It is currently 21 Feb 2018, 08:58

### 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

# The greatest common factor of positive integers m and n is 12. What is

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43851
The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

08 Jul 2015, 02:43
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:57) correct 30% (00:55) wrong based on 281 sessions

### HideShow timer Statistics

The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?

A. 2
B. 12
C. 24
D. 144
E. 288

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________
SVP
Joined: 08 Jul 2010
Posts: 1955
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

08 Jul 2015, 02:50
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?

A. 2
B. 12
C. 24
D. 144
E. 288

Kudos for a correct solution.

METHOD-1

Given : GCD of (m and n) = 12 = 2^2*3

i.e. m and n are both multiples of 2^2*3

i.e. m^2 and n^2 will both be multiples of (2^2*3)^2 = 2^4*3^2

i.e. 2m^2 and 2n^2 will both be multiples of 2(2^2*3)^2 = 2^5*3^2 = 288

METHOD-2

Let, m = 12 and n = 24
i.e. GCD of m and n = 12

2m^2 = 288
2n^2 = 1152
i.e. GCD of 2m^2 and 2n^2 = 288

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Current Student
Joined: 20 Mar 2014
Posts: 2683
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

08 Jul 2015, 03:31
3
KUDOS
Bunuel wrote:
The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?

A. 2
B. 12
C. 24
D. 144
E. 288

Kudos for a correct solution.

GCD (m,n)=12

Thus $$m = 2^2*3*p$$
and $$n = 2^2*3*q$$, with p,q co-primes

Now $$2m^2 = 2^5*3^2*p^2$$
and $$2n^2 = 2^5*3^2*q^2$$

Thus GCD ($$2m^2, 2n^2$$) = $$2^5*3^2$$ = 288. Thus E is the correct answer.
Math Expert
Joined: 02 Sep 2009
Posts: 43851
Re: The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

13 Jul 2015, 01:24
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Bunuel wrote:
The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?

A. 2
B. 12
C. 24
D. 144
E. 288

Kudos for a correct solution.

800score Official Solution:

Suppose we factorize m and n into prime factors. The greatest common factor of positive integers m and n is 12 so the only prime factors m and n have in common are 2, 2 and 3. (12 = 2 × 2 × 3).

If we factorize m² into prime factors we will get each of prime factors of m twice. The same happens to n². So the only prime factors m² and n² would have in common are 2, 2, 2, 2 and 3, 3.

If we factorize 2m² into prime factors we will get the same prime factors as for m² and one more prime factor “2”. The same happens to n². So the only prime factors 2m² and 2n² would have in common are 2, 2, 2, 2, 2 and 3, 3. By factoring those we get the greatest common factor of 2m² and 2n².

2 × 2 × 2 × 2 × 2 × 3 × 3 = 288.

_________________
Senior Manager
Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 432
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

22 Jul 2015, 08:30
Hello,

I have a question. Can we also use the relationship between LCM and GCF to find the solution?

So, we would say:
m*n =12*x, where x is the LCM. Then,
m^2*n^2 = (12x)^2
m^2*n^2 = (12x)^2 = 144x^2. Finally,

2(m)^2 * 2 (n)^2 = 2 (144x^2)
2(m)^2 * 2 (n)^2 = 228*2x^2.

So, we end up with 228, which is E.

Is this correct?
Non-Human User
Joined: 09 Sep 2013
Posts: 13815
Re: The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

06 Aug 2016, 10:23
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.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 13815
Re: The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

16 Aug 2017, 08:34
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.
_________________
VP
Joined: 22 May 2016
Posts: 1336
The greatest common factor of positive integers m and n is 12. What is [#permalink]

### Show Tags

16 Aug 2017, 13:03
Bunuel wrote:
The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?

A. 2
B. 12
C. 24
D. 144
E. 288

Kudos for a correct solution.

Kinda dorky, but I'm all for simple if it works. I just wrote out, in stages, what factors m and n had to have.

LCM of m and n is 12
12 = 2 * 2 * 3

m: 2, 2, 3
n: 2, 2, 3

Variables squared? Each number has exactly one copy, so

m$$^2$$: 2, 2, 3, 2, 2, 3
n$$^2$$: 2, 2, 3, 2, 2, 3

Then each term * 2?

2m$$^2$$: 2, 2, 3, 2, 2, 3, 2
2n$$^2$$: 2, 2, 3, 2, 2, 3, 2

Both have 2$$^5$$, 3$$^2$$. (32 * 9) = 288

_________________

At the still point, there the dance is. -- T.S. Eliot
Formerly genxer123

The greatest common factor of positive integers m and n is 12. What is   [#permalink] 16 Aug 2017, 13:03
Display posts from previous: Sort by