GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Nov 2018, 01:05

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. # Are the positive integers x and y consecutive?  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Manager Status: Never ever give up on yourself.Period. Joined: 23 Aug 2012 Posts: 140 Location: India Concentration: Finance, Human Resources GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33 GPA: 3.5 WE: Information Technology (Investment Banking) Are the positive integers x and y consecutive? [#permalink] ### Show Tags 06 Jan 2013, 07:04 6 00:00 Difficulty: 75% (hard) Question Stats: 56% (01:47) correct 44% (02:16) wrong based on 127 sessions ### HideShow timer Statistics Are the positive integers x and y consecutive? (1) x^2 - y^2 = 2y + 1 (2) x^2 - xy - x = 0 _________________ Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beat-it-no-one-wants-to-be-defeated-journey-570-to-149968.html VP Status: Been a long time guys... Joined: 03 Feb 2011 Posts: 1159 Location: United States (NY) Concentration: Finance, Marketing GPA: 3.75 Re: Are the positive integers x and y consecutive? [#permalink] ### Show Tags 06 Jan 2013, 10:00 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 _________________ Senior Manager Joined: 27 Jun 2012 Posts: 375 Concentration: Strategy, Finance Schools: Haas EWMBA '17 Re: Are the positive integers x and y consecutive? [#permalink] ### Show Tags 06 Jan 2013, 22:24 3 1 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. _________________ Thanks, Prashant Ponde Tough 700+ Level RCs: Passage1 | Passage2 | Passage3 | Passage4 | Passage5 | Passage6 | Passage7 Reading Comprehension notes: Click here VOTE GMAT Practice Tests: Vote Here PowerScore CR Bible - Official Guide 13 Questions Set Mapped: Click here Finance your Student loan through SoFi and get$100 referral bonus : Click here

Math Expert
Joined: 02 Sep 2009
Posts: 50578
Re: Are the positive integers x and y consecutive?  [#permalink]

### Show Tags

07 Jan 2013, 02:55
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
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 8766
Re: Are the positive integers x and y consecutive?  [#permalink]

### Show Tags

14 Oct 2017, 01:14
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: Are the positive integers x and y consecutive? &nbs [#permalink] 14 Oct 2017, 01:14
Display posts from previous: Sort by