It is currently 19 Oct 2017, 17:04

### 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

# What is the greatest possible common divisor of two differen

Author Message
TAGS:

### Hide Tags

Intern
Joined: 22 Oct 2012
Posts: 7

Kudos [?]: 26 [1], given: 1

What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

22 Nov 2012, 10:22
1
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

70% (00:57) correct 30% (00:54) wrong based on 280 sessions

### HideShow timer Statistics

What is the greatest possible common divisor of two different positive integers which are less than 144?

A. 143
B. 142
C. 72
D. 71
E. 12

Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?
[Reveal] Spoiler: OA

Last edited by Bunuel on 22 Nov 2012, 11:52, edited 2 times in total.
Renamed the topic and edited the question.

Kudos [?]: 26 [1], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17361 [4], given: 232

Location: Pune, India
Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

23 Nov 2012, 20:57
4
KUDOS
Expert's post
4
This post was
BOOKMARKED
cv3t3l1na wrote:
What is the greatest possible common divisor of two different positive integers which are less than 144?

A. 143
B. 142
C. 72
D. 71
E. 12

Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?

First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.

Think:
2 and 3 have GCD (greatest common divisor) of 1
2 and 4 have GCD of 2.
3 and 4 have GCD (greatest common divisor) of 1
So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.

Now think: 143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)

Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.

It's a very intuitive concept. Take some numbers to comprehend it fully. These posts will also be helpful:

http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17361 [4], given: 232

Intern
Joined: 25 Jun 2012
Posts: 36

Kudos [?]: 30 [1], given: 4

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

02 Dec 2012, 17:21
1
KUDOS
The largest prime whose multiple of 2 is less than 144.

71 is prime.

71 * 2 < 144

Kudos [?]: 30 [1], given: 4

Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123

Kudos [?]: 124 [0], given: 14

Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

01 May 2013, 10:18
VeritasPrepKarishma wrote:
cv3t3l1na wrote:
What is the greatest possible common divisor of two different positive integers which are less than 144?

A. 143
B. 142
C. 72
D. 71
E. 12

Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?

First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.

Think:
2 and 3 have GCD (greatest common divisor) of 1
2 and 4 have GCD of 2.
3 and 4 have GCD (greatest common divisor) of 1
So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.

Now think: 143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)

Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.

It's a very intuitive concept. Take some numbers to comprehend it fully. These posts will also be helpful:

http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/

Just to confirm, the only reason 143 is not the answer is because of the fact that the question mentioned 'two different positive numbers' right?
_________________

Feed me some KUDOS! *always hungry*

Kudos [?]: 124 [0], given: 14

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 627

Kudos [?]: 1355 [0], given: 136

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

01 May 2013, 12:12
Quote:
Just to confirm, the only reason 143 is not the answer is because of the fact that the question mentioned 'two different positive numbers' right?

Let the two positive integers be a,b where both a,b<144. Now, let the required GCD be k. Thus, a = kM and b = kN, where M,N are positive integers and are not equal.

If k = 143, then the only way a<144 is if M = 1.Similarly, even for b, N=1. But as M is not equal to N, this is an invalid option.

The same for k=142 and 72.However, for k = 71, we can have M=1,N=2 OR M=2,N=1.

D.

If they wouldn't have mentioned that fact, we could have chosen the same value for M=N=1.
_________________

Kudos [?]: 1355 [0], given: 136

Manager
Status: *Lost and found*
Joined: 25 Feb 2013
Posts: 123

Kudos [?]: 124 [0], given: 14

Location: India
Concentration: General Management, Technology
GMAT 1: 640 Q42 V37
GPA: 3.5
WE: Web Development (Computer Software)
Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

02 May 2013, 08:12
vinaymimani wrote:
Quote:
Just to confirm, the only reason 143 is not the answer is because of the fact that the question mentioned 'two different positive numbers' right?

Let the two positive integers be a,b where both a,b<144. Now, let the required GCD be k. Thus, a = kM and b = kN, where M,N are positive integers and are not equal.

If k = 143, then the only way a<144 is if M = 1.Similarly, even for b, N=1. But as M is not equal to N, this is an invalid option.

The same for k=142 and 72.However, for k = 71, we can have M=1,N=2 OR M=2,N=1.

D.

If they wouldn't have mentioned that fact, we could have chosen the same value for M=N=1.

Got it! as you said...if the numbers could have been same, we could have used 143 as both the integers and the GCD wud have been 143!

Thanks Vinay!
_________________

Feed me some KUDOS! *always hungry*

Kudos [?]: 124 [0], given: 14

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7674

Kudos [?]: 17361 [0], given: 232

Location: Pune, India
Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

02 May 2013, 10:12
arpanpatnaik wrote:
VeritasPrepKarishma wrote:
cv3t3l1na wrote:
What is the greatest possible common divisor of two different positive integers which are less than 144?

A. 143
B. 142
C. 72
D. 71
E. 12

Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?

First of all, what is the greatest common divisor of 143 and 142? It is 1. You are looking for the common divisor. 142 and 143 will have no common divisor except 1.

Think:
2 and 3 have GCD (greatest common divisor) of 1
2 and 4 have GCD of 2.
3 and 4 have GCD (greatest common divisor) of 1
So if you were to select 2 numbers less than 5 with the greatest GCD, you need to select 2 and 4, not 3 and 4.

Now think: 143 = 11 * 13
The greatest possible divisor it will have with another number less than 144 will be either 11 or 13. Let's move on.
142 = 2*71
The greatest possible divisor it can have with another number less than 144 can be 71 (say, if the other selected integer is 71)

Do you think another number less than 144 could have a GCD of greater than 71? No because when you split a number into two factors, one of them will be at least 2. If it is greater than 2, the other factor will obviously be less than 71.

It's a very intuitive concept. Take some numbers to comprehend it fully. These posts will also be helpful:

http://www.veritasprep.com/blog/2011/09 ... c-or-math/
http://www.veritasprep.com/blog/2011/09 ... h-part-ii/

Just to confirm, the only reason 143 is not the answer is because of the fact that the question mentioned 'two different positive numbers' right?

Yes, if the two numbers can be the same, then the numbers themselves will be the GCD and hence 143 will be the answer.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17361 [0], given: 232

Intern
Joined: 11 Sep 2012
Posts: 7

Kudos [?]: 4 [0], given: 0

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

03 May 2013, 13:28
I am not entirely sharp because of a day of studying, but isn't it just that 71 is the GCD of x and y because x and y would then be respectably 71 and 142? Nothing more nothing less.

Kudos [?]: 4 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16652

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

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

05 Jul 2014, 14:43
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

Math Expert
Joined: 02 Sep 2009
Posts: 41891

Kudos [?]: 128909 [0], given: 12183

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

05 Jul 2014, 14:58
cv3t3l1na wrote:
What is the greatest possible common divisor of two different positive integers which are less than 144?

A. 143
B. 142
C. 72
D. 71
E. 12

Can someone explain why the answer is 71 if we assume that the integers are 143 and 142?

Similar question to practice: what-is-the-smallest-possible-common-multiple-of-two-integer-130418.html
_________________

Kudos [?]: 128909 [0], given: 12183

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16652

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

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

22 Aug 2015, 02:44
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

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16652

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

Re: What is the greatest possible common divisor of two differen [#permalink]

### Show Tags

28 Jun 2017, 02:41
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: What is the greatest possible common divisor of two differen   [#permalink] 28 Jun 2017, 02:41
Display posts from previous: Sort by