Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50042

If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
12 Jun 2014, 07:37
Question Stats:
54% (02:10) correct 46% (01:58) wrong based on 513 sessions
HideShow timer Statistics




Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
12 Jun 2014, 07:37
SOLUTIONIf \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b\)?Notice that two statements together are obviously sufficient to answer the question. When you see such question you should be extremely cautious when choosing C for an answer. Chances are that the question is a "C trap" question ("C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together). (1) \(a + 3b = 61\). Let the greatest common divisor of \(a\) and \(b\) be \(d\), then \(a=md\) and \(b=nd\), for some positive integers \(m\) and \(n\). So, we'll have \((md)+3(nd)=d(m+3n)=61\). Now, since 61 is a prime number (61=1*61) then \(d=1\) and \(m+3n=61\) (vice versa is not possible because \(m\) and \(n\) are positive integers and therefore \(m+3n\) cannot equal to 1). Hence we have that the GCD(x, y)=d=1. Sufficient. (2) \(5a  b = 1\) > \(5a=b+1\). \(5a\) and \(b\) are consecutive integers. Two consecutive integers are coprime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5a\) and \(b\) don't share any common factor but 1, thus \(a\) and \(b\) also don't share any common factor but 1. Hence, the GCD(x, y) is 1. Sufficient. Answer: D. Try NEW divisibility PS question.
_________________
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




Retired Moderator
Joined: 17 Sep 2013
Posts: 349
Concentration: Strategy, General Management
WE: Analyst (Consulting)

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
12 Jun 2014, 08:32
D I am not sure if there is any standard approach for these...Just hit out some numbers For I: I see that when A is odd say 3 then B is even 52..As B is an integer..the value of A will go down by 3 slots for each increase in B..So there is no case such that A and B will have any common factor other than 1 For II: You can again try a few..you can see that it is again 1...
_________________
Appreciate the efforts...KUDOS for all Don't let an extra chromosome get you down..



Senior Manager
Joined: 13 Jun 2013
Posts: 276

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
12 Jun 2014, 10:58
Bunuel wrote: If \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b\)? (1) \(a + 3b = 61\) (2) \(5a  b = 1\) Kudos for a correct solution. Let k be the greatest common divisor of a and b such that a=kx and b=ky, where x and y are coprime positive integers St. 1; a+3b=61; kx+3ky=61; x+3y=(61/k) now since 61 is a prime number therefore maximum value of k is 1 hence sufficient st.2 5ab=1 5kxky=1 5xy=(1/k) since x and y are integers, therefore 5xy will only be integer if k=1 hence sufficient therefore answer should be D



Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
15 Jun 2014, 04:57
SOLUTIONIf \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b\)?Notice that two statements together are obviously sufficient to answer the question. When you see such question you should be extremely cautious when choosing C for an answer. Chances are that the question is a "C trap" question ("C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together). (1) \(a + 3b = 61\). Let the greatest common divisor of \(a\) and \(b\) be \(d\), then \(a=md\) and \(b=nd\), for some positive integers \(m\) and \(n\). So, we'll have \((md)+3(nd)=d(m+3n)=61\). Now, since 61 is a prime number (61=1*61) then \(d=1\) and \(m+3n=61\) (vice versa is not possible because \(m\) and \(n\) are positive integers and therefore \(m+3n\) cannot equal to 1). Hence we have that the GCD(x, y)=d=1. Sufficient. (2) \(5a  b = 1\) > \(5a=b+1\). \(5a\) and \(b\) are consecutive integers. Two consecutive integers are coprime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5a\) and \(b\) don't share any common factor but 1, thus \(a\) and \(b\) also don't share any common factor but 1. Hence, the GCD(x, y) is 1. Sufficient. Answer: D. Kudos points given to correct solutions above.Try NEW divisibility PS question.
_________________
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: 10 Mar 2014
Posts: 199

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
14 Aug 2014, 01:53
manpreetsingh86 wrote: Bunuel wrote: If \(a\) and \(b\) are positive integers, what is the greatest common divisor of \(a\) and \(b\)? (1) \(a + 3b = 61\) (2) \(5a  b = 1\) Kudos for a correct solution. Let k be the greatest common divisor of a and b such that a=kx and b=ky, where x and y are coprime positive integers St. 1; a+3b=61; kx+3ky=61; x+3y=(61/k) now since 61 is a prime number therefore maximum value of k is 1 hence sufficient st.2 5ab=1 5kxky=1 5xy=(1/k) since x and y are integers, therefore 5xy will only be integer if k=1 hence sufficient therefore answer should be D in st2 we can also say that bis multiple of 3. so this can be odd or even. so at a time b can be odd then a is even. or if b is even then a is odd. so GCD of a odd and even no. is 1. st2 is straight . numbers are coprime



Manager
Joined: 21 Apr 2016
Posts: 178

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
11 Nov 2016, 20:18
Is there a compilation of such 700 level questions?
I really like these. Sometimes some of them are tricky.
Could someone please point me to any collection that you are aware of.
Many thanks!



Math Expert
Joined: 02 Sep 2009
Posts: 50042

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
12 Nov 2016, 03:39



NonHuman User
Joined: 09 Sep 2013
Posts: 8536

Re: If a and b are positive integers, what is the greatest commo
[#permalink]
Show Tags
15 Nov 2017, 22:31
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




Re: If a and b are positive integers, what is the greatest commo &nbs
[#permalink]
15 Nov 2017, 22:31






