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

 It is currently 07 Feb 2016, 16:30

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Intern
Joined: 06 Sep 2012
Posts: 42
Concentration: Social Entrepreneurship
Followers: 0

Kudos [?]: 35 [2] , given: 42

If x and y are positive integers, what is the GCF of x and y [#permalink]  15 Dec 2012, 10:30
2
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:12) correct 40% (01:21) wrong based on 272 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
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62117 [4] , given: 9440

Re: If x and y are positive integers, what is the GCF of x and y [#permalink]  16 Dec 2012, 08:23
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
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.

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

Kudos [?]: 35 [0], given: 42

Re: If x and y are positive integers, what is the GCF of x and y [#permalink]  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.

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!

Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62117 [1] , given: 9440

Re: If x and y are positive integers, what is the GCF of x and y [#permalink]  16 Dec 2012, 08:57
1
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.

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.
_________________
Intern
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]  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.
Intern
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]  04 Apr 2013, 09:42
1
KUDOS
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
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]  01 May 2013, 06:46
|x-y|=1 = Does GCF can be -1.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 69

Kudos [?]: 874 [0], given: 135

Re: If x and y are positive integers, what is the GCF of x and y [#permalink]  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.
_________________
Intern
Joined: 16 Nov 2013
Posts: 30
Location: United States
Concentration: Entrepreneurship, General Management
GPA: 3.49
Followers: 1

Kudos [?]: 72 [0], given: 20

If x and y are positive integers, what is the greatest commo [#permalink]  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) $$x^2 - 2xy + y^2 = 1$$
Math Expert
Joined: 02 Sep 2009
Posts: 31286
Followers: 5345

Kudos [?]: 62117 [0], given: 9440

Re: If x and y are positive integers, what is the greatest commo [#permalink]  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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 8167
Followers: 416

Kudos [?]: 111 [0], given: 0

Re: If x and y are positive integers, what is the GCF of x and y [#permalink]  08 Oct 2015, 07:05
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.
_________________
Re: If x and y are positive integers, what is the GCF of x and y   [#permalink] 08 Oct 2015, 07:05
Similar topics Replies Last post
Similar
Topics:
11 If x and y are positive integers, what is the remainder when x^y is 7 12 Jun 2015, 02:20
24 x/y=5.35 If x and y are positive integers, then what is the 14 05 Oct 2010, 18:39
1 If x and y are positive integers such that x = 8y +12 . What 7 25 Apr 2010, 06:51
1 If x and y are positive integers and x> y, then what is the value of x 9 11 Jan 2010, 23:10
3 In the fraction x/y, where x and y are positive integers, what is the 8 05 Oct 2006, 00:23
Display posts from previous: Sort by