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.
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Back to our problemEven 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!
Attachment:
UCSD EDU-Maths-Sets.pdf [237.04 KiB]
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