GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Jul 2018, 07:51

### 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

# 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: 47168
The greatest common factor of positive integers m and n is 12. What is  [#permalink]

### Show Tags

08 Jul 2015, 03:43
10
00:00

Difficulty:

25% (medium)

Question Stats:

69% (00:58) correct 31% (00:54) wrong based on 305 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.

_________________
SVP
Joined: 08 Jul 2010
Posts: 2120
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, 03:50
4
1
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

##### General Discussion
Current Student
Joined: 20 Mar 2014
Posts: 2641
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, 04:31
3
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: 47168
Re: The greatest common factor of positive integers m and n is 12. What is  [#permalink]

### Show Tags

13 Jul 2015, 02:24
1
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: 423
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, 09:30
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?
SC Moderator
Joined: 22 May 2016
Posts: 1835
The greatest common factor of positive integers m and n is 12. What is  [#permalink]

### Show Tags

16 Aug 2017, 14:03
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

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

The greatest common factor of positive integers m and n is 12. What is &nbs [#permalink] 16 Aug 2017, 14:03
Display posts from previous: Sort by

# Events & Promotions

 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®.