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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
14 Feb 2012, 05:05

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).

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
14 Feb 2012, 05:24

5

This post received KUDOS

Expert's post

4

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.

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
14 Feb 2012, 05:27

Expert's post

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. _________________

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
05 May 2013, 08:23

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?

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
18 Aug 2014, 06:46

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

Re: m = 4n + 9, where n is a positive integer. What is the greatest common [#permalink]
10 Sep 2015, 00:17

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. _________________

Low GPA MBA Acceptance Rate Analysis Many applicants worry about applying to business school if they have a low GPA. I analyzed the low GPA MBA acceptance rate at...

In out-of-the-way places of the heart, Where your thoughts never think to wander, This beginning has been quietly forming, Waiting until you were ready to emerge. For a long...