May 24 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. May 25 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. May 27 01:00 AM PDT  11:59 PM PDT All GMAT Club Tests are free and open on May 27th for Memorial Day! May 27 10:00 PM PDT  11:00 PM PDT Special savings are here for Magoosh GMAT Prep! Even better  save 20% on the plan of your choice, now through midnight on Tuesday, 5/27 May 30 10:00 PM PDT  11:00 PM PDT Application deadlines are just around the corner, so now’s the time to start studying for the GMAT! Start today and save 25% on your GMAT prep. Valid until May 30th.
Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 05 Feb 2014
Posts: 42

x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
Updated on: 22 Jun 2014, 13:10
Question Stats:
44% (02:06) correct 56% (02:25) wrong based on 373 sessions
HideShow timer Statistics
x + 2 = y + 2 what is the value of x + y ? (1) xy < 0 (2) x > 2 and y < 2 I don't have the official answer. Got this question off a video on youtube, i don't agree with the answer he gives so want your thoughts on this.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by gauravsoni on 22 Jun 2014, 13:05.
Last edited by Bunuel on 22 Jun 2014, 13:10, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
22 Jun 2014, 13:11
x + 2 = y + 2 what is the value of x + y ?Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\). (1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient. (2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient. Answer: D. Hope it's clear.
_________________




Manager
Status: suffer now and live forever as a champion!!!
Joined: 01 Sep 2013
Posts: 103
Location: India
Dheeraj: Madaraboina
GPA: 3.5
WE: Information Technology (Computer Software)

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
24 Jun 2014, 05:25
Bunuel wrote: x + 2 = y + 2 what is the value of x + y ?
Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\).
(1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient.
(2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient.
Answer: D.
Hope it's clear. hi bunuel, following is my interpretation of the this problem . Could you please tell me where i am wrong Stmt 1: XY <0 Case 1: XY <0 (POSITIVE) (NEGATIve) Case 2: XY < 0 (Negative) (Positive) Both cases satisy to give X+Y = 4 Stmt 1 Sufficient . STMT2: X > 2 AND Y < 2 From above statement X is always postive and Y may be negative (or) Positive. case 1: x+2 = y+2 (x+2) = (y+2) case 2: x+2 = Y+2 (X+2) = (Y+2) How can we get X+Y = 4 from here on and also from your above solution, i am unable to figure out if x and y are not equal, how come there will be only one solution . Ex : if x= 5 (5>2) and y = 1 (1<2) x+y = 6 and there are many values for x+y . Help is appreciated. Thanks in advance.



Math Expert
Joined: 02 Sep 2009
Posts: 55267

x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
24 Jun 2014, 05:58
dheeraj24 wrote: Bunuel wrote: x + 2 = y + 2 what is the value of x + y ?
Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\).
(1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient.
(2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient.
Answer: D.
Hope it's clear. hi bunuel, following is my interpretation of the this problem . Could you please tell me where i am wrong Stmt 1: XY <0 Case 1: XY <0 (POSITIVE) (NEGATIve) Case 2: XY < 0 (Negative) (Positive) Both cases satisy to give X+Y = 4 Stmt 1 Sufficient . STMT2: X > 2 AND Y < 2 From above statement X is always postive and Y may be negative (or) Positive. case 1: x+2 = y+2 (x+2) = (y+2) case 2: x+2 = Y+2 (X+2) = (Y+2) How can we get X+Y = 4 from here on and also from your above solution, i am unable to figure out if x and y are not equal, how come there will be only one solution . Ex : if x= 5 (5>2) and y = 1 (1<2) x+y = 6 and there are many values for x+y . Help is appreciated. Thanks in advance. Your logic for the first statement is not clear. How did you derive that since x and y have the opposite signs x + y must be 4? Please reread the solution above. x + 2 = y + 2 is true in two cases: (i) \(x=y\) (ii) \(x+y=4\) Now, let me ask you a question: is it possible to have x=y case for either of the statements? The answer is NO. Hence we must have the second case which says that x+y=4.
_________________



Intern
Joined: 19 Mar 2015
Posts: 10

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
04 Oct 2015, 22:42
Bunuel wrote: x + 2 = y + 2 what is the value of x + y ?
Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\).
(1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient.
(2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient.
Answer: D.
Hope it's clear. Hi Bunuel, This was my way of understanding. x+2 = y+2 So we have 2 possibilities either both sides the same sign or different sign. a) Both same sign : x+2 = y+2>x=y b) Diff sign : x+2 = y2> x+y=4 Anything wrong in this? Even from your explanation how can we derive that xy<0? For this to happen x and y need to be of different signs. But it is not necessary that they are of opp sign. It can be possible that x=y=2 which implies xy>0. What is that I am missing her. Help!



Math Expert
Joined: 02 Sep 2009
Posts: 55267

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
05 Oct 2015, 02:09
Johnjojop wrote: Bunuel wrote: x + 2 = y + 2 what is the value of x + y ?
Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\).
(1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient.
(2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient.
Answer: D.
Hope it's clear. Hi Bunuel, This was my way of understanding. x+2 = y+2 So we have 2 possibilities either both sides the same sign or different sign. a) Both same sign : x+2 = y+2>x=y b) Diff sign : x+2 = y2> x+y=4 Anything wrong in this? Even from your explanation how can we derive that xy<0? For this to happen x and y need to be of different signs. But it is not necessary that they are of opp sign. It can be possible that x=y=2 which implies xy>0. What is that I am missing her. Help! x + 2 = y + 2 is true in two cases: (i) \(x=y\) (ii) \(x+y=4\) Next, (1) says that xy < 0. Is it possible to have the first case from above? If x = y, then xy = x^2 >= 0, not < 0, thus the first case is out and we get \(x+y=4\).
_________________



SVP
Joined: 26 Mar 2013
Posts: 2178

x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
06 Oct 2015, 05:19
Bunuel wrote: x + 2 = y + 2 what is the value of x + y ?
Square both sides: \(x^2+4x+4=y^2+4y+4\) > \(x^2y^2+4x4y=0\) > \((x+y)(xy)+4(xy)=0\) > \((xy)(x+y+4)=0\) > either \(x=y\) or \(x+y=4\).
(1) xy<0 > the first case is not possible, since if \(x=y\), then \(xy=x^2\geq{0}\), not \(<0\) as given in this statement, hence we have the second case: \(x+y=4\). Sufficient.
(2) x>2 and y<2. This statement implies that \(x\neq{y}\), therefore \(x+y=4\). Sufficient.
Answer: D.
Hope it's clear. Bunuel, When is it right to square both sides of absolute question? and it is wrong? I appreciate if you can elaborate with examples the correct and wrong if there are. thanks for advance



CEO
Joined: 20 Mar 2014
Posts: 2626
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

Re: If x+2=y+2, what is the value of x+y?
[#permalink]
Show Tags
01 Feb 2016, 18:18
MathRevolution wrote: If x+2=y+2, what is the value of x+y?
1) xy<0 2) x>2 and y<2
* A solution will be posted in two days. Given, \(x+2 = y+2\)> \(x+2 = \pm (y+2)\) > either x=y or x+y=4 Per statement 1, xy<0 > x=y can not be true, leaving us with x+y=4. Sufficient. Per statement 2, x>2 and y<2 , again x=y can not be possible., leaving us with x+y=4. Sufficient. D is thus the correct answer.



Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7367
GPA: 3.82

Re: If x+2=y+2, what is the value of x+y?
[#permalink]
Show Tags
03 Feb 2016, 22:46
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution. If x+2=y+2, what is the value of x+y? 1) xy<0 2) x>2 and y<2 In the original condition, it becomes x+2=±(y+2). x=y or x+y=4 are derived from x+2=y+2 or x+2=(y+2). Then, there are 2 variables(x,y) and 1 equation(x+2=y+2), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer. For 1), since x≠y, x+y=4, which is unique and sufficient. For 2), since x≠y, x+y=4, which is unique and sufficient. Therefore, the answer is D. For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spareThe oneandonly World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only $149 for 3 month Online Course""Free Resources30 day online access & Diagnostic Test""Unlimited Access to over 120 free video lessons  try it yourself"



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: If x+2=y+2, what is the value of x+y?
[#permalink]
Show Tags
04 Feb 2016, 09:43
MathRevolution wrote: If x+2=y+2, what is the value of x+y?
1) xy<0 2) x>2 and y<2
* A solution will be posted in two days. Given: x+2=y+2 which is true only if case 1: when x = y case 2: When x+y = 4 e.g. x=2 and y=6 or x=3 and y=7 etc Question : x+y=?Statement 1: xy<0i.e. x is not equal to y i.e. Case 2 is implied i.e. x+y=4 SUFFICIENT Statement 2: x>2 and y<2i.e. x is not equal to y i.e. Case 2 is implied i.e. x+y=4 SUFFICIENT Answer: Option D Engr2012 : This question is available on GMAT CLUB already.
_________________
Prosper!!!GMATinsightBhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhihttp://www.GMATinsight.com/testimonials.htmlACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



Manager
Joined: 07 May 2015
Posts: 78

Re: If x+2=y+2, what is the value of x+y?
[#permalink]
Show Tags
06 Feb 2016, 12:11
Hi Engr2012What am i missing in this? x+2 = y+2 ==> Square both sides ==> x^2 + 4 + 4x = y^2 + 4 + 4y ==> x^2  y^2 = 4x + 4y ==> (xy)(x+y) = 4(xy) ==> Cancelling xy from both sides ==> x+y = 4 Please help me understand. Thanks in advance! Engr2012 wrote: MathRevolution wrote: If x+2=y+2, what is the value of x+y?
1) xy<0 2) x>2 and y<2
* A solution will be posted in two days. Given, \(x+2 = y+2\)> \(x+2 = \pm (y+2)\) > either x=y or x+y=4 Per statement 1, xy<0 > x=y can not be true, leaving us with x+y=4. Sufficient. Per statement 2, x>2 and y<2 , again x=y can not be possible., leaving us with x+y=4. Sufficient. D is thus the correct answer.



CEO
Joined: 20 Mar 2014
Posts: 2626
Concentration: Finance, Strategy
GPA: 3.7
WE: Engineering (Aerospace and Defense)

If x+2=y+2, what is the value of x+y?
[#permalink]
Show Tags
06 Feb 2016, 12:24
neeraj609 wrote: Hi Engr2012What am i missing in this? x+2 = y+2 ==> Square both sides ==> x^2 + 4 + 4x = y^2 + 4 + 4y ==> x^2  y^2 = 4x + 4y ==> (xy)(x+y) = 4(xy) ==> Cancelling xy from both sides ==> x+y = 4 Please help me understand. Thanks in advance! Engr2012 wrote: MathRevolution wrote: If x+2=y+2, what is the value of x+y?
1) xy<0 2) x>2 and y<2
* A solution will be posted in two days. Given, \(x+2 = y+2\)> \(x+2 = \pm (y+2)\) > either x=y or x+y=4 Per statement 1, xy<0 > x=y can not be true, leaving us with x+y=4. Sufficient. Per statement 2, x>2 and y<2 , again x=y can not be possible., leaving us with x+y=4. Sufficient. D is thus the correct answer. You can not eliminate (xy) unless categorically mentioned that x is not equal to y. When you cancel this factor, you are assuming that x= y. This is one of the most common mistake people do in DS questions involving algebraic expressions. Once you get (xy)(x+y) = 4(xy) > (xy) (x+y+4)=0 So you get either x=y or x+y = 4 You need to use the given statements to eliminate one of the 2 above possible scenarios to evaluate sufficiency of the statements



Manager
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
14 Feb 2017, 23:58
Another probable way to arrive at the solution!Option DX + 2 = Y + 2; X + Y = ? I: XY < 0 i.e., X & Y have opposite signs : X<0 & Y>0 or X>0 & Y<0 : For X<0 & Y>0 : (X+2) = (Y+2) : X + Y =4 : For X>0 & Y<0 : (X+2) = (Y+2) : X + Y =4 Sufficient! II: X > 2 & Y < 2 : X >2 & 0<Y<2 OR X>2 & Y<0 : For X >2 & 0<Y<2: (X+2) = (Y+2) : X + Y =4 : For X>2 & Y<0: (X+2) = (Y+2) : X + Y =4 Sufficient!
_________________



Intern
Joined: 25 Aug 2017
Posts: 1

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
08 Sep 2017, 02:32
guys i think we can solve this question in much easier way such questions are straight forward questions we can follow algebraic method according to that either sie of mod can have four conditions but in this case only two conditions are possible i.e. either both positive (i am talking about whole modulus functionnot just x and y signs ) or one of them will be negative
we get x=y in case one and in case two we get x+y=4 this means either x will be equal to y which is not possible in both STATEMENTS so we left with only one case that is two in both statments we can get the value of x+y=4 irrespective of x and y values we need to find the value of (x+y)
note: wrote case and statments dont undrstand them as same



NonHuman User
Joined: 09 Sep 2013
Posts: 11007

Re: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
Show Tags
16 Sep 2018, 06:11
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: x + 2 = y + 2 what is the value of x + y ?
[#permalink]
16 Sep 2018, 06:11






