Last visit was: 24 Jun 2024, 00:49 It is currently 24 Jun 2024, 00:49
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
SORT BY:
Date
User avatar
Manager
Manager
Joined: 16 Jan 2009
Posts: 236
Own Kudos [?]: 946 [250]
Given Kudos: 16
Concentration: Technology, Marketing
GMAT 1: 700 Q50 V34
GPA: 3
WE:Sales (Telecommunications)
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [113]
Given Kudos: 82435
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30623 [9]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
User avatar
Intern
Intern
Joined: 29 Jun 2011
Posts: 9
Own Kudos [?]: 17 [3]
Given Kudos: 0
Location: Ireland
Concentration: (trading as) Test Prep Dublin
 Q50  V40
Send PM
Re: DS_GCD [#permalink]
3
Kudos
What is the greatest common divisor of positive integers M and N ???
1)M is a prime number
2)2N=7M

If we look at statement 2 and plug in numbers we'll quickly see it's not sufficient.

Let M=2 then N = 7 GCD=1.
Let M=6 then N = 21 GCD=3.

S2 basically tells us that 2 is a factor of M and 7 is a factor of N. But we don't know if they have more shared factors or not.
Insufficient.

Does that make sense Akshaydiljit?

Originally posted by testprepDublin on 04 Jul 2011, 08:53.
Last edited by testprepDublin on 05 Jul 2011, 02:14, edited 1 time in total.
User avatar
Manager
Manager
Joined: 29 Jun 2011
Posts: 68
Own Kudos [?]: 51 [4]
Given Kudos: 29
GPA: 3.5
WE 1: Information Technology(Retail)
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
2
Kudos
2
Bookmarks
OA is C.

1)m is prime
Clearly insufficient.

2)2n=7m
can be written as n= 7m/2. n & m are integers.
Put m=1,2,3,4 .... therefore m has to be a multiple of 2.
Insufficient.

Combined-
m is prime(stat1) and m= multiple of 2(stat2)

Hence m=2 & n=7

GCF is 1.
User avatar
Senior Manager
Senior Manager
Joined: 17 Apr 2013
Status:Verbal Forum Moderator
Posts: 360
Own Kudos [?]: 2218 [0]
Given Kudos: 298
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.


Greatest Common divisor and Highest common factor are same thing Bunuel?

Because n= 7m/2 (Taking both this is true only for m = 2) So Greatest common divisor is 2 not 1, Isn't it?
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [0]
Given Kudos: 82435
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Expert Reply
honchos wrote:
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.


Greatest Common divisor and Highest common factor are same thing Bunuel?

Because n= 7m/2 (Taking both this is true only for m = 2) So Greatest common divisor is 2 not 1, Isn't it?


Yes, GCD and GCF are the same thing.

But couldn't understand your second point: the greatest common divisor of 2 and 7 is 1. How can it be 2? Is 7 divisible by 2?
User avatar
Senior Manager
Senior Manager
Joined: 17 Apr 2013
Status:Verbal Forum Moderator
Posts: 360
Own Kudos [?]: 2218 [0]
Given Kudos: 298
Location: India
GMAT 1: 710 Q50 V36
GMAT 2: 750 Q51 V41
GMAT 3: 790 Q51 V49
GPA: 3.3
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Bunuel,
Our m is coming as 2, so isn't 2 a GCD, Or may be I have misunderstood the solution?
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [0]
Given Kudos: 82435
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Expert Reply
honchos wrote:
Bunuel,
Our m is coming as 2, so isn't 2 a GCD, Or may be I have misunderstood the solution?


The question asks: what is the greatest common divisor of positive integers m and n?

We got that m=2 and n=7. What is the greatest common divisor of 2 and 7? Is it 2? No, it's 1.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19044
Own Kudos [?]: 22475 [1]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
1
Bookmarks
Expert Reply
lahoosaher wrote:
What is the greatest common divisor of positive integers m and n.

(1) m is a prime number
(2) 2n=7m


We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don’t know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C
Manager
Manager
Joined: 11 Jun 2015
Posts: 73
Own Kudos [?]: 30 [0]
Given Kudos: 86
Location: India
Concentration: Marketing, Leadership
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.



2) 2n=7m --> m/n=2/7

n=3.5m

GCF(m,3.5m)= m ? is this correct ? Its not sufficient because we dont have the value of M ?
Retired Moderator
Joined: 22 Aug 2013
Posts: 1182
Own Kudos [?]: 2532 [0]
Given Kudos: 459
Location: India
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
renjana wrote:
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.



2) 2n=7m --> m/n=2/7

n=3.5m

GCF(m,3.5m)= m ? is this correct ? Its not sufficient because we dont have the value of M ?



Hello

Yes, I think you have concluded properly. GCF of m & 3.5m will depend on the value of m. Eg, if m= 2, then 3.5m = 7, and their GCF will be 1.
However, if m= 4, then 3.5m= 14, and their GCF will be 2. So GCF can take multiple values depending on the value of m.
VP
VP
Joined: 15 Dec 2016
Posts: 1361
Own Kudos [?]: 219 [0]
Given Kudos: 188
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.


Hi Bunuel - when you combine the statements, you mentioned that m = 2

How can you be sure that n = 7 always ? Why can't n = 14 for example (When m = 2)

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 93968
Own Kudos [?]: 634430 [0]
Given Kudos: 82435
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Expert Reply
jabhatta2 wrote:
Bunuel wrote:
What is the greatest common divisor of positive integers m and n?

(1) m is a prime number --> if \(m=2=prime\) and \(n=1\) then \(GCD(m,n)=1\) but if \(m=2=prime\) and \(n=4\) then \(GCD(m,n)=2\). Two different answers, hence not sufficient.

(2) 2n=7m --> \(\frac{m}{n}=\frac{2}{7}\) --> \(m\) is a multiple of 2 and \(n\) is a multiple of 7, but this is still not sufficient: if \(m=2\) and \(n=7\) then \(GCD(m,n)=1\) (as both are primes) but if \(m=4\) and \(n=14\) then \(GCD(m,n)=2\) (basically as \(\frac{m}{n}=\frac{2x}{7x}\) then as 2 and 7 are primes then \(GCD(m, n)=x\)). Two different answers, hence not sufficient.

(1)+(2) Since from (1) \(m=prime\) and from (2) \(\frac{m}{n}=\frac{2}{7}\) then \(m=2=prime\) and \(n=7\), hence \(GCD(m,n)=1\). Sufficient.

Answer: C.


Hi Bunuel - when you combine the statements, you mentioned that m = 2

How can you be sure that n = 7 always ? Why can't n = 14 for example (When m = 2)

Thank you


(2) says that 2n = 7m. If you substitute m = 2, there you'd get n = 7.
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1734 [1]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
1
Kudos
Expert Reply
Video solution from Quant Reasoning starts at 13:15
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
Manager
Manager
Joined: 27 Apr 2020
Posts: 101
Own Kudos [?]: 21 [0]
Given Kudos: 24
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
ScottTargetTestPrep wrote:
lahoosaher wrote:
What is the greatest common divisor of positive integers m and n.

(1) m is a prime number
(2) 2n=7m


We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don’t know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C


Can you help me understand this more?

If using both statements , we plug in values in , 2n=7m .Then we will be arriving at different values? what to do in that case?
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 1734 [0]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Expert Reply
[/quote]

Can you help me understand this more?

If using both statements , we plug in values in , 2n=7m .Then we will be arriving at different values? what to do in that case?[/quote]

Could you clarify your question please? I also suggest watching my video solution above if you haven't already.
Director
Director
Joined: 01 Mar 2015
Posts: 533
Own Kudos [?]: 370 [1]
Given Kudos: 762
Location: India
GMAT 1: 740 Q47 V44
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
1
Kudos
ManyataM wrote:
ScottTargetTestPrep wrote:
lahoosaher wrote:
What is the greatest common divisor of positive integers m and n.

(1) m is a prime number
(2) 2n=7m


We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don’t know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C


Can you help me understand this more?

If using both statements , we plug in values in , 2n=7m .Then we will be arriving at different values? what to do in that case?


2n=7m tells us that 7m is Even
For 7m to be even, m has to be Even
We know that m is Prime : 2 is the only prime even number

So m=2
And n has to be 7

Posted from my mobile device
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19044
Own Kudos [?]: 22475 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: What is the greatest common divisor of positive integers m and n ? [#permalink]
Expert Reply
ManyataM wrote:
ScottTargetTestPrep wrote:
lahoosaher wrote:
What is the greatest common divisor of positive integers m and n.

(1) m is a prime number
(2) 2n=7m


We need to determine the greatest common divisor, or the greatest common factor (GCF), of integers m and n.

Statement One Alone:

m is a prime number.

Since we don’t know anything about n, statement one is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

2n = 7m

We can manipulate the equation 2n = 7m:

n = 7m/2

n/m = 7/2

Even with the equation rewritten, we see that there are many options for m and n, and thus there are many different GCFs for m and n. For instance, if n = 7 and m = 2, then the GCF is 1. However, if n = 14 and m = 4, then the GCF is 2. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using statements one and two, we know that m is prime and that n/m = 7/2. Therefore, m must equal 2 and n must equal 7. When m is 2 and n is 7, the GCF is 1.

Answer: C


Can you help me understand this more?

If using both statements , we plug in values in , 2n=7m .Then we will be arriving at different values? what to do in that case?


Solution:

If there are no restrictions on n and m other than that both of them are positive (which is the case when we assume only statement two), then the equation 2n = 7m indeed has more than one solution (such as n = 21, m = 6 or n = 28, m = 8 or n = 35, m = 10). However, when we use both statements, we are told that m is a prime number. Furthermore, m must be even since 7m equals an even number (2n is even regardless of the value of n). Since m is even and prime, the only possible value for m is 2. Thus, the only possible value of n is 7.
Current Student
Joined: 20 Oct 2018
Posts: 43
Own Kudos [?]: 9 [0]
Given Kudos: 247
Location: United States
GPA: 3.5
Send PM
What is the greatest common divisor of positive integers m and n ? [#permalink]
lahoosaher wrote:
What is the greatest common divisor of positive integers m and n ?

(1) m is a prime number
(2) 2n = 7m


Statement 1:

Let's consider two scenarios:
(1) M = 2 and N = 3, then GCF = 1 (note: GCF of any two consecutive integers is equal to 1.)
(2) M = 2 and N = 4, then GCF = 2

So we've got two different answers to the GCF so not sufficient.

Statement 2:
If 2n=7m then that means that N = (7M)/2. Now remember that the stem provides us with the information that M and N are both integers. So the quotient of (7M)/2 MUST be an integer, and the only way that (7M)/2 can be an integer is if M is EVEN. Okay but again, this statement alone isn't sufficient, but lets just test two scenarios to confirm:

So now we need to find the GCF of (7M)/2 and M because N = (7M/2).
(1) M = 2 then GCF = 1
(2) M = 4 then GCF = 2

(1) and (2) together:
Well since M must be both a prime number, AND an even number then the only number that M can be is 2. So the GCF of (7M)/2 and M is gcf(7, 2) = 1.
GMAT Club Bot
What is the greatest common divisor of positive integers m and n ? [#permalink]
 1   2   
Moderator:
Math Expert
93968 posts