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# How many distinct prime divisors does a positive integer [m]

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Manager
Joined: 23 Jan 2013
Posts: 133
Concentration: Technology, Other
Schools: Berkeley Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
How many distinct prime divisors does a positive integer [m]  [#permalink]

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Updated on: 31 May 2014, 15:54
3
00:00

Difficulty:

85% (hard)

Question Stats:

34% (01:39) correct 66% (01:15) wrong based on 98 sessions

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How many distinct prime divisors does a positive integer $$n$$ have?

(1) $$2n$$ has one distinct prime divisor.

(2) $$3n$$ has one distinct prime divisor.

M18-37

Originally posted by shelrod007 on 31 May 2014, 10:33.
Last edited by Bunuel on 31 May 2014, 15:54, edited 1 time in total.
Renamed the topic and edited the question.
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Joined: 13 Jun 2013
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31 May 2014, 12:56
shelrod007 wrote:
How many distinct prime divisors does a positive integer N have?

A. 2N has one prime divisor
B. 3N has one prime divisor

A) both N=1 and N=2 satisfy this statement. hence insufficient
B) both N=1 and N=3 satisfy this statement. hence insufficient

combining A and B we have N=1. hence C
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Joined: 02 Sep 2009
Posts: 54440
Re: How many distinct prime divisors does a positive integer [m]  [#permalink]

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31 May 2014, 15:54
1
shelrod007 wrote:
How many distinct prime divisors does a positive integer $$n$$ have?

(1) $$2n$$ has one distinct prime divisor.

(2) $$3n$$ has one distinct prime divisor.

M18-37

How many distinct prime divisors does a positive integer $$n$$ have?

(1) $$2n$$ has one distinct prime divisor --> obviously that only prime divisor of $$2n$$ is 2. So, $$2n$$ can be 2, 4, 8, ... Which means that $$n$$ can be 1, 2, 4, ... If $$n=1$$ then it has no prime divisor but if $$n$$ is any other value (2, 4, ...) then it has one prime divisor: 2 itself. Not sufficient.

(2) $$3n$$ has one distinct prime divisor. Basically the same here: the only prime divisor of $$3n$$ must be 3. So, $$3n$$ can be 3, 9, 27, ... Which means that $$n$$ can be 1, 3, 9, ... If $$n=1$$ then it has no prime divisor but if $$n$$ is any other value (3, 9, ...) then it has one prime divisor: 3 itself. Not sufficient.

(1)+(2) From above the only possible value of $$n$$ is 1, and 1 has no prime divisor. Sufficient.

P.S. Please name the topics properly. Check rule #3 here: rules-for-posting-please-read-this-before-posting-133935.html
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Re: How many distinct prime divisors does a positive integer [m]  [#permalink]

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16 Aug 2017, 23:55
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Re: How many distinct prime divisors does a positive integer [m]   [#permalink] 16 Aug 2017, 23:55
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# How many distinct prime divisors does a positive integer [m]

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