Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 29 Nov 2011
Posts: 78

m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
14 Feb 2012, 05:16
Question Stats:
49% (01:43) correct 51% (02:01) wrong based on 222 sessions
HideShow timer Statistics
m = 4n + 9, where n is a positive integer. What is the greatest common factor of m and n? (1) m = 9s, where s is a positive integer. (2) n = 4t, where t is a positive integer.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47978

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
14 Feb 2012, 06:24
m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer > since m is a multiple of 9 and is equal to 4n+ 9, then n must also be a multiple of 9 (in order 4n+ 9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient. USEFUL PROPERTY: if \(a\) and \(b\) are multiples of \(k\) and are \(k\) units apart from each other then \(k\) is greatest common divisor of \(a\) and \(b\). For example if \(a\) and \(b\) are multiples of 7 and \(a=b+7\) then 7 is GCD of \(a\) and \(b\). (2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient. Answer: A.
_________________
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




Manager
Joined: 09 Nov 2010
Posts: 61
Location: Paris, FRANCE

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
14 Feb 2012, 05:55
Smita04 wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer. (2) n = 4t, where t is a positive integer. GCD? Do you mean Lowest Common Multiple or Greatest Common Factor?
_________________
Nicholas MOSES
GMAT/Academic Manager c/o MBA Center Paris



Manager
Joined: 31 Jan 2012
Posts: 73

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
14 Feb 2012, 06:05
I think he means GCF.
A is sufficient because you know M is a multiple of 9. Since 9s is a multiple of 9 regardless of what s. You know N and M is consecutive multiples of 9 because their difference is 9. You know N is a multiple of 9 since if you add 9 to a number the only way it will form a multiple of 9 if it was already a multiple of 9.
Since you know their consecutive multiples of 9, their GCF is also 9.
B) Not enough info. You're not sure what number M is since, 4X+9 could be prime (13,17) or a multiple of 3 (21) or 5(25).
Therefore answer A is sufficient.



Math Expert
Joined: 02 Sep 2009
Posts: 47978

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
14 Feb 2012, 06:27



Manager
Joined: 14 Nov 2011
Posts: 131
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
05 May 2013, 09:23
Bunuel wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer > since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.
USEFUL PROPERTY: if \(a\) and \(b\) are multiples of \(k\) and are \(k\) units apart from each other then \(k\) is greatest common divisor of \(a\) and \(b\). For example if \(a\) and \(b\) are multiples of 7 and \(a=b+7\) then 7 is GCD of \(a\) and \(b\).
(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.
Answer: A. Hi Bunnel, Had the question stem been like this > m=3n+9, then the GCF would hav been 3 right?



Senior Manager
Joined: 21 Jan 2010
Posts: 296

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
05 May 2013, 11:12
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?
(1) m = 9s, where s is a positive integer. (2) n = 4t, where t is a positive integer.
Bunnel : Interesting way of Defining the GCD of two numbers.
My thought process : 1)m=9s but m=4n+9. > n is definately a multiple of 9. Hence GCD of m and n is 9. Sufficient.
2)n=4t. Doesn't help to establish any relation b/w m and n more than whatever is already mentioned. Insufficient.
Hence A



Current Student
Joined: 05 Sep 2013
Posts: 5
Location: United States
Concentration: Finance, Strategy
GPA: 3.16

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
18 Aug 2014, 07:46
This is a problem from Manhattan advanced math.
m = 4n + 9
1) m = 9s 9s = 4n +9 n = (9s  9) n = 9(s1)/4 > (s1) must be multiple of 4 (n is integer) > s could be 5, 9, 13, 17,... testing numbers for s, we can see that the GCD is always 9
suff
2) n = 4t testing: if t = 1, n = 4 and m = 25 > GCD = 1 ( you could stop here if you are 100% sure about stat 1) if t = 2, n = 8 and m = 41 > GCD = 1 if t = 3, n =12 and m = 57 > GCD = 3
Not suff



Manager
Joined: 30 Jul 2013
Posts: 125
Concentration: Strategy, Sustainability

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
11 May 2018, 12:45
Bunuel wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer > since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.
USEFUL PROPERTY: if \(a\) and \(b\) are multiples of \(k\) and are \(k\) units apart from each other then \(k\) is greatest common divisor of \(a\) and \(b\). For example if \(a\) and \(b\) are multiples of 7 and \(a=b+7\) then 7 is GCD of \(a\) and \(b\).
(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.
Answer: A. Why is it obvious that just because GCD of m and 4n is 9 therefore GCD of m and n will also be 9?



Math Expert
Joined: 02 Sep 2009
Posts: 47978

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
11 May 2018, 13:17
ramalo wrote: Bunuel wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer > since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.
USEFUL PROPERTY: if \(a\) and \(b\) are multiples of \(k\) and are \(k\) units apart from each other then \(k\) is greatest common divisor of \(a\) and \(b\). For example if \(a\) and \(b\) are multiples of 7 and \(a=b+7\) then 7 is GCD of \(a\) and \(b\).
(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.
Answer: A. Why is it obvious that just because GCD of m and 4n is 9 therefore GCD of m and n will also be 9? If the greatest common divisor of m and n were more that 9, say 18, then it would mean then 18 is a factor of both m and n, so 18 would also be a factor of m and 4*n and the GCD of m and 4n would not be 9.
_________________
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



DS Forum Moderator
Joined: 27 Oct 2017
Posts: 674
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)

Re: m = 4n + 9, where n is a positive integer. What is the greatest common
[#permalink]
Show Tags
11 May 2018, 19:54
GCD = Greatest common divisor The greatest common divisor is also known as the greatest common factor (GCF), highest common factor (HCF), greatest common measure (GCM), or highest common divisor. GMAC prefers the term GCD rustypolymath wrote: Smita04 wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer. (2) n = 4t, where t is a positive integer. GCD? Do you mean Lowest Common Multiple or Greatest Common Factor?
_________________
SC: Confusable words All you need for Quant, GMAT PS Question Directory,GMAT DS Question Directory Error log/Key Concepts Combination Concept: Division into groups Question of the Day (QOTD) Free GMAT CATS




Re: m = 4n + 9, where n is a positive integer. What is the greatest common &nbs
[#permalink]
11 May 2018, 19:54






