If m is divisible by 3, how many prime factors does m have? : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 Feb 2017, 20:00

### 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

# Events & Promotions

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

# If m is divisible by 3, how many prime factors does m have?

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

### Hide Tags

Director
Joined: 03 Sep 2006
Posts: 879
Followers: 6

Kudos [?]: 799 [0], given: 33

If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

26 Jan 2012, 05:36
10
This post was
BOOKMARKED
00:00

Difficulty:

85% (hard)

Question Stats:

37% (02:17) correct 63% (01:12) wrong based on 199 sessions

### HideShow timer Statistics

If m is divisible by 3, how many prime factors does m have?

(1) $$\frac{m}{3}$$ is divisible by 3

(2) $$\frac{m}{3}$$ has two different prime factors
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 37114
Followers: 7255

Kudos [?]: 96630 [2] , given: 10770

Re: Prime Factors [#permalink]

### Show Tags

26 Jan 2012, 06:50
2
This post received
KUDOS
Expert's post
LM wrote:
If m is divisible by 3, how many prime factors does m have?

1) $$\frac{m}{3}$$ is divisible by 3

2) $$\frac{m}{3}$$ has two different prime factors

If m is divisible by 3, how many prime factors does m have?

(1) $$\frac{m}{3}$$ is divisible by 3 --> $$\frac{m}{3}=3k$$ --> $$m=3^2*k$$ --> $$m$$ has at least one prime 3, but it can have more than one, in case $$k$$ has some number of other primes. Not sufficient

2) $$\frac{m}{3}$$ has two different prime factors --> first of all 3 is a factor of $$m$$, so 3 is one of the primes of $$m$$ for sure.

Now, if power of 3 in $$m$$ is more than or equal to 2 then $$m$$ will have have only two prime factors: 3 and one other, example: $$m=18$$, (as in $$\frac{m}{3}$$ one 3 will be reduced, at least one more 3 will be left, plus one other, to make the # of different factors of $$\frac{m}{3}$$ equal to two. Thus $$m$$ will have 3 and some other prime as a prime factors).

But if $$m$$ has 3 in power of one then $$m$$ will have 3 prime factors: 3 and two others, example $$m=30$$ (one 3 will be reduced in $$m$$ and $$\frac{m}{3}$$ will have some other two prime factors, which naturally will be the primes of $$m$$ as well). Not sufficient.

(1)+(2) From (1) $$3^2$$ is a factor of $$m$$, thus from (2) $$m$$ has only two distinct prime factors: 3 and one other. Sufficient.

Answer: C.
_________________
Manager
Status: Employed
Joined: 17 Nov 2011
Posts: 100
Location: Pakistan
Concentration: International Business, Marketing
GMAT 1: 720 Q49 V40
GPA: 3.2
WE: Business Development (Internet and New Media)
Followers: 7

Kudos [?]: 139 [0], given: 10

Re: Prime Factors [#permalink]

### Show Tags

26 Jan 2012, 07:04
Just one thought bunuel..... The question asks for "how many prime factors". It does not ask for "how many DIFFERENT prime factors". If combined the statements tell us that $$3^2$$ is a prime factor and there is a different prime factor as well, we still do not know how many times that "different" prime factor repeats. So my question is, when the question ask for number of prime factors, does it mean we should be looking at "different" prime factors or should we count the different factors each time they are repeated as well..
_________________

"Nowadays, people know the price of everything, and the value of nothing." Oscar Wilde

Math Expert
Joined: 02 Sep 2009
Posts: 37114
Followers: 7255

Kudos [?]: 96630 [0], given: 10770

Re: Prime Factors [#permalink]

### Show Tags

26 Jan 2012, 07:31
omerrauf wrote:
Just one thought bunuel..... The question asks for "how many prime factors". It does not ask for "how many DIFFERENT prime factors". If combined the statements tell us that $$3^2$$ is a prime factor and there is a different prime factor as well, we still do not know how many times that "different" prime factor repeats. So my question is, when the question ask for number of prime factors, does it mean we should be looking at "different" prime factors or should we count the different factors each time they are repeated as well..

Well, the real GMAT question will ask about "distinct primes", to avoid such technicalities, though we can say that it's implied here.
_________________
Manager
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 18 [0], given: 19

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

25 Mar 2013, 19:52
Hi Bunuel,

I answer B, since statement 2 says it has 2 different primes factor (3 included for sure) answering directly to the question. Why (2) it's insufficient? I didn't understand your approach, please explain. Thanks!
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Math Expert
Joined: 02 Sep 2009
Posts: 37114
Followers: 7255

Kudos [?]: 96630 [0], given: 10770

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

26 Mar 2013, 00:40
marcovg4 wrote:
Hi Bunuel,

I answer B, since statement 2 says it has 2 different primes factor (3 included for sure) answering directly to the question. Why (2) it's insufficient? I didn't understand your approach, please explain. Thanks!

The second statement says that m/3 has two different prime factors, NOT m.

If m = 18, then m/3 = 6 (6 has two different prime factors: 2, and 3). 18 has two different prime factors 2 and 3.
If m = 30, then m/3 = 10 (10 has two different prime factors: 2, and 5). 30 has three different prime factors 2, 3 and 5.

Thus this statement is NOT sufficient.

Does this make sense?
_________________
Senior Manager
Joined: 17 Dec 2012
Posts: 447
Location: India
Followers: 26

Kudos [?]: 407 [1] , given: 14

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

26 Mar 2013, 01:46
1
This post received
KUDOS
LM wrote:
If m is divisible by 3, how many prime factors does m have?

1) $$\frac{m}{3}$$ is divisible by 3

2) $$\frac{m}{3}$$ has two different prime factors

Given:

m= 3s

Statement 1:

m = 9r

Not sufficient as r may be formed of 1 or more prime factors.

Statement 2:

m/3 = p*q

Not sufficient because p or q may be 3.

So we need to find whether p or q is 3.

Taken together:

1. Since m is divisible by 9 from statement 1, m/3 is divisible by 3.

2. From (1) above , we can say that the RHS in statement 2 is a product of 3. i.e., one of p or q is 3.

3. From (2) above, we can say that m has two different prime factors since m/3 = p*q and if say p is 3, then m=3*3*q

Therefore the answer is choice C.
_________________

Srinivasan Vaidyaraman
Sravna
http://www.sravnatestprep.com

Classroom and Online Coaching

Manager
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 18 [0], given: 19

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

26 Mar 2013, 05:26
Yes Bunuel, thanks!

Posted from my mobile device
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Manager
Joined: 05 Nov 2012
Posts: 171
Followers: 1

Kudos [?]: 33 [0], given: 57

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

27 Mar 2013, 15:59
@Bunuel

second statement says m has two different prime factors. Can it be taken as it has only 2 different prime factors? if m/3 is 42, the second statement is still true!?
Math Expert
Joined: 02 Sep 2009
Posts: 37114
Followers: 7255

Kudos [?]: 96630 [0], given: 10770

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

28 Mar 2013, 02:58
Amateur wrote:
@Bunuel

second statement says m has two different prime factors. Can it be taken as it has only 2 different prime factors? if m/3 is 42, the second statement is still true!?

Please check here: if-m-is-divisible-by-3-how-many-prime-factors-does-m-have-126571.html#p1202604
_________________
Director
Joined: 28 Jul 2011
Posts: 563
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE: Accounting (Commercial Banking)
Followers: 3

Kudos [?]: 219 [0], given: 16

Re: Prime Factors [#permalink]

### Show Tags

30 Mar 2013, 03:56
Bunuel wrote:
LM wrote:
If m is divisible by 3, how many prime factors does m have?

1) $$\frac{m}{3}$$ is divisible by 3

2) $$\frac{m}{3}$$ has two different prime factors

If m is divisible by 3, how many prime factors does m have?

(1) $$\frac{m}{3}$$ is divisible by 3 --> $$\frac{m}{3}=3k$$ --> $$m=3^2*k$$ --> $$m$$ has at least one prime 3, but it can have more than one, in case $$k$$ has some number of other primes. Not sufficient

2) $$\frac{m}{3}$$ has two different prime factors --> first of all 3 is a factor of $$m$$, so 3 is one of the primes of $$m$$ for sure.

Now, if power of 3 in $$m$$ is more than or equal to 2 then $$m$$ will have have only two prime factors: 3 and one other, example: $$m=18$$, (as in $$\frac{m}{3}$$ one 3 will be reduced, at least one more 3 will be left, plus one other, to make the # of different factors of $$\frac{m}{3}$$ equal to two. Thus $$m$$ will have 3 and some other prime as a prime factors).

But if $$m$$ has 3 in power of one then $$m$$ will have 3 prime factors: 3 and two others, example $$m=30$$ (one 3 will be reduced in $$m$$ and $$\frac{m}{3}$$ will have some other two prime factors, which naturally will be the primes of $$m$$ as well). Not sufficient.

(1)+(2) From (1) $$3^2$$ is a factor of $$m$$, thus from (2) $$m$$ has only two distinct prime factors: 3 and one other. Sufficient.

Answer: C.

Hi Bunnel,

Can you please explain me the statement.

(1)+(2) From (1) $$3^2$$ is a factor of $$m$$, thus from (2) $$m$$ has only two distinct prime factors: 3 and one other. Sufficient.

I didn't get how you got the answer after combing the two
_________________

+1 Kudos If found helpful..

Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 64

Kudos [?]: 605 [0], given: 355

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

18 Feb 2014, 05:12
My way:

First of all we are told that m = 3k where 'k' is an integer. How many different prime factors does 'm' have?

Statement 1: m = 9k, nothing about prime factors
Statement 2: m/3 has two different prime factors. Well if m = 3k then 3k/3 = k has two different prime factors but no info on 'm' yet. 'k' could have 3 among its factors or not. Therefore since we are asked about different prime factors then this statement alone is not sufficient.

Statements 1 and 2 together tell us that 9k/3=3k has two different prime factors. Since m = 3k then it must be that 'k' is another different prime factors Therefore C is our answer

Hope this helps
Cheers
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13971
Followers: 591

Kudos [?]: 167 [0], given: 0

Re: If m is divisible by 3, how many prime factors does m have? [#permalink]

### Show Tags

15 Sep 2015, 22:41
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.
_________________
Re: If m is divisible by 3, how many prime factors does m have?   [#permalink] 15 Sep 2015, 22:41
Similar topics Replies Last post
Similar
Topics:
23 How many prime factors does positive integer n have? 10 06 Apr 2015, 06:08
7 How many prime factors does x^37 have? 8 09 Mar 2015, 04:38
5 How many prime factors does N have? 9 06 Oct 2012, 00:31
6 How many prime factors does positive integer n have? 4 29 Mar 2011, 11:30
1 If m is divisible by 3, how many prime factors does m have? 4 21 Jun 2010, 23:12
Display posts from previous: Sort by

# If m is divisible by 3, how many prime factors does m have?

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

 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®.