first off, it doesn't really matter how many numbers are in the sets, because the range of the sets is what matters.

before looking at the statements, think about the possibilities for the individual sets:

* there's no minimum range necessary for either set; in fact, the individual sets can even have a range of zero, and still produce as large a combined range as you want.
for instance, set A could consist of twenty copies of the number 0, and set B could consist of forty copies of the number 100. in this case, each of the sets has a range of 0, but the combined range is 100.

* there's also no maximum range necessary, especially because there are no upper bounds imposed on the range of anything in the problem.

therefore, even if you combine the two statements:
* the range of set B could be really small. for instance, if set A is twenty 0's, and set B is twenty 99's and twenty 100's, then both conditions are satisfied, but the range of set B is only 1.
* the range of set B could also be huge. for instance, set A could range from 0-100, and set B could range from 100-1000. in that case, the range of set B is 900.

answer = e

augusto wrote:Hi Guys,

I might be really wrong, but can you have duplicate elements in a set?

Definition 1 A set is a collection of distinct objects.
The objects can be real, physical things, or abstract, mathematical things.
The number of such objects can be finite or infinite. The only important
thing is that the objects be distinct, i.e., uniquely identifiable.

(taken from https://www.ces.clemson.edu/~mjs/courses ... theory.pdf)

But anyway I think the correct answer is E, because with both stems you can find scenarios where the range of B is greater than 45 and less than 45.

yeah, you're right: even if the numbers in the sets are required to be distinct, the answer is still e.

if set A = integers 1-20, set B = integers 21-60, then answer = "no"
if set A = evens 2-40, set B = evens 42-120, then answer = "yes"
answer = e

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in any case, yes, the formal mathematical definition of a set requires that its members be distinct. but i can guarantee you that you will not have to know that in order to get questions right on the gmat; there's just no way they'd require that degree of esoteric mathematical knowledge, unless they explicitly included the word "distinct" in their problem statements.

this is one of the dangers of using unsourced problems: they may require knowledge that the gmat doesn't actually test, or, in extreme situations, they may even use terminology in ways that contravene the rules followed by the gmat itself. only use problems from trusted sources!

also, i'll have to go back and look, but i could swear up and down that i've seen at least one official problem containing something like "the set {2, 3, 3, 4, 4, x, y}", which would mean that the gmat technically allows repeated members in "sets".

one more thing: there's a certain amount of ambiguity inherent in this topic anyway, because, in common statistical parlance, a "data set" is definitely allowed to have repeat values.