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

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Joined: 23 Jan 2013
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Concentration: Technology, Other
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How many distinct prime divisors does a positive integer [m] [#permalink] New post 31 May 2014, 09:33
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 May 2014, 14:54, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Algebra [#permalink] New post 31 May 2014, 11:56
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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Re: How many distinct prime divisors does a positive integer [m] [#permalink] New post 31 May 2014, 14:54
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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.

Answer: C.

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Re: How many distinct prime divisors does a positive integer [m]   [#permalink] 31 May 2014, 14:54
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