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Can distinct factors of a positive integer be negative?

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Can distinct factors of a positive integer be negative?  [#permalink]

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New post 27 Jul 2018, 02:56
Hi, can somebody help me with these concept questions?

1. Can distinct factors of a positive integer be negative. For example we have a number 100 and it asks for how many distinct factors it has. Do we count the negative numbers too?

2. I came accross one question where in the answer it said "Factor of a Negative number is undefined" I can't find that question any more but can somebody validate this please?

Thank you very much.
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Re: Can distinct factors of a positive integer be negative?  [#permalink]

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New post 27 Jul 2018, 03:32
alexlearning17 wrote:
Hi, can somebody help me with these concept questions?

1. Can distinct factors of a positive integer be negative. For example we have a number 100 and it asks for how many distinct factors it has. Do we count the negative numbers too?

2. I came accross one question where in the answer it said "Factor of a Negative number is undefined" I can't find that question any more but can somebody validate this please?

Thank you very much.


Great question. I found this post which can help you https://gmatclub.com/forum/number-of-di ... l#p1121158

Let us know if you still have questions ?
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Re: Can distinct factors of a positive integer be negative?  [#permalink]

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New post 27 Jul 2018, 03:37
workout wrote:
alexlearning17 wrote:
Hi, can somebody help me with these concept questions?

1. Can distinct factors of a positive integer be negative. For example we have a number 100 and it asks for how many distinct factors it has. Do we count the negative numbers too?

2. I came accross one question where in the answer it said "Factor of a Negative number is undefined" I can't find that question any more but can somebody validate this please?

Thank you very much.


Great question. I found this post which can help you https://gmatclub.com/forum/number-of-di ... l#p1121158

Let us know if you still have questions ?


THank you and how about the 2nd question? I couldn't find it anywhere.
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Re: Can distinct factors of a positive integer be negative?  [#permalink]

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New post 27 Jul 2018, 03:46
1
alexlearning17 wrote:
workout wrote:
alexlearning17 wrote:
Hi, can somebody help me with these concept questions?

1. Can distinct factors of a positive integer be negative. For example we have a number 100 and it asks for how many distinct factors it has. Do we count the negative numbers too?

2. I came accross one question where in the answer it said "Factor of a Negative number is undefined" I can't find that question any more but can somebody validate this please?

Thank you very much.


Great question. I found this post which can help you https://gmatclub.com/forum/number-of-di ... l#p1121158

Let us know if you still have questions ?


THank you and how about the 2nd question? I couldn't find it anywhere.


From the definition of a Factor, factors are possible for negative numbers.

But from GMAT perspective, factors are always POSITIVE. I also believe to remove ambiguity GMAT will always be more clear and use the term "positive factors" in question statements.

For your reference, more on Number theory here https://gmatclub.com/forum/math-number- ... 88376.html
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Re: Can distinct factors of a positive integer be negative?  [#permalink]

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New post 30 Jul 2018, 12:47
alexlearning17 wrote:
Hi, can somebody help me with these concept questions?

1. Can distinct factors of a positive integer be negative. For example we have a number 100 and it asks for how many distinct factors it has. Do we count the negative numbers too?

2. I came accross one question where in the answer it said "Factor of a Negative number is undefined" I can't find that question any more but can somebody validate this please?

Thank you very much.


I've never seen an official GMAT problem that asked about negative factors, so you probably don't have to worry about them either way.

I'd guess that the problem you're referring to wasn't an official problem, and it sounds like it might not have been a very well written problem, either! An answer choice saying 'factor of a negative number is undefined' doesn't sound very GMAT-like. Think about it like this: if that's the right answer to the problem, then you could pick that answer without even doing any work or really thinking about it, just because you memorized that fact. If it's the wrong answer, then you could eliminate it without doing any work. Either way, including an answer choice like that makes the problem easier for no reason and rewards people for just memorizing some random math fact, which the GMAT doesn't like to do. They'd rather make you do some mental work to get the answer.

The GMAT is also usually pretty clear when something could be ambiguous. If it's not totally obvious whether you're looking at positive numbers, or both positive and negative, the text of the problem will probably say something like 'f is a positive integer' to make it clear.
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Re: Can distinct factors of a positive integer be negative? &nbs [#permalink] 30 Jul 2018, 12:47
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