It is currently 20 Oct 2017, 07:40

### 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

# m = 4n + 9, where n is a positive integer. What is the greatest common

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

### Hide Tags

Manager
Joined: 29 Nov 2011
Posts: 81

Kudos [?]: 375 [0], given: 37

m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

14 Feb 2012, 05:16
7
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

48% (01:50) correct 52% (02:01) wrong based on 163 sessions

### HideShow timer Statistics

m = 4n + 9, where n is a positive integer. What is the greatest common factor of m and n?

(1) m = 9s, where s is a positive integer.
(2) n = 4t, where t is a positive integer.
[Reveal] Spoiler: OA

Kudos [?]: 375 [0], given: 37

Manager
Joined: 09 Nov 2010
Posts: 64

Kudos [?]: 54 [0], given: 3

Location: Paris, FRANCE
Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

14 Feb 2012, 05:55
Smita04 wrote:
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?

(1) m = 9s, where s is a positive integer.
(2) n = 4t, where t is a positive integer.

GCD? Do you mean Lowest Common Multiple or Greatest Common Factor?
_________________

Nicholas MOSES

GMAT/Academic Manager
c/o MBA Center Paris

Kudos [?]: 54 [0], given: 3

Manager
Joined: 31 Jan 2012
Posts: 74

Kudos [?]: 26 [0], given: 2

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

14 Feb 2012, 06:05
I think he means GCF.

A is sufficient because you know M is a multiple of 9. Since 9s is a multiple of 9 regardless of what s. You know N and M is consecutive multiples of 9 because their difference is 9. You know N is a multiple of 9 since if you add 9 to a number the only way it will form a multiple of 9 if it was already a multiple of 9.

Since you know their consecutive multiples of 9, their GCF is also 9.

B) Not enough info. You're not sure what number M is since, 4X+9 could be prime (13,17) or a multiple of 3 (21) or 5(25).

Therefore answer A is sufficient.

Kudos [?]: 26 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128977 [8], given: 12185

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

14 Feb 2012, 06:24
8
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?

(1) m = 9s, where s is a positive integer --> since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.

USEFUL PROPERTY:
if $$a$$ and $$b$$ are multiples of $$k$$ and are $$k$$ units apart from each other then $$k$$ is greatest common divisor of $$a$$ and $$b$$. For example if $$a$$ and $$b$$ are multiples of 7 and $$a=b+7$$ then 7 is GCD of $$a$$ and $$b$$.

(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.

Answer: A.
_________________

Kudos [?]: 128977 [8], given: 12185

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128977 [0], given: 12185

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

14 Feb 2012, 06:27
kys123 wrote:
I think he means GCF.

A is sufficient because you know M is a multiple of 9. Since 9s is a multiple of 9 regardless of what s. You know N and M is consecutive multiples of 9 because their difference is 9. You know N is a multiple of 9 since if you add 9 to a number the only way it will form a multiple of 9 if it was already a multiple of 9.

Since you know their consecutive multiples of 9, their GCF is also 9.

B) Not enough info. You're not sure what number M is since, 4X+9 could be prime (13,17) or a multiple of 3 (21) or 5(25).

Therefore answer A is sufficient.

m cannot be 17 or 21 as in this case n won't be a multiple of 4.
_________________

Kudos [?]: 128977 [0], given: 12185

Manager
Joined: 14 Nov 2011
Posts: 145

Kudos [?]: 20 [0], given: 103

Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)
Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

05 May 2013, 09:23
Bunuel wrote:
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?

(1) m = 9s, where s is a positive integer --> since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.

USEFUL PROPERTY:
if $$a$$ and $$b$$ are multiples of $$k$$ and are $$k$$ units apart from each other then $$k$$ is greatest common divisor of $$a$$ and $$b$$. For example if $$a$$ and $$b$$ are multiples of 7 and $$a=b+7$$ then 7 is GCD of $$a$$ and $$b$$.

(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.

Answer: A.

Hi Bunnel,

Had the question stem been like this > m=3n+9, then the GCF would hav been 3 right?

Kudos [?]: 20 [0], given: 103

Senior Manager
Joined: 21 Jan 2010
Posts: 329

Kudos [?]: 225 [0], given: 12

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

05 May 2013, 11:12
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?

(1) m = 9s, where s is a positive integer.
(2) n = 4t, where t is a positive integer.

Bunnel : Interesting way of Defining the GCD of two numbers.

My thought process :
1)m=9s but m=4n+9. -> n is definately a multiple of 9. Hence GCD of m and n is 9. Sufficient.

2)n=4t. Doesn't help to establish any relation b/w m and n more than whatever is already mentioned. Insufficient.

Hence A

Kudos [?]: 225 [0], given: 12

Current Student
Joined: 05 Sep 2013
Posts: 5

Kudos [?]: 7 [0], given: 2

Location: United States
Concentration: Finance, Strategy
Schools: LBS '18 (A)
GMAT 1: 750 Q49 V42
GPA: 3.16
Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

18 Aug 2014, 07:46
This is a problem from Manhattan advanced math.

m = 4n + 9

1) m = 9s
9s = 4n +9
n = (9s - 9)
n = 9(s-1)/4 -> (s-1) must be multiple of 4 (n is integer) -> s could be 5, 9, 13, 17,...
testing numbers for s, we can see that the GCD is always 9

suff

2) n = 4t
testing:
if t = 1, n = 4 and m = 25 -> GCD = 1 ( you could stop here if you are 100% sure about stat 1)
if t = 2, n = 8 and m = 41 -> GCD = 1
if t = 3, n =12 and m = 57 -> GCD = 3

Not suff

Kudos [?]: 7 [0], given: 2

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16634

Kudos [?]: 273 [0], given: 0

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]

### Show Tags

02 Dec 2016, 10:49
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: m = 4n + 9, where n is a positive integer. What is the greatest common   [#permalink] 02 Dec 2016, 10:49
Display posts from previous: Sort by

# m = 4n + 9, where n is a positive integer. What is the greatest common

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne 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®.