Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 05 May 2016, 13:36

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 23 Jan 2013
Posts: 173
Concentration: Technology, Other
Schools: Haas
GMAT Date: 01-14-2015
WE: Information Technology (Computer Software)
Followers: 3

Kudos [?]: 37 [0], given: 41

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

### Show Tags

31 May 2014, 10:33
1
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

44% (01:54) correct 56% (00:41) wrong based on 30 sessions

### HideShow timer Statictics

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, 15:54, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
Joined: 13 Jun 2013
Posts: 279
Followers: 14

Kudos [?]: 271 [0], given: 13

### Show Tags

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
Math Expert
Joined: 02 Sep 2009
Posts: 32657
Followers: 5658

Kudos [?]: 68746 [0], given: 9818

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

### Show Tags

31 May 2014, 15:54
Expert's post
1
This post was
BOOKMARKED
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.

_________________
Re: How many distinct prime divisors does a positive integer [m]   [#permalink] 31 May 2014, 15:54
Similar topics Replies Last post
Similar
Topics:
16 How many different prime factors does positive integer n have? 15 14 May 2015, 05:25
13 How many prime factors does positive integer n have? 6 06 Apr 2015, 07:08
5 How many distinct factors does positive integer k have? 6 25 Nov 2014, 08:33
3 How many prime factors does positive integer n have? 4 29 Mar 2011, 12:30
1 How many divisors does positive integer have? 1.The 5 25 Nov 2010, 19:39
Display posts from previous: Sort by