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how many positive factors does a real number has ?

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by goelmohit2002 » Tue Sep 15, 2009 11:24 am
Hi All,

Can someone please tell how many positive factors does a real non integer number has ? For e.g. how many positive factors 2.4 has ? Is 1 a factor of 2.4 ? If no why 1 is not a factor of 2.4 ?

Thanks
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by Ian Stewart » Tue Sep 15, 2009 2:44 pm
We only discuss factors when talking about integers (and GMAT divisibility questions are always restricted to positive integers), so it makes no mathematical sense to ask how many factors 2.4 has.
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by goelmohit2002 » Tue Sep 15, 2009 9:49 pm
Ian Stewart wrote:We only discuss factors when talking about integers (and GMAT divisibility questions are always restricted to positive integers), so it makes no mathematical sense to ask how many factors 2.4 has.
Thanks a lot Ian !!!


Just for clarification...do you mean to say that any non integer real number has zero positive factors ?
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by Ian Stewart » Wed Sep 16, 2009 6:07 am
goelmohit2002 wrote: Just for clarification...do you mean to say that any non integer real number has zero positive factors ?
Not quite; asking how many factors 0.53 has is like asking how many factors a salmon has - the question doesn't mean anything, so there's no way to answer it. Of course, you'll never be asked such a question on the GMAT, so it's not something to be concerned about.
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by goelmohit2002 » Wed Sep 16, 2009 6:12 am
Ian Stewart wrote:
goelmohit2002 wrote: Just for clarification...do you mean to say that any non integer real number has zero positive factors ?
Not quite; asking how many factors 0.53 has is like asking how many factors a salmon has - the question doesn't mean anything, so there's no way to answer it. Of course, you'll never be asked such a question on the GMAT, so it's not something to be concerned about.
Thanks a lot Ian....actually I was stumped by one question that I came across.

How many positive factors does X has ?
1) X^2 has four positive factors.
2) 2X has three positive factors.

OA = A. Can you please tell how can it be A...here I think A can only be correct answer if X is non integer real number......

Kindly help !
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by Ian Stewart » Wed Sep 16, 2009 8:36 am
goelmohit2002 wrote: Thanks a lot Ian....actually I was stumped by one question that I came across.

How many positive factors does X has ?
1) X^2 has four positive factors.
2) 2X has three positive factors.

OA = A. Can you please tell how can it be A...here I think A can only be correct answer if X is non integer real number......
That cannot be a real GMAT question - where is it from? If a number has exactly four positive divisors, then its prime factorization must either be in the form p^3, or pq, where p and q are different primes. If x^2 is equal to either p^3 or pq, then x is not an integer. So, if Statement 1 is true, the question doesn't make any sense; does that make Statement 1 sufficient? Impossible to say; it's a meaningless question.

With Statement 2, if a number has three positive factors, its prime factorization must be in the form p^2, where p is prime. If we knew x was a positive integer (and in any real GMAT question about divisibility, you would be told this, since otherwise the question 'how many factors does x have?' is meaningless), then we would be certain that x = 2, and the Statement would be sufficient. If x doesn't need to be an integer - well, then again we're looking at a question that does not test divisibility in the way the GMAT does. There isn't anything to gain from studying this question.
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by goelmohit2002 » Wed Sep 16, 2009 9:36 am
Thanks Ian. Just one small related query of factor question....the following is a question where it looks statement 1 is similar to the above discussion....

Can you please tell do we need to consider "n" as integer here or real number of n is also possible if nothing is mentioned...

Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

OA = C.

Here IMO A can be ruled out only if n is not an integer something like 30^(1/2)

Please help !
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by kyabe » Wed Sep 16, 2009 9:43 am
goelmohit2002 wrote:Thanks Ian. Just one small related query of factor question....the following is a question where it looks statement 1 is similar to the above discussion....

Can you please tell do we need to consider "n" as integer here or real number of n is also possible if nothing is mentioned...

Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

OA = C.

Here IMO A can be ruled out only if n is not an integer something like 30^(1/2)

Please help !
n would be positive integer..
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by goelmohit2002 » Wed Sep 16, 2009 10:09 am
kyabe wrote: n would be positive integer..
Thanks Kyabe !

But as we discussed in case of factors.....n has to be integer....n can't be real....so why are we considering n to be real in 30 factor case....but not considering X to be real in that X^2 has 4 factors ?

Basically if we take first statements of the above questions:

1) X^2 has four positive factors.
Our Analysis => Above is wrong...since no integer X is there where X^2 has four factors. Here we are saying that X has to be integer.

2. 30 is a factor of n^2
Here we say that n can be real too i.e. 30^(1/2)

why not the same is applicable for statement 1 above....if we replace n by X....more or less statement becomes same....one is asking number of factors and other is asking which all factors ?

Please tell what I am missing here ?
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by Ian Stewart » Wed Sep 16, 2009 10:32 am
goelmohit2002 wrote:Thanks Ian. Just one small related query of factor question....the following is a question where it looks statement 1 is similar to the above discussion....

Can you please tell do we need to consider "n" as integer here or real number of n is also possible if nothing is mentioned...

Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

OA = C.

Here IMO A can be ruled out only if n is not an integer something like 30^(1/2)

Please help !
Again, the question only makes sense if n is an integer. A real GMAT question would say 'is 30 a factor of positive integer n?' Where are these questions from?
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by goelmohit2002 » Wed Sep 16, 2009 10:37 am
Ian Stewart wrote:
goelmohit2002 wrote:Thanks Ian. Just one small related query of factor question....the following is a question where it looks statement 1 is similar to the above discussion....

Can you please tell do we need to consider "n" as integer here or real number of n is also possible if nothing is mentioned...

Is 30 a factor of n?

(1) 30 is a factor of n^2
(2) 30 is a factor of 2n

OA = C.

Here IMO A can be ruled out only if n is not an integer something like 30^(1/2)

Please help !
Again, the question only makes sense if n is an integer. A real GMAT question would say 'is 30 a factor of positive integer n?' Where are these questions from?
Thanks a lot Ian !!!

Please see the link below for the above question.

https://www.takegmat.com/index.php/gmat- ... ciency-56/

The last poster there came up with answer C and claims to be following Manhattan approach.

Can you please help tell what indeed is the case ?
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by Ian Stewart » Wed Sep 16, 2009 10:55 am
goelmohit2002 wrote: Please see the link below for the above question.

https://www.takegmat.com/index.php/gmat- ... ciency-56/

The last poster there came up with answer C and claims to be following Manhattan approach.

Can you please help tell what indeed is the case ?
Yeah, that's just not a well-written question, as I explained above. A and C are both perfectly defensible answers. It's best to work from better quality sources.
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by goelmohit2002 » Wed Sep 16, 2009 10:57 am
Ian Stewart wrote:
goelmohit2002 wrote: Please see the link below for the above question.

https://www.takegmat.com/index.php/gmat- ... ciency-56/

The last poster there came up with answer C and claims to be following Manhattan approach.

Can you please help tell what indeed is the case ?
Yeah, that's just not a well-written question, as I explained above. A and C are both perfectly defensible answers. It's best to work from better quality sources.
Thanks a lot Ian....

just came across the correct version of the question which is under the same line of thought as you suggested above

https://www.beatthegmat.com/ds-t33804.html
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by goelmohit2002 » Thu Sep 17, 2009 4:35 am
Hi Ian,

Can you please help resolve one related factor doubt. Can you please tell how the answer to following question is A. IMO it should be D

Is integer N a prime number ?
1) All the prime factors of N are greater than root N.
2) All the prime factors of N are greater than N/2.
OA = A.
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