sanju09 wrote:x and y are positive integers. For some natural number n, is (x ^ n + y ^ n)/(x + y) an integer?
(1) (x ^ 3 + y ^ 3)/(x + y) is an integer.
(2) (x ^ 4 + y ^ 4)/(x + y) is not an integer.

For those those who aren't certain what is meant by "natural numbers," they are the same as positive integers. That said, I'm pretty sure that the GMAT doesn't use the term "natural numbers."

We can see from the statements (which are always true) that the answer must be E.
The question is, "Is (x ^ n + y ^ n)/(x + y) an integer?"
Statement (1) tells us that it is an integer when n=3, and statement (2) tells is that it is not an integer when n=4. Since we don't know the value of n, we can't definitively answer the original question.

sanju09 wrote:x and y are positive integers. For some natural number n, is (x ^ n + y ^ n)/(x + y) an integer?
(1) (x ^ 3 + y ^ 3)/(x + y) is an integer.
(2) (x ^ 4 + y ^ 4)/(x + y) is not an integer.

The wording of the question is ambiguous. If you interpret the question as Brent does above (that is, if you interpret it to mean "n is a positive integer. Is (x ^ n + y ^ n)/(x + y) an integer?", then the answer is certainly E.

If, on the other hand, you interpret it to mean "Does there exist a positive integer for which (x ^ n + y ^ n)/(x + y) is an integer?", which is a perfectly valid interpretation of the question as it is worded, then you certainly don't need any additional information at all to answer the question: when n=1, the expression will clearly be equal to an integer (it will equal 1). I suppose that would make the answer D, though it's not a DS format you'd ever see on the GMAT.