the only two classes - would Option E still make sense?

The reason I think Option A checks out is because you need to know math to study physics. Some people studying physics have a good foundation in math, so they don’t need the class while others do. This isn’t an opinion - it’s generally known that physics problems rely on mathematics and not the other way around.