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

It is currently 30 Aug 2016, 01:17
GMAT Club Tests

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many prime factors does N have?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 27 Apr 2012
Posts: 62
Location: United States
GMAT Date: 06-11-2013
GPA: 3.5
WE: Marketing (Consumer Products)
Followers: 1

Kudos [?]: 45 [0], given: 21

GMAT ToolKit User Premium Member
How many prime factors does N have? [#permalink]

Show Tags

New post 06 Oct 2012, 01:31
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (02:20) correct 47% (01:24) wrong based on 95 sessions

HideShow timer Statistics

How many prime factors does N have?

(1) N is a factor of 7200
(2) 180 is a factor of N
[Reveal] Spoiler: OA
1 KUDOS received
Manager
Manager
User avatar
Status: Fighting hard
Joined: 04 Jul 2011
Posts: 72
GMAT Date: 10-01-2012
Followers: 2

Kudos [?]: 54 [1] , given: 84

Re: how many prime factors n has? [#permalink]

Show Tags

New post 06 Oct 2012, 01:56
1
This post received
KUDOS
First I chose E because I was of the opinion we need to get the count of the different prime factors and I did not know how many times the prime factors would be repeated. Then reworked to come to the opinion that "C" should be right answer.

Statement 1 : N is a factor of 7200. Could be 360, 180, 24, 3, 2, 5 etc... There could be different combination of prime factors possible.
Statement 2 : 180 is a factor of N. Could be again 180, 360, 1260 etc...There could be different number of prime factors possible.

Statement 1 + Statement 2 = i)N is less than or equal to 7200 and greater than or equal to 180.
ii)In order to satisfy both statements the number "N" when factorized will contain only 3 prime factors - (2^n)*(3^m)*(5^p)
_________________

I will rather do nothing than be busy doing nothing - Zen saying


Last edited by Pansi on 06 Oct 2012, 01:58, edited 2 times in total.
1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 819 [1] , given: 43

Re: how many prime factors n has? [#permalink]

Show Tags

New post 06 Oct 2012, 01:56
1
This post received
KUDOS
shivanigs wrote:
Hi,

Request help with the following question.Thanks..

How many prime factors does N have?

1. N is a factor of 7200
2.180 is a factor of N


(1) 7200 has plenty of divisors, 1, 2, 3, 4, 6, ...
Not sufficient.

(2) There are many multiples of 180, so N can be 180, 360, 540,..., 7*180,...
Not sufficient.

(1) and (2): We can deduce that 7200 = AN, for some integer A. Also, N = 180B, for some integer B. In conclusion, 7200 = 180AB, from which AB = 40. B must be a factor of 40. The prime factors of 180 are 2, 3, and 5. The prime factors of 40 are 2 and 5. In conclusion, the prime factors of N = 180B are 2, 3 and 5 only.
Sufficient.

Answer C.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Intern
Intern
avatar
Joined: 28 Aug 2012
Posts: 46
Location: Austria
GMAT 1: 770 Q51 V42
Followers: 3

Kudos [?]: 41 [0], given: 3

Re: How many prime factors does N have? [#permalink]

Show Tags

New post 06 Oct 2012, 02:17
Wouldn't a real gmat question state that we are looking for the number of distinct prime factors?
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 819 [0], given: 43

Re: How many prime factors does N have? [#permalink]

Show Tags

New post 06 Oct 2012, 02:27
Zinsch123 wrote:
Wouldn't a real gmat question state that we are looking for the number of distinct prime factors?


On the GMAT yes, I think so. They are quite pedantic, so almost sure, they would explicitly stress "distinct".
But, for example, there is no particular reason to count how many prime factors 32 has. You are either interested in how many (distinct) prime factors a number has, or how many distinct factors it has. I don't think you would count 5 prime factors of 32...
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 90

Kudos [?]: 819 [1] , given: 43

Re: how many prime factors n has? [#permalink]

Show Tags

New post 06 Oct 2012, 08:21
1
This post received
KUDOS
EvaJager wrote:
shivanigs wrote:
Hi,

Request help with the following question.Thanks..

How many prime factors does N have?

1. N is a factor of 7200
2.180 is a factor of N


(1) 7200 has plenty of divisors, 1, 2, 3, 4, 6, ...
Not sufficient.

(2) There are many multiples of 180, so N can be 180, 360, 540,..., 7*180,...
Not sufficient.

(1) and (2): We can deduce that 7200 = AN, for some integer A. Also, N = 180B, for some integer B. In conclusion, 7200 = 180AB, from which AB = 40. B must be a factor of 40. The prime factors of 180 are 2, 3, and 5. The prime factors of 40 are 2 and 5. In conclusion, the prime factors of N = 180B are 2, 3 and 5 only.
Sufficient.

Answer C.



It just occurred to me that I could summarize the the above reasoning for (1) and (2) in the following way:

N is a divisor of 7200, which has prime factors 2, 3, and 5. Therefore, N can have at most three prime divisors: 2, 3, and 5. N must not have all of them.
Since 180 is a factor of N and has prime factors 2, 3, and 5, necessarily N must have at least the same prime factors, and ALL of them.
Therefore, in conclusion, N must have exactly three prime factor: 2, 3, and 5.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 54

Kudos [?]: 516 [0], given: 355

GMAT ToolKit User
Re: How many prime factors does N have? [#permalink]

Show Tags

New post 12 Jan 2014, 14:37
shivanigs wrote:
How many prime factors does N have?

(1) N is a factor of 7200
(2) 180 is a factor of N


Statement 1

Since 7200 has 3, 2 and 5 then N being a factor of this could have a maximum of 3 different prime factors but not sufficient

Statement 2

Since 180 is a factor of N, then N has at least 2,3, and 5 again as prime factors but not enough

Statement 1 and 2

Combining both we get that N must have 3 prime factors

Hence C

Hope it helps
Cheers!
J :)
Moderator
Moderator
User avatar
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 42

Kudos [?]: 616 [0], given: 723

Premium Member Reviews Badge
Re: How many prime factors does N have? [#permalink]

Show Tags

New post 14 Jan 2014, 23:18
shivanigs wrote:
How many prime factors does N have?

(1) N is a factor of 7200
(2) 180 is a factor of N



Sol: As per St 1, we have 7200/N= I where I is some integer
Factorizing 3600, we get : 7200= (2^5*3^2*5^2)/ I = N
Now if I is 1 then N will have 2,3 and 5 as prime factors
But I =25 then N will have only 2 and 3 as prime factors

Thus at the most N can have 3 prime factors but it can have less as well So A and D ruled out. This statement basically says the number of Prime factors of N will be less than or equal to 3

St2 N= 180 *A where A is some Integer
N= 2^2*3^2*5 *A
Thus N will surely have at 2,3 and 5 as prime factors but Integer A can take any value ie. It can be 6 or some other prime say 11 or multiple of 2 primes say 11 and 13.

So B ruled out. This statement tells us that number of prime factors of N will be greater than or equal to 3.

Combining we get we N has 3 factors only

Ans C
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11141
Followers: 511

Kudos [?]: 134 [0], given: 0

Premium Member
Re: How many prime factors does N have? [#permalink]

Show Tags

New post 27 Sep 2015, 08:13
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: How many prime factors does N have?   [#permalink] 27 Sep 2015, 08:13
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic How many positive factors does N have? SamTheLearner 1 26 Jan 2016, 05:55
19 Experts publish their posts in the topic How many different prime factors does positive integer n have? Bunuel 16 14 May 2015, 05:25
6 Experts publish their posts in the topic If F is the prime factorization of N!, how many factors in F have an e Bunuel 12 09 Apr 2015, 07:33
18 Experts publish their posts in the topic How many prime factors does positive integer n have? Bunuel 8 06 Apr 2015, 07:08
5 How many prime factors does positive integer n have? banksy 4 29 Mar 2011, 12:30
Display posts from previous: Sort by

How many prime factors does N have?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.