Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 16 Jan 2009
Posts: 349
Concentration: Technology, Marketing
GPA: 3
WE: Sales (Telecommunications)

What is the greatest common divisor of positive integers m [#permalink]
Show Tags
Updated on: 28 Dec 2013, 03:51
4
This post received KUDOS
48
This post was BOOKMARKED
Question Stats:
64% (00:55) correct 36% (00:48) wrong based on 1101 sessions
HideShow timer Statistics
What is the greatest common divisor of positive integers m and n. (1) m is a prime number (2) 2n=7m
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Lahoosaher
Originally posted by lahoosaher on 07 Jun 2009, 11:12.
Last edited by Bunuel on 28 Dec 2013, 03:51, edited 2 times in total.
Edited the question and added the OA



Director
Joined: 23 May 2008
Posts: 746

Re: DS : GCD [#permalink]
Show Tags
07 Jun 2009, 18:29
1
This post received KUDOS
amolsk11 wrote: what is the greatest common divisor of the positive integers m and n. 1)m is prime 2)2n=7m m&n GCF? 1) m is prime no info on n, insuff 2) 2n=7m; n=7/2 m or 1:3.5 ratio n could be 2, m could be 7, GCF=1 n could be 8, m could be 28, GCF=4 nsuff together m has to be 7 for n to be an integer, GCF=1



Intern
Joined: 17 May 2011
Posts: 6

Re: DS : GCD [#permalink]
Show Tags
04 Jul 2011, 03:50
1
This post was BOOKMARKED
option 2 gives 2n=7m. Therefore n=7m/2 HCF of m and 7m/2 is always m/2. So answer should be optin 2 right. what do you think guys



Manager
Joined: 29 Jun 2011
Posts: 148
WE 1: Information Technology(Retail)

Re: what is the greatest common divisor of the positive integers [#permalink]
Show Tags
02 Mar 2012, 11:48
1
This post was BOOKMARKED
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.



Math Expert
Joined: 02 Sep 2009
Posts: 44655

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
02 Mar 2012, 12:20
15
This post received KUDOS
Expert's post
31
This post was BOOKMARKED
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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 05 Jun 2012
Posts: 1

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
24 Sep 2012, 22:02
1) This statement says that M is Prime no, So N can be Prime/Composite. If N is Prime , clearly GCD will be 1, If N is composite also GCD will be 1( Except when M itself is a divisor of N, means N<>kM(not equals)), If N=kM then GCD(M,N) will be M it self.(where k is an integer)
2)2N=7M, its clearly not sufficient.
Combining:
From the statement 1, if we can get N=kM or not(where k is an integer) then we will be sure whats the GCD. As from the statement 2, we can see that N=7/2 M, and 7/2 is not an integer. So clearly GCD will be 1.
So answer is C.
If it is stupid but it works, it isn't stupid.



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 554
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
24 Sep 2013, 11:07
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?
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 44655

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
24 Sep 2013, 15:12
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?
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 554
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
24 Sep 2013, 23:12
Bunuel, Our m is coming as 2, so isn't 2 a GCD, Or may be I have misunderstood the solution?
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Math Expert
Joined: 02 Sep 2009
Posts: 44655

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
25 Sep 2013, 00:54



Director
Status: Verbal Forum Moderator
Joined: 17 Apr 2013
Posts: 554
Location: India
GMAT 1: 710 Q50 V36 GMAT 2: 750 Q51 V41 GMAT 3: 790 Q51 V49
GPA: 3.3

Re: What is the greatest common divisor of the positive integers [#permalink]
Show Tags
25 Sep 2013, 01:26
Bunuel wrote: 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. Got it, may be I am getting panic as my exam is coming closer, so could not see even clear things.
_________________
Like my post Send me a Kudos It is a Good manner. My Debrief: http://gmatclub.com/forum/howtoscore750and750imovedfrom710to189016.html



Current Student
Joined: 26 Mar 2016
Posts: 2
Location: India
GPA: 3.4

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
03 Oct 2016, 09:19
I marked B for this question.
My reasoning is  2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7
My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'?



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3356

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
03 Oct 2016, 09:52
puchku wrote: I marked B for this question.
My reasoning is  2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7
My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'? Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on. When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1.
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way? New > How ApplicantLab made me reach my 10 years long MBA dream?



Current Student
Joined: 26 Mar 2016
Posts: 2
Location: India
GPA: 3.4

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
03 Oct 2016, 12:14
abhimahna wrote: puchku wrote: I marked B for this question.
My reasoning is  2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7
My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'? Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on. When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1. But even without considering Statement 1, on the basis of Statement 2 we can say that GCM(m.n) will be m/2 For example m=2 => n=7 => GCD(2,7) = m/2 = 1 m=4 => n=14 => GCD(4,14) = m/2 = 2 Now, even though the actual values are different here, can't we assume that we know the values of 'm' and 'n' (since we want to find their GCD), and thus, in turn, we know the value of GCD which is m/2 But since this is an official question and the answer is C, I am guessing that in DS questions, we have to be able to determine exact values and not such relations



Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3356

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
04 Oct 2016, 09:58
1
This post received KUDOS
puchku wrote: abhimahna wrote: puchku wrote: I marked B for this question.
My reasoning is  2n = 7m Since 2 and 7 don't have any common factors other than 1, 'm' must be a multiple of 2 and 'n' a multiple of 7. So GCD(m,n) = m/2 = n/7
My doubt is, in such questions are we not allowed to deduce an answer in terms of variables 'm' and 'n'? Try taking the values of m = 2,4,6 and as we know n = 7m/2, we can have n = 7,14,21, and so on. When combined with Statement 1, we can say m could be only 2. Thus n could be only 7. Hence, HCF= 1. But even without considering Statement 1, on the basis of Statement 2 we can say that GCM(m.n) will be m/2 For example m=2 => n=7 => GCD(2,7) = m/2 = 1 m=4 => n=14 => GCD(4,14) = m/2 = 2 Now, even though the actual values are different here, can't we assume that we know the values of 'm' and 'n' (since we want to find their GCD), and thus, in turn, we know the value of GCD which is m/2 But since this is an official question and the answer is C, I am guessing that in DS questions, we have to be able to determine exact values and not such relationsHighlighted line above is the rule for DS questions. We should have a definite answer to arrive at any conclusion.
_________________
How I improved from V21 to V40! ? How to use this forum in THE BEST way? New > How ApplicantLab made me reach my 10 years long MBA dream?



Director
Joined: 26 Oct 2016
Posts: 673
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
26 Jan 2017, 12:07
(1) No info about n but we could test below values as well that will make this statement insufficient. if m = 3 (which is prime) and n = 6, then the gcf is 3. if m = 3 (which is prime) and n = 5, then the gcf is 1. insufficient. (2)In the case of this statement, you can divide by 2m on both sides, to give n/m = 7/2. (you could also divide by 7n, to give m/n = 2/7.) so, the ratio of n to m is 7:2. if they're actually 7 and 2, the gcf is 1. if they're multiples of these numbers, then the gcf is not 1. (for instance, if they're 14 and 4, the gcf is 2.) insufficient.  (together) if you need a prime, and the ratio is 7 to 2, then the numbers must actually be 7 and 2. sufficient.
_________________
Thanks & Regards, Anaira Mitch



Intern
Joined: 22 Jan 2017
Posts: 34

What is the greatest common divisor of positive integers m [#permalink]
Show Tags
15 Jul 2017, 23:55
What is the greatest common divisor of positive integers m and n.
(1) m is a prime number (2) 2n=7m
Statement 1: m is prime. Lots of numbers are prime. INSUFFICIENT.
Statement 2: 2n = 7m
n is a multiple of 7, m is a multiple of 2.
n could be 7 and m could be 2. In that case the GCF is 1. n could be 35 and m could be 10, in which case the GCF is going to be 5. INSUFFICIENT.
Statements 1 & 2:
If m has to be prime, the only prime multiple of 2 is 2. So m = 2 and n = 7. Therefore the GCF 1 is.
(C)



Director
Joined: 12 Nov 2016
Posts: 774

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
17 Jul 2017, 20:55
lahoosaher wrote: What is the greatest common divisor of positive integers m and n.
(1) m is a prime number (2) 2n=7m St 1 Obv insuff no info about n St 2 n =7m/2  which must an integer so m must be a multiple of "2" and n must be a multiple of 7 but this could mean several values such as 2, 4 ,8 St 1 and St 2 The only prime number that is a multiple of 2 is 2 so n must be 7 and m must be 2 C



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2493
Location: United States (CA)

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
30 Jul 2017, 17:35
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
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Senior Manager
Joined: 29 Jun 2017
Posts: 260

Re: What is the greatest common divisor of positive integers m [#permalink]
Show Tags
15 Oct 2017, 23:56
lahoosaher wrote: What is the greatest common divisor of positive integers m and n.
(1) m is a prime number (2) 2n=7m each 1 and 2 are not sufficient. use both 1 and 2 m=2n/7 m must be interger, so n must be divided by 7. if n/7 is more than 2, m can not be price. so n must be 7 m must be 2.




Re: What is the greatest common divisor of positive integers m
[#permalink]
15 Oct 2017, 23:56



Go to page
1 2
Next
[ 21 posts ]



