November 22, 2018 November 22, 2018 10:00 PM PST 11:00 PM PST Mark your calendars  All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA) November 24, 2018 November 24, 2018 07:00 AM PST 09:00 AM PST Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 475
Location: United Kingdom
Concentration: International Business, Strategy
GPA: 2.9
WE: Information Technology (Consulting)

If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
Updated on: 26 Apr 2016, 08:14
Question Stats:
50% (01:23) correct 50% (01:36) wrong based on 1739 sessions
HideShow timer Statistics
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? (1) x = 12u, where u is an integer. (2) y = 12z, where z is an integer. For me its B and this is how I solved it. Is my solution correct?
Question is asking for GCD of x and y.
GCF or GCD is the product of common prime factors with lowest exponents. for example GF of 12 and 24 is
12 = 2^2 * 3^1 24 = 2^3 * 3^1
GCF = 2^2 * 3^1 = 12
Coming back to the question and considering statement 1
x is a multiple of 12
So if we put different values of x in the our equation GCF will be different. Therefore this statement is INSUFFICIENT.
Considering statement 2
Y=12z, where z is an integer. Y is a multiple of 12. i.e Y can be 12, 24, 36. And therefore x can be 192, 204 etc.
So if y = 12 then x = 108
Prime factors of 12 = 2^2 *3^1 Prime factors of 108 = 2^2 * 3^3 GCF = 2^2 * 3^1 = 12
Now if y = 24, x = 204
Prime factors of 24 = 2^3 * 3 ^1 Prime factors of 204 = 2^2 * 3^1 * 17 GCF = 2^2 * 3 = 12
So GCF or GCF will be 12 and therefore B alone is sufficient to answer this question. Am I right guys? Unfortunately OA is not provided.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Best Regards, E.
MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Originally posted by enigma123 on 29 Jan 2012, 17:25.
Last edited by Bunuel on 26 Apr 2016, 08:14, edited 3 times in total.
Added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
29 Jan 2012, 17:39
If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?Given: \(x=8y+12\). (1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient. (2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient. Answer: B. Hope it's clear.
_________________
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: 16 Dec 2011
Posts: 42
GMAT Date: 04232012

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
12 Feb 2012, 22:35
bunuel where enigma123 is wrong in her explanation , i think her way is also correct, by putting values we can easily get to know relevant options, i think by substitiuing varoius values of Y like Y= 12, 24, 36 it becomes little bit lengthy , plz correct me if i am wrong.
rgds pbull



Intern
Joined: 06 Jan 2012
Posts: 26
Location: United States

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
23 Mar 2012, 12:17
If x an y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y 1. x = 12u where u is an integer 2. y = 12z where z is an integer
_________________
If you like my post, consider giving KUDOS



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
23 Mar 2012, 12:23



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
05 Jul 2013, 01:44



Intern
Joined: 08 Sep 2012
Posts: 7

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
26 Aug 2013, 21:51
[quote="enigma123"]x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y? (1) X=12u, where u is an integer. (2) Y=12z, where z is an integer. 1) x = 12u > 12u = 8y + 12 > y = 3(u  1)/2 Keeping in mind y is a positive integer, u = 3, 5, 7... > x = 36, 60, 84 and y = 3, 6, 9..and GCD of x and y is = 3, 6, 3 etc. Since GCD is not constant we cannot determine it. 2) y = 12z > x = 8 Ã— 12z + 12 = 12(8z + 1). Now z = 1, 2, 3, 4... > y = 12, 24, 36, 48... and x = 12 Ã— 9, 12 Ã— 17, 12 Ã— 25...you can see that GCD is 12 for every pair of x and y. Hence, 2 answers the question. Source: http://totalgadha.com/mod/forum/discuss.php?d=130



Intern
Joined: 17 Mar 2014
Posts: 36
Location: India
Concentration: Strategy, Marketing
WE: Medicine and Health (Health Care)

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
20 Sep 2014, 08:44
Bunuel wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
Given: \(x=8y+12\).
(1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient.
(2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient.
Answer: B.
Hope it's clear. BunuelAre (kq + 1 , q) always coprimes? where k and q are any positive integers?



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
20 Sep 2014, 12:35
tushain wrote: Bunuel wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
Given: \(x=8y+12\).
(1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient.
(2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient.
Answer: B.
Hope it's clear. BunuelAre (kq + 1 , q) always coprimes? where k and q are any positive integers? Yes. kq and kq + 1 are consecutive integers, thus they do not share any common factor but 1, thus q and kq + 1 must also be coprime.
_________________
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: 14 Jun 2014
Posts: 4

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
06 Dec 2014, 06:53
Hi Bunuel,
Please can you identify the gap in my understanding?
x= 8y + 12 x = 4(2y+3)
From 1: x = 12 u => x = 4 X 3 X U This means that (2y+3) must be a multiple of 3. The only way this can happen is if y is a multiple of 3. Lets say y = 3z
x = 4 X 3 X (2z+1)
y = 3 z
z and 2z+1 are coprime.
So the HCF is 3.



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
06 Dec 2014, 07:16



Intern
Joined: 14 Jun 2014
Posts: 4

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
06 Dec 2014, 10:28
Bunuel wrote: dmgmat2014 wrote: Hi Bunuel,
Please can you identify the gap in my understanding?
x= 8y + 12 x = 4(2y+3)
From 1: x = 12 u => x = 4 X 3 X U This means that (2y+3) must be a multiple of 3. The only way this can happen is if y is a multiple of 3. Lets say y = 3z
x = 4 X 3 X (2z+1)
y = 3 z
z and 2z+1 are coprime.
So the HCF is 3. What if z and 4 have some common factors? For example, consider z=2. Thank you. I knew I was missing something



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2702
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
07 Nov 2015, 06:09
enigma123 wrote: x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) X=12u, where u is an integer. (2) Y=12z, where z is an integer.
x=8y+12 = 4(2y+3) i.e. x is a Multiple of 4 Statement 1: X=12u i.e. x is a multiple of 12 i.e. y must be a multiple of 3 but since y may be an even multiple of 3 or an odd multiple of 3 so GCD will have different values. Hence, NOT SUFFICIENT Statement 2: Y=12z i.e. y must be a multiple of 3 as well 4 for such value of y, x must be a multiple of 12 e.g. @y=12, x = 4*27, GCD = 12 @y=24, x = 4*51, GCD = 12 but since y is an even multiple of 3 so GCD will have constant value. Hence, SUFFICIENT Answer: Option B
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6535
GPA: 3.82

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
10 Nov 2015, 10:15
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y? (1) X=12u, where u is an integer. (2) Y=12z, where z is an integer. There are 2 variables (x,y), one equation (x=8y+12), and 2 more equations are given from the 2 conditions; there is high chance (D) will be our answer. From condition 1, 12u=8y+12, 8y=12(u1), 2y=3(u1), from x=4(2y+3), this has to be a multiple of y=3, but x is a multiple of 4, so we cannot decide the GCD; this is insufficient. From condition 2, x=8(12z)+12=12(8z+1), z cannot equal 8z+1, the GCD(x,y)=12, so this is sufficient, and the answer becomes (B). For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $99 for 3 month Online Course" "Free Resources30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons  try it yourself"



Current Student
Joined: 12 Aug 2015
Posts: 2632

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
16 Mar 2016, 08:57



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1319
Location: Malaysia

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
27 Mar 2017, 21:36
Bunuel wrote: tushain wrote: Bunuel wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
Given: \(x=8y+12\).
(1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient.
(2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient.
Answer: B.
Hope it's clear. BunuelAre (kq + 1 , q) always coprimes? where k and q are any positive integers? Yes. kq and kq + 1 are consecutive integers, thus they do not share any common factor but 1, thus q and kq + 1 must also be coprime. Dear Bunuel, Could you please help to explain why are we considering 8z & 8z+1 in this case?
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/



Math Expert
Joined: 02 Sep 2009
Posts: 50730

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
27 Mar 2017, 22:56



Current Student
Joined: 22 Sep 2016
Posts: 179
Location: India
GPA: 4

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
05 Aug 2017, 18:18
Bunuel wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
Given: \(x=8y+12\).
(1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient.
(2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient.
Answer: B.
Hope it's clear. Bunuel You blow my mind! Incredible!
_________________
Desperately need 'KUDOS' !!



Manager
Joined: 03 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
08 Aug 2017, 03:17
1) x=12u u=1,2,3,4...... Than x=12, 36, 48,...... Y= x12/8=0,3,4..... different GCDNot sufficient
2) Y=12z x=8*12z+12=12(8z+1)a z=1, 2, 3, 4..... Than y=12*1, 12*3, 12*4,.... x= 12*9, 12*17, 12*25, 12*33(do not calculate just plugin in a Common between x&y is 12 hence sufficient



Manager
Joined: 31 Dec 2016
Posts: 76

Re: If x and y are positive integers such that x = 8y + 12, what is the
[#permalink]
Show Tags
09 Aug 2017, 19:50
Bunuel wrote: tushain wrote: Bunuel wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y?
Given: \(x=8y+12\).
(1) x = 12u, where u is an integer > \(x=12u\) > \(12u=8y+12\) > \(3(u1)=2y\) > the only thing we know from this is that 3 is a factor of \(y\). Is it GCD of \(x\) and \(y\)? Not clear: if \(x=36\), then \(y=3\) and \(GCD(x,y)=3\) but if \(x=60\), then \(y=6\) and \(GCD(x,y)=6\) > two different answers. Not sufficient.
(2) y = 12z, where z is an integer > \(y=12z\) > \(x=8*12z+12\) > \(x=12(8z+1)\). So, we have \(y=12z\) and \(x=12(8z+1)\). Now, as \(z\) and \(8z+1\) do not share any common factor but 1 (8z and 8z+1 are consecutive integers and consecutive integers do not share any common factor 1. As 8z has all factors of z then z and 8z+1 also do not share any common factor but 1). Thus, 12 must be GCD of \(x\) and \(y\). Sufficient.
Answer: B.
Hope it's clear. BunuelAre (kq + 1 , q) always coprimes? where k and q are any positive integers? Yes. kq and kq + 1 are consecutive integers, thus they do not share any common factor but 1, thus q and kq + 1 must also be coprime. This question is beyond esoteric. Not saying, I don't easily understand what coprimes are and how you set up that formula. However, I didn't know KQ+1 and Q are coprimes




Re: If x and y are positive integers such that x = 8y + 12, what is the &nbs
[#permalink]
09 Aug 2017, 19:50



Go to page
1 2
Next
[ 27 posts ]



