Find all School-related info fast with the new School-Specific MBA Forum

It is currently 05 Sep 2015, 02:18
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are positive integers such that x = 8y + 12, what

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1719
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 79

Kudos [?]: 514 [0], given: 109

If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 31 Aug 2010, 00:22
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

45% (03:02) correct 55% (01:45) wrong based on 176 sessions
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
[Reveal] Spoiler: OA

_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Intern
Intern
avatar
Joined: 09 Mar 2010
Posts: 39
Concentration: Technology, General Management
Schools: McCombs '14
Followers: 0

Kudos [?]: 10 [1] , given: 17

GMAT ToolKit User
Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 31 Aug 2010, 01:14
1
This post received
KUDOS
Stat 1: x= 12u returns
x= 12u and y=3/2(u-1)
GCD of x and y varies for u=0 and u is +ve

Stat 2: y=12z returns
x=12(8z+1),y=12z
GCD for any inter value of z is 12.

Hence statement 2 alone is sufficient.

answer:B
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4756

Kudos [?]: 50398 [4] , given: 7544

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 31 Aug 2010, 03:52
4
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
metallicafan wrote:
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


Given: \(x=8y+12\).

(1) \(x=12u\) --> \(12u=8y+12\) --> \(3(u-1)=2y\) --> 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) \(y=12z\) --> \(x=8*12z+12\) --> \(x=12(8z+1)\) --> so 12 is a factor both \(x\) and \(y\).

Is it GCD of \(x\) and \(y\)? Why can not it be more than 12, for example 13, 16, 24, ... We see that factors of \(x\) are 12 and \(8z+1\): so if \(8z+1\) has some factor >1 common with \(z\) then GCD of \(x\) and \(y\) will be more than 12 (for example if \(z\) and \(8z+1\) are multiples of 5 then \(x\) would be multiple of \(12*5=60\) and \(y\) also would be multiple of \(12*5=60\), so GCD of \(x\) and \(y\) would be more than 12). But \(z\) and \(8z+1\) CAN NOT share any common factor >1, as \(8z+1\) is a multiple of \(z\) plus 1, so no factor of \(z\) will divide \(8z+1\) evenly, which means that GCD of \(x\) and \(y\) can not be more than 12. \(GCD(x,y)=12\). Sufficient.

Answer: B.

Hope it's clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1719
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 79

Kudos [?]: 514 [0], given: 109

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 31 Aug 2010, 12:14
Wow, is that a 700 question?
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1719
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 79

Kudos [?]: 514 [0], given: 109

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 21 Sep 2010, 11:32
kalrac wrote:
Stat 1: x= 12u returns
x= 12u and y=3/2(u-1)
GCD of x and y varies for u=0 and u is +ve

Stat 2: y=12z returns
x=12(8z+1),y=12z
GCD for any inter value of z is 12.

Hence statement 2 alone is sufficient.

answer:B


I don't understand the quoted solution, can someone please explain it?

Thanks!
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4756

Kudos [?]: 50398 [2] , given: 7544

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 21 Sep 2010, 11:39
2
This post received
KUDOS
Expert's post
metallicafan wrote:
kalrac wrote:
Stat 1: x= 12u returns
x= 12u and y=3/2(u-1)
GCD of x and y varies for u=0 and u is +ve

Stat 2: y=12z returns
x=12(8z+1),y=12z
GCD for any inter value of z is 12.

Hence statement 2 alone is sufficient.

answer:B


I don't understand the quoted solution, can someone please explain it?

Thanks!


I think the quoted solution refers to the following rule: 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 \(b\).

So if we apply this rule to (2) we would have: both \(x\) and \(y\) are multiple of 12 and are 12 apart each other, so 12 is GCD of \(x\) and \(y\).
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Manager
Manager
avatar
Joined: 19 Sep 2010
Posts: 186
Followers: 2

Kudos [?]: 65 [0], given: 18

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 16 Oct 2010, 07:40
great question...
Manager
Manager
avatar
Joined: 07 Jun 2010
Posts: 86
Followers: 1

Kudos [?]: 25 [0], given: 0

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 16 Feb 2011, 13:23
Bunuel,

You wrote:

(1) x=12u --> 12u=8y+12 --> 3(u-1)=2y --> the only thing we know from this is that 3 is a multiple of y.

How do we know that 3 is a muliple of y? I mean, I worked it out by plugging in values for u and found that it is true, but is there some property of the formula that gives it away?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29210
Followers: 4756

Kudos [?]: 50398 [0], given: 7544

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 16 Feb 2011, 13:34
Expert's post
abmyers wrote:
Bunuel,

You wrote:

(1) x=12u --> 12u=8y+12 --> 3(u-1)=2y --> the only thing we know from this is that 3 is a multiple of y.

How do we know that 3 is a muliple of y? I mean, I worked it out by plugging in values for u and found that it is true, but is there some property of the formula that gives it away?


3(u-1)=2y --> the only thing we know from this is that 3 is a factor of y --> 3(u-1) is a multiple of 3, so must be 2y as they are equal. Now, 2y to be multiple of 3 then y must be multiple of 3.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. 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?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

Director
Director
avatar
Joined: 08 Jun 2010
Posts: 801
Followers: 0

Kudos [?]: 53 [0], given: 192

Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 01 Mar 2013, 03:39
I fail

not easy at all

I want to follow this posting.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6222
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 15 Mar 2014, 18:15
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

Intern
Intern
avatar
Status: Researching for Schools
Joined: 21 Apr 2013
Posts: 21
Location: United States
Concentration: Leadership, General Management
GMAT 1: 640 Q45 V34
GMAT 2: 730 Q49 V40
WE: Project Management (Computer Software)
Followers: 0

Kudos [?]: 7 [0], given: 76

Premium Member Reviews Badge
Re: If x and y are positive integers such that x = 8y + 12, what [#permalink] New post 25 Mar 2014, 09:38
x = 8y + 12 simplifies to x=4(2y+3)

Statement 1:
substituting x=12u

12u=4(2y+3)
3u=2y-3
3(u-1)=2y

So u should be greater than 1 and should be odd (because u-1 is a multiple of 2)
Checking for values

u x y GCD
3 36 3 3
5 60 6 6

So statement 1 not sufficient

Statement 2:
substituting y=12z

x=4(12z+3)
x=12(4z+1)

Checking for values

z x y GCD
1 60 12 12
2 108 24 12
3 154 36 12
we can check for more values but usually we would see any variations withing 1st 3-4 values.

Answer is B.
Re: If x and y are positive integers such that x = 8y + 12, what   [#permalink] 25 Mar 2014, 09:38
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x and y are positive integers, is x a factor of 12? summer101 5 26 Jul 2013, 01:38
73 Experts publish their posts in the topic x and y are positive integers such that x=8y+12, what is the enigma123 12 29 Jan 2012, 17:25
16 Experts publish their posts in the topic If x and y are positive integers such that x = 8y + 12, what rafi 13 17 Sep 2010, 03:23
1 If x and y are positive integers such that x = 8y +12 . What Hussain15 7 25 Apr 2010, 06:51
1 Experts publish their posts in the topic If x and y are positive integers and x> y, then what is the value of x study 5 11 Jan 2010, 23:10
Display posts from previous: Sort by

If x and y are positive integers such that x = 8y + 12, what

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.