Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 04:29

### 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 prime divisors does positive integer N have? 1) 2N

Author Message
Director
Joined: 24 Oct 2005
Posts: 659
Location: London
Followers: 1

Kudos [?]: 16 [0], given: 0

How many prime divisors does positive integer N have? 1) 2N [#permalink]

### Show Tags

16 May 2006, 08:13
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

### HideShow timer Statistics

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

How many prime divisors does positive integer N have?
1) 2N has one prime divisor
2) 3N has one prime divisor

Director
Joined: 16 Aug 2005
Posts: 940
Location: France
Followers: 1

Kudos [?]: 23 [0], given: 0

### Show Tags

16 May 2006, 08:22
N = positive integer = {1, 2, 3, 4, ...}

Taking (1)
If 2N has one prime divisor, it has to be 2.
So N=1
Sufficient

Taking (2)
Same way, the prime divisor is 3
So, N=1
Sufficient

Hence D
Senior Manager
Joined: 09 Mar 2006
Posts: 445
Followers: 1

Kudos [?]: 8 [0], given: 0

### Show Tags

16 May 2006, 08:40
C it is

1) if 2N has 1 prime divisor, N=2 (1 prime divisor ) or N=1 (no prime divisors) so insuff.

2) as above so insuff.

(1) + (2) imply that N=1, so it has no prime divisors so it is sufficient
Manager
Joined: 28 Mar 2006
Posts: 157
Followers: 1

Kudos [?]: 5 [0], given: 0

### Show Tags

16 May 2006, 08:48
B it should be.

A is insufficient as if N = 1 then 2N, i.e 2*1 = 2 has just one prime divisor.
if N = 2, then 2N, 2*2 also has ust one prime divisor i.e 2
so inufficient.

B.....3N if N = 1, then one prime divisor i.e 3
else for neother value of N, it will have more than one divisor.
hence B is sufficient.
Director
Joined: 16 Aug 2005
Posts: 940
Location: France
Followers: 1

Kudos [?]: 23 [0], given: 0

### Show Tags

16 May 2006, 08:50
agree with deowl .... thinking too fast (meaning not thinking).
Director
Joined: 24 Oct 2005
Posts: 659
Location: London
Followers: 1

Kudos [?]: 16 [0], given: 0

### Show Tags

16 May 2006, 08:58
deowl wrote:
C it is

1) if 2N has 1 prime divisor, N=2 (1 prime divisor ) or N=1 (no prime divisors) so insuff.

2) as above so insuff.

(1) + (2) imply that N=1, so it has no prime divisors so it is sufficient

Deowl, sorryr for being a dumbo. I still dont get it.

2N has 1 prime divisor. Doesnt that mean N can only take the value of 1?
ie. N=1 , only one prime divisor (2),
N=2, two prime divisors (2,2)
N=3, two prime divisors (2,3)

So, only N=1 satisfies this equation.

Can you pls tell me where I have gone wrong in my understanding?
VP
Joined: 29 Dec 2005
Posts: 1343
Followers: 10

Kudos [?]: 62 [0], given: 0

### Show Tags

16 May 2006, 08:59
remgeo wrote:
How many prime divisors does positive integer N have?
1) 2N has one prime divisor
2) 3N has one prime divisor

i guess C as well.

from i.
if n = 2, 2n = 4 and it has only one prime divisor i.e. 2.
if n = 1, 2n = 2 and it has only one prime divisor i.e. 2.

from ii.
if n = 3, 3n = 9 and it has only one prime divisor i.e. 3.
if n = 1, 3n = 3 and it has only one prime divisor i.e. 3.

from i and ii, n should be 1.
Manager
Joined: 14 Mar 2006
Posts: 208
Followers: 2

Kudos [?]: 9 [0], given: 0

### Show Tags

16 May 2006, 10:17
I go with B.

stmt 2: if n=2 then 3n=6 So, there are 2 primary divisors 2 and 3. therefore, n has to be 1.
Manager
Joined: 14 Mar 2006
Posts: 208
Followers: 2

Kudos [?]: 9 [0], given: 0

### Show Tags

16 May 2006, 10:21
shampoo wrote:
I go with B.

stmt 2: if n=2 then 3n=6 So, there are 2 primary divisors 2 and 3. therefore, n has to be 1.

grrrr. but if n=3 as Prof said then 3n=9 and one prime divisor.

I am chaning my ans to C
Manager
Joined: 14 Mar 2006
Posts: 208
Followers: 2

Kudos [?]: 9 [0], given: 0

### Show Tags

16 May 2006, 10:22
What would you say about the difficulty level of this question?
Senior Manager
Joined: 09 Mar 2006
Posts: 445
Followers: 1

Kudos [?]: 8 [0], given: 0

### Show Tags

16 May 2006, 11:50
remgeo wrote:

Deowl, sorryr for being a dumbo. I still dont get it.

2N has 1 prime divisor. Doesnt that mean N can only take the value of 1?
ie. N=1 , only one prime divisor (2),
N=2, two prime divisors (2,2)
N=3, two prime divisors (2,3)

So, only N=1 satisfies this equation.

Can you pls tell me where I have gone wrong in my understanding?

When you are counting factors (divisors) of an integer, you should only count different ones.
16 May 2006, 11:50
Display posts from previous: Sort by