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# How many prime factors does positive integer N have? (1) N/5

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How many prime factors does positive integer N have? (1) N/5 [#permalink]  04 Sep 2008, 02:18
How many prime factors does positive integer N have?
(1) N/5 is a prime number.
(2) 3N^2 has two different prime number.
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Re: prime factors of n [#permalink]  04 Sep 2008, 02:42

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.
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Re: prime factors of n [#permalink]  04 Sep 2008, 04:46
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
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Re: prime factors of n [#permalink]  04 Sep 2008, 04:52
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.
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Re: prime factors of n [#permalink]  04 Sep 2008, 07:03
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.
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Re: prime factors of n [#permalink]  04 Sep 2008, 07:24
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 .
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Re: prime factors of n [#permalink]  04 Sep 2008, 07:28
arjtryarjtry,

Is this gmatclub problem? If yes, we can suggest them to remove the ambiguity from the question.
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Re: prime factors of n [#permalink]  04 Sep 2008, 10:42
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!
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Re: prime factors of n [#permalink]  04 Sep 2008, 11:16
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 ?
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Re: prime factors of n [#permalink]  04 Sep 2008, 22:50
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?
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Re: prime factors of n [#permalink]  04 Sep 2008, 23:26
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?
Re: prime factors of n   [#permalink] 04 Sep 2008, 23:26
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