In a group of 30 students, 8 are enrolled in an English

ggarr, you said 7 are enrolled in both the classes, means these 7 students should belong to the numbers given for both classes i.e. 16+8=24. If yes, then what justifies 20 students taking only one class which also come from 16+8= 24 ?

I think I was careless the first time around. This is my second go.
Stem: 24 are enrolled in E, A or E and A. 6 are in neither.
1) if 20 are in A or E and 6 are in neither then 4 are in both
2) 30 students in total, 24 are enrolled in E, A or E and A and 3 are in neither. 30 - 3 = 27 students in E, A or E and A. insufficient and inconsistent

now I'm getting A. hmmmm

I completely overlooked the 16+8=24 part. please ignore that post.

Still, OA is D , my friend.

To find how many students are enrolled in both we can use any of the following two formulas:

Both=ENG+ALG+none-Total
or
Both=Total-(ENG(only)+ALG(only))-none

Let`s plug in what is given in the question, we get;

Both=8+16+none-30
or
Both=30-(ENG(only)+ALG(only))-none, these are the formulas we have;

1st- gives us (ENG(only)+ALG(only)), insuf, still need the # of none
2nd- gives #none- suff

So, my answer is B

Set x=students who take both Algebra and English, Venn Diagram formula gives:
16 + 8 - x + neither = 30
-x + neither = 6
We are trying to find x

(1) Knowing that students taking exactly one class = 20, you can obtain:
20 + x + neither = 30
x + neither = 10
Using equation above, you can solve for "neither":
2*neither = 16
neither = 8
Plug this in, you should get x = 2
SUFFICIENT

(2) Neither = 3
Plug in, you get x = -9!!!
I would say it is sufficient, but neither = 3 doesn't make any sense. Think about it. If you have total of 30 students, 3 doesn't take any class, you have 27 students total taking English, Algebra, or both. This number should be no more than (16+8 =) 24. This is impossible.
I would say SUFFICIENT, but bad given number.

Explain please. I guess, it's E

Yes, agree A.

I forgot about second equation. Given two equation we can find two unknow variables.

Thank you!

Though probably OA is D, assuming we do not calculate...

I do agree with bkk145,
1) is sufficient and it is proven
2) is sufficient to find an ANSWER to the problem even if it is -3 persons who take both subjects

So the answer is D