Author 
Message 
Current Student
Joined: 11 May 2008
Posts: 551

How many prime factors does positive integer N have? (1) N/5
[#permalink]
Show Tags
04 Sep 2008, 03:18
How many prime factors does positive integer N have? (1) N/5 is a prime number. (2) 3N^2 has two different prime number. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.



VP
Joined: 17 Jun 2008
Posts: 1474

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 03:42
Answer is B.
From stmt 1, N is a multiple of 5 in such that N is obtained by multiplying 5 with another prime number.
Thus, N can be 10, 15, 25, 35, 55...... i.e. N can have 1 prime factor (e.g. 25) or 2 (e.g. 10, 15,...)....hence not sufficient.
From stmt2, 3 is already a prime factor. Hence, in order for 3N^2 to have two different prime factor, N^2 has to be a perfect square of a prime number. This implies that N itself is a prime number and hence will have only one prime factor. Hence, sufficient.



Manager
Joined: 15 Jul 2008
Posts: 205

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 05:46
arjtryarjtry wrote: How many prime factors does positive integer N have? (1) N/5 is a prime number. (2) 3N^2 has two different prime number. D. If N/5 is a prime number, then N=5*x where x is a prime number. So N has only two prime factors. if 3*N^2 has two different prime factors, then 3 is one of them and N is the other. In this case, N has to be a prime number and hence will have only one prime factor



Senior Manager
Joined: 16 Jul 2008
Posts: 279
Schools: INSEAD Dec'10

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 05:52
IMO C. 1) N = 5a, where a is any prime number. N can have one or two prime factors. Not sufficient 2) 3N^2 has two different prime factors. Not sufficient, because N can have one prime factor, or two prime factors (f.ex. N=21=3*7). Combine both  N can be 25 or 15, i.e. two prime factors.
_________________
http://applicant.wordpress.com/



SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 08:03
arjtryarjtry wrote: How many prime factors does positive integer N have? (1) N/5 is a prime number. (2) 3N^2 has two different prime number. (1) N/5 is a prime number. N= 5* x it doesn't matter.. whether x=5 or 3 .. N has two prime factors. N=5*5 ( two prime factors.... though not two different prime factors.) Question is How many prime factors does positive integer N have? Ans 2(2) 3N^2 has two different prime number.[/ N must be prime number. sufficient. D. If question Says How many different prime factors does positive integer N have? then Ans would be C.
_________________
Your attitude determines your altitude Smiling wins more friends than frowning



Manager
Joined: 15 Jul 2008
Posts: 205

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 08:24
x2suresh wrote: arjtryarjtry wrote: How many prime factors does positive integer N have? (1) N/5 is a prime number. (2) 3N^2 has two different prime number. (1) N/5 is a prime number. N= 5* x it doesn't matter.. whether x=5 or 3 .. N has two prime factors. N=5*5 ( two prime factors.... though not two different prime factors.) Question is How many prime factors does positive integer N have? Ans 2(2) 3N^2 has two different prime number.[/ N must be prime number. sufficient. D. If question Says How many different prime factors does positive integer N have? then Ans would be C. another good catch gosh... hopefully the real test will leave no room for ambiguity .



SVP
Joined: 07 Nov 2007
Posts: 1728
Location: New York

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 08:28
arjtryarjtry, Is this gmatclub problem? If yes, we can suggest them to remove the ambiguity from the question.
_________________
Your attitude determines your altitude Smiling wins more friends than frowning



Intern
Joined: 06 Aug 2007
Posts: 37

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 11:42
A. N/5 = prime
N = 5*P (P can be 2, 3 or ....)
No.of prime factors = 2
B. 3*N^2 = prime
3 = prime, N^2 = prime, N = prime
No.of prime factors = 2
So D!



Senior Manager
Joined: 31 Jul 2008
Posts: 269

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 12:16
i think it shud be A
because in 2 statement :
3*N^2 has two Different prime factors :
Now why should we assume that N itself is prime
how about if N = 6 , in this case also the number of different prime factors will 2 i.e 2,3
so as per 2 statement ans can be N has 2 prime factors or just 1
what say ?



Senior Manager
Joined: 16 Jul 2008
Posts: 279
Schools: INSEAD Dec'10

Re: prime factors of n
[#permalink]
Show Tags
04 Sep 2008, 23:50
Nerdboy wrote: IMO C.
1) N = 5a, where a is any prime number. N can have one or two prime factors. Not sufficient 2) 3N^2 has two different prime factors. Not sufficient, because N can have one prime factor, or two prime factors (f.ex. N=21=3*7).
Combine both  N can be 25 or 15, i.e. two prime factors. Guys, I messed up completely. If N can be 25 or 15, then answer is E  assuming we are looking for different prime factors. If we are looking for number of prime factors, not necessarily different, then it should be A. OA?
_________________
http://applicant.wordpress.com/



VP
Joined: 17 Jun 2008
Posts: 1474

Re: prime factors of n
[#permalink]
Show Tags
05 Sep 2008, 00:26
While I await the OA....I have one question here. If I take the number 25, do I say, it has two prime factors? does it not have only one prime factor and that is 5? 25 can be divided by 5 and 5 is a prime factor. why do I have to count 5 again? == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.




Re: prime factors of n &nbs
[#permalink]
05 Sep 2008, 00:26






