It is currently 24 Nov 2017, 06:24

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the greatest common factor of two integers, m and n, is

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

Hide Tags

2 KUDOS received
Director
Director
User avatar
Joined: 07 Jun 2004
Posts: 610

Kudos [?]: 955 [2], given: 22

Location: PA
If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 20 Mar 2011, 09:52
2
This post received
KUDOS
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

40% (01:24) correct 60% (02:04) wrong based on 164 sessions

HideShow timer Statistics

If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15.
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Kudos [?]: 955 [2], given: 22

2 KUDOS received
Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 12

Kudos [?]: -14 [2], given: 15

GMAT ToolKit User
Re: If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 14 May 2015, 23:26
2
This post received
KUDOS
2
This post was
BOOKMARKED
In such questions with a common GCD, I find it convenient to take the numbers as:

m=56*x
n=56*y

Also we know that the LCM is 840:
so we can write

56*x*a=840 => x*a=15
56*y*b=840 => y*b=15

Where a & b are two integers.

We get the four options for the two pairs and solve as has been shown above.

Hope it helps.

Kudos [?]: -14 [2], given: 15

2 KUDOS received
Intern
Intern
avatar
Joined: 29 Mar 2015
Posts: 12

Kudos [?]: -14 [2], given: 15

GMAT ToolKit User
Re: If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 16 Sep 2015, 03:07
2
This post received
KUDOS
1
This post was
BOOKMARKED
Yes in that case, combining the two equations will lead to a unique solution i.e. 56*(5+3)=56*8=448 & the answer would be C.

Kudos [?]: -14 [2], given: 15

1 KUDOS received
Manager
Manager
User avatar
Joined: 20 Jul 2011
Posts: 144

Kudos [?]: 81 [1], given: 15

GMAT Date: 10-21-2011
Re: Number Prop DS [#permalink]

Show Tags

New post 05 Sep 2011, 12:21
1
This post received
KUDOS
Quote:
If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15.


prime factors of 56: 7, 2, 2, 2
prime factors of 840: 7, 2, 2, 2, 3, 5

From Statement 1
m = 56*3 or m=56
Insufficient

From Statement 2

m=56; n=840
sufficient

Answer: B
_________________

"The best day of your life is the one on which you decide your life is your own. No apologies or excuses. No one to lean on, rely on, or blame. The gift is yours - it is an amazing journey - and you alone are responsible for the quality of it. This is the day your life really begins." - Bob Moawab

Kudos [?]: 81 [1], given: 15

Director
Director
avatar
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 871

Kudos [?]: 401 [0], given: 123

Reviews Badge
Re: Number Prop DS [#permalink]

Show Tags

New post 20 Mar 2011, 10:02
s1 insufficient
Consider m=56*3 and n=56*5
consider m = 56 and n=56*15

s2 sufficient
m=56 and n=56*15

Hence B

Posted from my mobile device

Kudos [?]: 401 [0], given: 123

Director
Director
avatar
Joined: 01 Feb 2011
Posts: 725

Kudos [?]: 147 [0], given: 42

Re: Number Prop DS [#permalink]

Show Tags

New post 20 Mar 2011, 11:22
1 not sufficient
as there more than one possible combination for m and n

m = (2^3)7(3) n = (2^3)7(5)

m = (2^3)7 n = (2^3)7(15)

2. Sufficient

only possible combination for m and n here is m = (2^3)7 n = (2^3)15

Hence answer is B.

Kudos [?]: 147 [0], given: 42

TOEFL Forum Moderator
avatar
Joined: 16 Nov 2010
Posts: 1602

Kudos [?]: 601 [0], given: 40

Location: United States (IN)
Concentration: Strategy, Technology
Premium Member Reviews Badge
Re: Number Prop DS [#permalink]

Show Tags

New post 20 Mar 2011, 20:12
56 = 2^3 * 7

So m and n have 2^3 * 7 as factor

840 = 7 * 120 = 7 * 5 * 24 = 7 * 5 * 3 * 2^3

(1), m is m is not divisible by 15, so m does not have 5 and 3 as factor


So m = 2^3 * 7 * k (where k is an intger other than 3 or 5)


Now m*n = 56 * 840

So n = 56/56k * 840 = 840/k , which is not sufficient as n could be 840, or 840/56 = 15


(2) n is divisible by 15, so n has 3 and 5 as factor

So n = 3*5* 2^3 * 7*p, where p is an integer

=> m = 56*840/15*56p = 56*56/56p, so m can be 56/p, now m has to be minimum 56, so p = 1, hence m = 56 and n = 840

So answer is B
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Kudos [?]: 601 [0], given: 40

Manager
Manager
avatar
Joined: 05 Jan 2011
Posts: 168

Kudos [?]: 198 [0], given: 8

Re: Number Prop DS [#permalink]

Show Tags

New post 21 Mar 2011, 22:10
Product of M & N= LCM *GCD
==>56*840
==>7^2*2^6*5*3

Stmt 1 m could be 7*2^3*5 or 7*2^3*3..
Stmt 2
Since GCD is 56 both m and n should have 7 *2^3
n =>7 *2^3 *3*5 (n is divisible by 15 so it should have 3 and 5 as a factor).. Sufficient

B

Kudos [?]: 198 [0], given: 8

Manager
Manager
avatar
Status: Joining Cranfield Sep 2014
Joined: 01 Sep 2012
Posts: 65

Kudos [?]: 38 [0], given: 60

Concentration: Technology, General Management
GMAT 1: 530 Q50 V14
GMAT 2: 630 Q48 V29
WE: Engineering (Energy and Utilities)
Reviews Badge
Re: If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 15 Oct 2013, 17:27
It is given GCF = 56 = 7 x 2 x 2 x 2
and LCM = 840 = 56 (GCF) x 15
For more fundamental elaboration:-
GCF and LCM
----------
7 |m , n
2 |m1, n1
2 |m2, n2
2 |m3, n3
--- 1 , 15
or
--- 3 , 5
From Statement 1 informs "m" is not divisible by 15, so in above illustration, we can have either 1 or 3 under "m", which makes the statement insufficient to identify the value of m,

From Statement 2 informs "n" is divisible by 15, so in above graphic illustration, we can establish that we will have 1 under "m" and 15 under "n", which is sufficient to derive both the value of n and m

The value of m = 1 x 2 x 2 x 2 x 7 = 56
The value of n = 15 x 2 x 2 x 2 x 7 = 840
m + n = 896

Kudos [?]: 38 [0], given: 60

Manager
Manager
avatar
Joined: 04 Oct 2013
Posts: 87

Kudos [?]: 87 [0], given: 45

Location: Brazil
GMAT 1: 660 Q45 V35
GMAT 2: 710 Q49 V38
Reviews Badge
Re: Number Prop DS [#permalink]

Show Tags

New post 16 Nov 2013, 15:00
gmatopoeia wrote:
Quote:

From Statement 1
m = 56*3 or m=56
Insufficient
[u]

Answer: B



For the sake of my comprehension, should m=56*5 be a possibility as well?

Kudos [?]: 87 [0], given: 45

Intern
Intern
avatar
Joined: 14 Jan 2012
Posts: 9

Kudos [?]: 18 [0], given: 17

what is the sum of the m and n? [#permalink]

Show Tags

New post 14 Sep 2015, 15:58
If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15

Kudos [?]: 18 [0], given: 17

SVP
SVP
User avatar
B
Joined: 06 Nov 2014
Posts: 1904

Kudos [?]: 542 [0], given: 23

Re: what is the sum of the m and n? [#permalink]

Show Tags

New post 14 Sep 2015, 20:34
To solve this, first we need to find the prime factors of 56 and 840

prime factors of 56 = 2, 2, 2, 7
prime factors of 840 = 2, 2, 2, 3, 5, 7

Statement 1
m = 56*3, n = 56*5 or m=56, n = 56*3*5
Insufficient

Statement 2
m=56; n=56*3*5
Sufficient

The correct answer choice is B

Kudos [?]: 542 [0], given: 23

Manager
Manager
avatar
B
Joined: 08 Jan 2015
Posts: 91

Kudos [?]: 23 [0], given: 654

Location: Thailand
GMAT 1: 540 Q41 V23
GMAT 2: 570 Q44 V24
GMAT 3: 550 Q44 V21
GMAT 4: 660 Q48 V33
GPA: 3.31
WE: Science (Other)
Re: If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 16 Sep 2015, 00:04
The answer of this question is apparently B but if the statement 2 change to "n is not divisible by 15", will the answer be C?

Kudos [?]: 23 [0], given: 654

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 15499

Kudos [?]: 283 [0], given: 0

Premium Member
Re: If the greatest common factor of two integers, m and n, is [#permalink]

Show Tags

New post 19 Jan 2017, 02:55
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Kudos [?]: 283 [0], given: 0

Re: If the greatest common factor of two integers, m and n, is   [#permalink] 19 Jan 2017, 02:55
Display posts from previous: Sort by

If the greatest common factor of two integers, m and n, is

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.