Are the positive integers x and y consecutive?

Oldest

Best Reply

Author

Message

TAGS:

Manager

Status: Never ever give up on youself.Period.

Joined: 23 Aug 2012

Posts: 133

Location: India

Concentration: Finance, Human Resources

Schools: HBS '15, Carroll '15

GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33

GPA: 3.5

WE: Information Technology (Investment Banking)

Followers: 5

Kudos [?]: 38 [0], given: 31

Are the positive integers x and y consecutive? [#permalink]

06 Jan 2013, 08:04

00:00

Question Stats:

38% (01:35) correct

61% (01:03) wrong

based on 1 sessions

Are the positive integers x and y consecutive?

(1) x^2 - y^2 = 2y + 1
(2) x^2 - xy - x = 0

[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
Beat it, no one wants to be defeated (My journey from 570 to 690) : beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html

Verbal GMAT Forum Moderator

Status: Preparing for the another shot...!

Joined: 03 Feb 2011

Posts: 1322

Location: India

Concentration: Finance, Marketing

GMAT 1: 720 Q V

GPA: 3.75

Followers: 63

Kudos [?]: 311 [0], given: 52

Re: Are the positive integers x and y consecutive? [#permalink]

06 Jan 2013, 11:00

daviesj wrote:

Are the positive integers x and y consecutive?
(1)x^2 - y^2 = 2y + 1
(2) x^2 - xy - x = 0

The question is basically asking whether x=y+1
Statement 1)
x^2 - y^2=2y+1 can be written as (x+y)(x-y)=2y+1.----equation 1
If we put x=y+1, then LHS must be equal to RHS.

Equation 1 can be written, after substituting x=y+1, as (2y+1)(1)=2y+1. They are equal. Hence x and y are consecutive.

Statement 2)
x(x-y-1)=0
The above equation can be equal to 0 only when x-y=1 because x is given to be positive.

Hope I am correct.
+1D
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting

Senior Manager

Joined: 27 Jun 2012

Posts: 413

Followers: 23

Kudos [?]: 193 [1] , given: 171

Re: Are the positive integers x and y consecutive? [#permalink]

06 Jan 2013, 23:24

This post received
KUDOS

You can simplify the first statement in following way:
(1) x^2-Y^2=2y+1
i.e. x^2 = Y^2 + 2y+1
i.e. x^2 = (y+1)^2
i.e. x=|y+1| = y + 1(taking positive root as both x & y are positive integers)
Hence (1) is SUFFICIENT as x & y are consecutive

(2) x^2-xy-x=0
i.e. x(x-y-1)=0
i.e. x=0 or x=y+1
As x is positive integer x<>0, thus x=y+1
Hence (2) is SUFFICIENT.

Choice (D) is the answer.
_________________

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11515

Followers: 1791

Kudos [?]: 9536 [0], given: 826

Re: Are the positive integers x and y consecutive? [#permalink]

07 Jan 2013, 03:55

daviesj wrote:

Are the positive integers x and y consecutive?

(1) x^2 - y^2 = 2y + 1
(2) x^2 - xy - x = 0

Similar question to practice: if-x-y-and-z-are-positive-integers-where-x-y-and-z-x-126859.html
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

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. NEW!!!

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. NEW!!!

What are GMAT Club Tests?
25 extra-hard Quant Tests

Find out what's new at GMAT Club - latest features and updates

Re: Are the positive integers x and y consecutive? [#permalink] 07 Jan 2013, 03:55

		Similar topics	Author	Replies	Last post
Similar Topics:		If x & y are consecutive positive integer multiples of	Praetorian	4	11 Sep 2003, 04:55
		If x, y, and z are 3 positive consecutive integers such that	rxs0005	3	23 Sep 2006, 05:50
		x and y are consecutive positive integers and x>y x^2	Hermione	5	24 Nov 2006, 23:28
		If x, y, and z are 3 positive consecutive integers such that	mm007	3	20 Dec 2006, 15:32
	1	x and y are consecutive positive integers and: \left{	study	7	25 Oct 2008, 21:16

Are the positive integers x and y consecutive?

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

Are the positive integers x and y consecutive?

Are the positive integers x and y consecutive?

Main navigation

GMAT Resources

Partners

MBA Resources