Ah, not understanding this...

This need not be true!

I would argue that the OA is incorrect if its C. The answer must be E. There could be a repetition of elements in B (or A).

Consider this example:

A: [1,2, 2, 3,3, 4,5,6,7,8,9,10,11,12,13,14,15]
B: [1, 2, 3]

In this case
B is subset of A.
Exactly 80% of elements of A are not part of B. (out of 15 unique elements, 12 are not part of B)

But knowing that B has 3 elements would in no way help you to find out number of elements in A.There is no such constraints on A or B that elements could not be repeated.

The answer must be E in my opinion.
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Probably you'd agree with the definition of subset as:
■Set A is called subset of B if every element of A is also an element of B. We write it as AB (read as "A is a subset of B" or "A is contained in B"). In such a case, we say BA ("B is a superset of A" or "B contains A").

Therefore, if A= [1,2,3,4,5] and
B= [2,2,2,2,2]
will have subset -superset relation. Try to use the calculation done above on this.
B is subset. B has 5 elements as per your calculation? right? exactly 80% of elements of A (4 out of 5) are not in B. So How many elements in A? 25?

Anyway, just presented my opinion!
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Yes, figure drawn by you is perfect! But, the conclusion drawn is not. 14 elemenets are not part of 80% doesnt imply that rest 20% =14. It only means that 14 elements of B are made of 20% elements of A. Same as following:
A= [1,2,3,4,5]
B=[2,2,2,2,2,2,2....,2] (14 times)

Thus it is not sufficient and must be E.

if it is indeed Gmatprep question then also it could be flawed. there are a few incorrect questions in gmatprep. for example check this post by none other than Bunuel.
all-the-clients-that-company-x-had-at-the-beginning-of-last-128023.html?hilit=gmatprep#p1049002
In fact I've seen other posts by Bunuel too where he has identified incorrect gmatprep questions and correctly so. problem is finding out that particular post from his 9000+ posts. May be someday I'll stumble upon such a post again
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Sometimes the student writes the question wrong, then it is unuseful in some how.

But for me as the question is posed per se, the answer is C

Basically it says: 14 = 0.2 x........I do not see a particular assumption here or inference
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KUDOS is the good manner to help the entire community.

Vips0000's concern is valid. Repetition of an element in the set can lead to further complexity around this problem. Now, the question whether to count only distinct elements/numbers or count element separately including repetitions remains open and debatable. I see several varying viewpoints around Set problems prepared by Prep companies or even in theories.

Still I believe using the same concept raised by Vips0000, we should arrive at the answer(C).

Lets take a look at below explanation (Courtesy UCSD - Maths dept) -- See attached paper if you want to dig down.
Since a set is an un-ordered collection of distinct objects, the following all describe the same 3-element set
{a, b, c} = {b, a, c} = {c, b, a} = {a, b, b, c, b}.
The first three are simply listing the elements in a different order. The last happens to mention some elements more than once. But, since a set consists of distinct objects, the elements of the set are still just a, b, c. Thus 3 elements.

Another way to think of this is:
Two sets A and B are equal if and only if every element of A is an element of B and every element of B is an element of A.
Thus, with A = {a, b, c} and B = {a, b, b, c, b}, we can see that everything in A is in B and everything in B is in A.
--Read further in the chapter if you wish to.

----------------------------
Back to our problem

Even if we count repeated elements in the set only once (i.e. count distinct) - by applying same concept - we should be able to find out how many elements are set A using statements (1) and (2).
A={1, 2, 2, 3, 4, 4, 5, 5, 5}
B={2,2,2,2,2}

Here set A has 5 elements (though repeated) and set B contains 1 element (i.e. 2 - though repeated) -> Hence 80% of of elements in set A are not in set B.

Similarly, if (statement 1) "Set B has 14 elements" and (statement 2) "Exactly 80% of the elements in set A are not in Set B" -> A should have 70 (distinct) elements, whether or not they are repeated inside the set. Note that question asks for 'how many elements?' -> 70 (not counting repeats)

Hence choice(C) should be the answer.

Feel free to correct if anything wrong!


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