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For some natural

by sanju09 » Fri Apr 03, 2009 4:05 am
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.
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Re: For some natural

by Brent@GMATPrepNow » Fri Apr 03, 2009 5:59 am
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.
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Re: For some natural

by Ian Stewart » Fri Apr 03, 2009 7:32 am
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.
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Brent and Ian

by sanju09 » Sat Apr 04, 2009 3:36 am
I must thank to both Brent and Ian here for correcting me. I am in the process of making my own questions for different competitions; and on this forum, I use to throw few of those just to check whether or not that's a possible GMAT seed and/or that's properly worded. Thanks for being there gentlemen!
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