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

It is currently 29 Aug 2015, 13:14
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, what is the GCF of x and y

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
1 KUDOS received
Intern
Intern
avatar
Joined: 06 Sep 2012
Posts: 42
Concentration: Social Entrepreneurship
Followers: 0

Kudos [?]: 21 [1] , given: 42

If x and y are positive integers, what is the GCF of x and y [#permalink] New post 15 Dec 2012, 10:30
1
This post received
KUDOS
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

61% (02:12) correct 39% (01:24) wrong based on 227 sessions
If x and y are positive integers, what is the GCF of x and y?

(1) When x is divided by y, the remainder is 1.
(2) x^2 - 2xy + y^2 = 1
[Reveal] Spoiler: OA
Expert Post
4 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29108
Followers: 4725

Kudos [?]: 49735 [4] , given: 7403

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 16 Dec 2012, 08:23
4
This post received
KUDOS
Expert's post
If x and y are positive integers, what is the GCF of x and y?

(1) When x is divided by y, the remainder is 1 --> x is one more than some multiple of y (x=yq+1). This implies that x and that multiple are consecutive integer. Now, two consecutive integers are co-prime, 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, we have that x and yq do not share any common factor but 1, thus x and y also do not share any common factor but 1, which means that the greatest common factor of x and y is 1. Sufficient.

(2) x^2 - 2xy + y^2 = 1 --> (x-y)^2=1 --> |x-y|=1 --> x and y are consecutive integers --> the greatest common factor of x and y is 1. Sufficient.

Answer: D.

Similar questions to practice:
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
_________________

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

Intern
Intern
avatar
Joined: 06 Sep 2012
Posts: 42
Concentration: Social Entrepreneurship
Followers: 0

Kudos [?]: 21 [0], given: 42

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 16 Dec 2012, 08:54
Bunuel wrote:
If x and y are positive integers, what is the GCF of x and y?

(1) When x is divided by y, the remainder is 1 --> x is one more than some multiple of y (x=yq+1). This implies that x and that multiple are consecutive integer. Now, two consecutive integers are co-prime, 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, we have that x and yq do not share any common factor but 1, thus x and y also do not share any common factor but 1, which means that the greatest common factor of x and y is 1. Sufficient.

(2) x^2 - 2xy + y^2 = 1 --> (x-y)^2=1 --> |x-y|=1 --> x and y are consecutive integers --> the greatest common factor of x and y is 1. Sufficient.

Answer: D.

Similar questions to practice:
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html



sorry, can you please elaborate on the red part? how did you solve (x-y)^2 to get |x-y|=1?
_________________

Life begins at the edge of your comfort zone.

Appreciate the +1!

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29108
Followers: 4725

Kudos [?]: 49735 [1] , given: 7403

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 16 Dec 2012, 08:57
1
This post received
KUDOS
Expert's post
JJ2014 wrote:
Bunuel wrote:
If x and y are positive integers, what is the GCF of x and y?

(1) When x is divided by y, the remainder is 1 --> x is one more than some multiple of y (x=yq+1). This implies that x and that multiple are consecutive integer. Now, two consecutive integers are co-prime, 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, we have that x and yq do not share any common factor but 1, thus x and y also do not share any common factor but 1, which means that the greatest common factor of x and y is 1. Sufficient.

(2) x^2 - 2xy + y^2 = 1 --> (x-y)^2=1 --> |x-y|=1 --> x and y are consecutive integers --> the greatest common factor of x and y is 1. Sufficient.

Answer: D.

Similar questions to practice:
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html



sorry, can you please elaborate on the red part? how did you solve (x-y)^2 to get |x-y|=1?


Take the square root from (x-y)^2=1 to get |x-y|=1.
_________________

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

Intern
Intern
avatar
Joined: 02 Apr 2013
Posts: 2
Location: United States
WE: Engineering (Computer Hardware)
Followers: 0

Kudos [?]: 5 [0], given: 1

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 03 Apr 2013, 20:37
I understand why the answer is D. However, in the first statement, the number x and y dont need to be consecutive numbers to get a remainder 1. for eg 4,9. The GCF is still 1 though.
1 KUDOS received
Intern
Intern
avatar
Joined: 28 Jan 2013
Posts: 8
Location: United States
Concentration: Strategy, Technology
GMAT Date: 04-20-2013
GPA: 3.2
WE: Analyst (Computer Software)
Followers: 0

Kudos [?]: 12 [1] , given: 4

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 04 Apr 2013, 09:42
1
This post received
KUDOS
cvaditya wrote:
I understand why the answer is D. However, in the first statement, the number x and y dont need to be consecutive numbers to get a remainder 1. for eg 4,9. The GCF is still 1 though.


You are correct but what bunuel said was also correct. He stated

x & ky are consecutive integers not x & y. in this case 9 & 8 (multiple of 4).

8 & 9 have GCF 1 then 4 & 9 can not have GCF greater than 1.

Does this help clarify ?
Intern
Intern
avatar
Joined: 20 Apr 2013
Posts: 24
Concentration: Finance, Finance
GMAT Date: 06-03-2013
GPA: 3.3
WE: Accounting (Accounting)
Followers: 0

Kudos [?]: 1 [0], given: 99

Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 01 May 2013, 06:46
|x-y|=1 = Does GCF can be -1.
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 629
Followers: 64

Kudos [?]: 770 [0], given: 135

Premium Member
Re: If x and y are positive integers, what is the GCF of x and y [#permalink] New post 01 May 2013, 07:12
Expert's post
Rajkiranmareedu wrote:
|x-y|=1 = Does GCF can be -1.


By definition, HCF of two or more integers is the largest positive integer which divides them without any remainder. For example, HCF of -4 and -2 is +2.
Nonetheless, in the given problem, it is mentioned that both x and y are positive. Thus, the GCF IS anyways positive.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Intern
Intern
User avatar
Joined: 16 Nov 2013
Posts: 32
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
Followers: 1

Kudos [?]: 55 [0], given: 20

If x and y are positive integers, what is the greatest commo [#permalink] New post 18 Nov 2013, 08:10
If x and y are positive integers, what is the greatest common factor of x and y?

1) When x is divided by y, the remainder is 1.
2) \(x^2 - 2xy + y^2 = 1\)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29108
Followers: 4725

Kudos [?]: 49735 [0], given: 7403

Re: If x and y are positive integers, what is the greatest commo [#permalink] New post 18 Nov 2013, 08:15
Expert's post
registerincog wrote:
If x and y are positive integers, what is the greatest common factor of x and y?

1) When x is divided by y, the remainder is 1.
2) \(x^2 - 2xy + y^2 = 1\)


Merging similar topics. Please refer to the solutions above.
_________________

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

Re: If x and y are positive integers, what is the greatest commo   [#permalink] 18 Nov 2013, 08:15
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic If x and y are positive integers, what is the value of (x+y) Baten80 1 22 Jan 2012, 07:20
12 Experts publish their posts in the topic If x and y are positive integers such that x = 8y + 12, what metallicafan 11 31 Aug 2010, 00:22
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
2 Experts publish their posts in the topic In the fraction x/y, where x and y are positive integers, what is the mahesh004 8 05 Oct 2006, 00:23
Display posts from previous: Sort by

If x and y are positive integers, what is the GCF of x and y

  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®.