Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 175
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)

Is x + y = 0
[#permalink]
Show Tags
Updated on: 29 Jul 2016, 00:56
Question Stats:
58% (01:47) correct 42% (01:46) wrong based on 297 sessions
HideShow timer Statistics
Is x + y = 0 (1) x + 2y = 0 (2) y + 2x = 0
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
WarLocK_____________________________________________________________________________ The War is oNNNNNNNNNNNNN for 720+ see my Test exp here http://gmatclub.com/forum/mytestexperience111610.htmldo not hesitate me giving kudos if you like my post.
Originally posted by Warlock007 on 01 May 2011, 10:37.
Last edited by Bunuel on 29 Jul 2016, 00:56, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Is x + y = 0?
[#permalink]
Show Tags
22 Jun 2012, 01:35
Is x + y = 0?Since absolute value is nonnegative the from \(x + y = 0\) we have that the sum of two nonnegative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\) (1) x + 2y = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=2\) and \(y=1\). Not sufficient. Notice that from this statement \(y=\frac{x}{2}\), so \(\frac{x}{2}\) equals to a nonnegative value (\(y\)), so \(\frac{x}{2}\geq{0}\) > \(x\leq{0}\). (2) y + 2x = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=2\) and \(x=1\). Not sufficient. Notice that from this statement \(x=\frac{y}{2}\), so \(\frac{y}{2}\) equals to a nonnegative value (\(x\)), so \(\frac{y}{2}\geq{0}\) > \(y\leq{0}\). (1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x2y=0\) and \(y2x=0\). Solving gives \(x=y=0\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html
_________________




Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 856

Re: Is x + y = 0
[#permalink]
Show Tags
02 May 2011, 04:54
only possible if x=y=0. a. x=6, y= 3 or x=y=0 Not sufficient b. y=6,x=3 x=y=0 not sufficient.
a+b sufficient.x =y=0



Retired Moderator
Joined: 16 Nov 2010
Posts: 1253
Location: United States (IN)
Concentration: Strategy, Technology

Re: Is x + y = 0
[#permalink]
Show Tags
02 May 2011, 19:30
(1) 2 + 21 = 0 2 + 21 = 0 0 + 0 = 0 (2) 2 + 21 = 0 2 + 21 = 0 0 + 0 = 0 (1) and (2) are insufficient (1) and (2) together: 0 + 0 = 0 So the expression can be 0 only when x and y are 0, if both x and y are negative/positive, x + y > 0. I wonder how the OA is D.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Senior Manager
Joined: 28 Dec 2010
Posts: 262
Location: India

Re: Is x + y = 0
[#permalink]
Show Tags
04 May 2011, 21:51
Warlock007 wrote: Is x + y = 0 1)x + 2y = 0 2)y + 2x = 0 I know its an easy one even i got answer in seconds but still need more perfection in fundamentals of mod questions m looking forward to a basic fundamental explanation of the same I think c). all the above are in absolute value. from question stem we see that for a sum of absolute value to be 0, both the terms should be equal to zero. even if one of the terms is not equal to zero, the sum will nto be equal to zero. statement 1 says: x + (positive no) = 0 i.e. either both zero or x = (2y) statement 2 says: y +(pos no) = 0 again either both zero or y = (2x) unless it is mentioed that x and y are positive, id say C. becuase it then becomes clear that x & y have to be zero and so x + y = 0. have i missed something?



Intern
Status: ThinkTank
Joined: 07 Mar 2009
Posts: 19

Re: Is x + y = 0
[#permalink]
Show Tags
05 May 2011, 12:49
Concepts tested is absolute value It can not be D the OA. It is most probably C Obviously on 1) and 2) we can plug 2 and 1 and 0 and 0 for x and y and get a Yes and No answer. Insuff However on 1+2) we get x + 4 /x/ = 0 so x is negative and 4 x = x so x =0 and therefore y is equal to 0. Suff Answer is C Hope this is helpful
_________________
http://www.hannibalprep.com



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9705
Location: Pune, India

Re: Is x + y = 0
[#permalink]
Show Tags
05 May 2011, 18:47
Warlock007 wrote: Is x + y = 0 1)x + 2y = 0 2)y + 2x = 0 I know its an easy one even i got answer in seconds but still need more perfection in fundamentals of mod questions m looking forward to a basic fundamental explanation of the same This is how you can reason it out theoretically: Question: Is x + y = 0 ? A mod is either positive or 0. It can never take a negative value. If sum of two mods is 0, they both individually have to be 0 to give a sum 0. So question comes down to: Is x = y = 0? 1)x + 2y = 0 Again, y will be either 0 or positive. So x will be 0 in first case (when y = 0) and negative in the second case (when y is positive) to give a sum of 0. Hence we cannot say whether x = y = 0. Not sufficient. 2)y + 2x = 0 Same is the case here. There is not reason why analysis of this equation should be any different from statement 1 since x and y are just interchanged. Together, either x = y=0 else x and y both are negative. If x and y both are negative, then x = 2y and y = 2x i.e. in absolute value terms, x is twice of y and y is twice of x which is not possible. Hence, the only way both statements will hold is if x = y = 0. Hence answer (C).
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Current Student
Joined: 29 Mar 2012
Posts: 295
Location: India
GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38

Re: Absolute Value
[#permalink]
Show Tags
21 Jun 2012, 21:54
nades09 wrote: Is x + y = 0?
1. x + 2y = 0 2. y + 2x = 0
Thanks Hi, x+y=0? or x=y? Both x and y are positive, so is it possible that x is negative of some positive quantity, thus, only possibility would be x=y=0? and that's the question. Using (1), y=x/2 or \(x \leq 0\), so, it is possible that x = 1, y = 1/2, then \(x+y \neq 0\) or x =0, y = 0, then \(x+y = 0\), Insufficient. Using (2); x=y/2 or \(y \leq 0\), so, it is possible that y = 1, x = 1/2, then \(x+y \neq 0\) or y = 0, x = 0, then \(x+y = 0\), Insufficient. Combining both, \(x \leq 0\), then x=y/2 implies, x=y/2 or 2x = y.......(a) Similarly, \(y \leq 0\), then y=x/2 implies, y=x/2 or x = 2y........(b) From (a) & (b) 4y=y, thus y=0 & x=0 Also, \(x+y = 0\). Sufficient. Answer is (C). Regards,



Director
Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)

Re: Is x + y = 0?
[#permalink]
Show Tags
24 Jun 2012, 13:38
nades09 wrote: Is x + y = 0?
(1) x + 2y = 0 (2) y + 2x = 0 (1) Not sufficient, but implies that x is not positive. (2) Again, not sufficient, but implies y is not positive. When considering (1) and (2) together, we can add the two equations sidebyside and obtain x + 2y + y + 2x = 0, and (x + x) + x + (y + y) +y = 0 + x + 0 + y = x + y = 0. We used the fact that if x is not positive (it is negative or 0), then x + x = 0. Correct answer  C.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Is x + y = 0?
[#permalink]
Show Tags
04 Jul 2013, 01:24
Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HERE
_________________



Director
Joined: 25 Apr 2012
Posts: 660
Location: India
GPA: 3.21
WE: Business Development (Other)

Re: Is x + y = 0?
[#permalink]
Show Tags
04 Jul 2013, 04:58
nades09 wrote: Is x + y = 0?
(1) x + 2y = 0 (2) y + 2x = 0 Since the Question stem is asking if sum of 2 absolute values (which are positive) equal to 0. We know that sum of 2 positive nos can be zero if both are zero. Hence Question asks if x=y=0 from St1 we have x+2y=0 Now if y is less than equal to 0 than we have x2y=0 or x=2y or x=0 if y is 0 If y>0 then x=2y Since using 1 we have more than 1 possible option therefore A,D ruled out From st 2 we have y+2x=0 If x is less than or equal to zero than y2x=0 or y=2x or if x=0 then y=0 If x>0 then y=2x Again more than 1 solution so Option B ruled out Combining both statement we get x=2y ,x=2y, y=2x and y=2x and x=0, y=0 Since x=0,y=0 is common from both equation we can say say that x+y=0 Note that x and y have to be 0 to satisfy all above equations.
_________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”



Senior Manager
Joined: 13 May 2013
Posts: 399

Re: Is x + y = 0?
[#permalink]
Show Tags
04 Jul 2013, 13:02
Is x + y = 0?
(1) x + 2y = 0
There are two ways we can solve. One is to get the positive and negative cases of y. On the other hand, we can isolate y as the question is looking for the value of y+x
x + 2y = 0 2y = x y = x/2 if y = x/2 then x/2 must be positive which means x is negative. Of course, x could also be zero meaning we don't know if the absolute value of x and y = 0 INSUFFICIENT
(2) y + 2x = 0 This is a similar statement to the above one, except we have the absolute value of x instead of y. y + 2x = 0 2x = y x = y/2 As with the above statement y/2 = an absolute value so y must be negative. However, it could also be = to zero. INSUFFICIENT
So....from 1 and 2 we know that x<=0 and y<=0 which means that: x + 2y = 0 x2y = 0
y + 2x = 0 y  2x = 0
y2x=x2y 3y=3x y=x=0 SUFFICIENT (C)



Current Student
Joined: 15 Sep 2013
Posts: 10

Re: Is x + y = 0?
[#permalink]
Show Tags
13 Oct 2013, 03:05
Bunuel wrote: Is x + y = 0?Since absolute value is nonnegative the from \(x + y = 0\) we have that the sum of two nonnegative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\) (1) x + 2y = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=2\) and \(y=1\). Not sufficient. Notice that from this statement \(y=\frac{x}{2}\), so \(\frac{x}{2}\) equals to a nonnegative value (\(y\)), so \(\frac{x}{2}\geq{0}\) > \(x\leq{0}\). (2) y + 2x = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=2\) and \(x=1\). Not sufficient. Notice that from this statement \(x=\frac{y}{2}\), so \(\frac{y}{2}\) equals to a nonnegative value (\(x\)), so \(\frac{y}{2}\geq{0}\) > \(y\leq{0}\). (1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x2y=0\) and \(y2x=0\). Solving gives \(x=y=0\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Hi Bunuel, why do the "equations from the statements transform to: \(x2y=0\) and \(y2x=0\)"? Shouldn't it be x + 2y = 0 and y +2x = 0? Hope you can help clarify.



Math Expert
Joined: 02 Sep 2009
Posts: 58402

Re: Is x + y = 0?
[#permalink]
Show Tags
13 Oct 2013, 04:11
pauc wrote: Bunuel wrote: Is x + y = 0?Since absolute value is nonnegative the from \(x + y = 0\) we have that the sum of two nonnegative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\) (1) x + 2y = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=2\) and \(y=1\). Not sufficient. Notice that from this statement \(y=\frac{x}{2}\), so \(\frac{x}{2}\) equals to a nonnegative value (\(y\)), so \(\frac{x}{2}\geq{0}\) > \(x\leq{0}\). (2) y + 2x = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=2\) and \(x=1\). Not sufficient. Notice that from this statement \(x=\frac{y}{2}\), so \(\frac{y}{2}\) equals to a nonnegative value (\(x\)), so \(\frac{y}{2}\geq{0}\) > \(y\leq{0}\). (1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x2y=0\) and \(y2x=0\). Solving gives \(x=y=0\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Hi Bunuel, why do the "equations from the statements transform to: \(x2y=0\) and \(y2x=0\)"? Shouldn't it be x + 2y = 0 and y +2x = 0? Hope you can help clarify. We have that \(x\leq{0}\) and \(y\leq{0}\), thus \(x=x\) and \(y=y\). Therefore \(x + 2y = 0\) becomes \(x2y=0\) and \(y + 2x = 0\) becomes \(y2x=0\). Hope it's clear.
_________________



Manager
Joined: 25 Sep 2015
Posts: 100
Location: United States
GPA: 3.26

Re: Is x + y = 0?
[#permalink]
Show Tags
12 Dec 2015, 22:21
Bunuel wrote: Is x + y = 0?Since absolute value is nonnegative the from \(x + y = 0\) we have that the sum of two nonnegative values equals to zero, which is only possible if both of them equal to zero. So, the question basically asks whether \(x=y=0\) (1) x + 2y = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(x=2\) and \(y=1\). Not sufficient. Notice that from this statement \(y=\frac{x}{2}\), so \(\frac{x}{2}\) equals to a nonnegative value (\(y\)), so \(\frac{x}{2}\geq{0}\) > \(x\leq{0}\). (2) y + 2x = 0. It's certainly possible that \(x=y=0\) but it's also possible that \(y=2\) and \(x=1\). Not sufficient. Notice that from this statement \(x=\frac{y}{2}\), so \(\frac{y}{2}\) equals to a nonnegative value (\(x\)), so \(\frac{y}{2}\geq{0}\) > \(y\leq{0}\). (1)+(2) We have that \(x\leq{0}\) and \(y\leq{0}\), hence equations from the statements transform to: \(x2y=0\) and \(y2x=0\). Solving gives \(x=y=0\). Sufficient. Answer: C. Hope it's clear. P.S. Please read and follow: rulesforpostingpleasereadthisbeforeposting133935.html Hi Bunuel, I solved this question in the following way  still got the right answer (not sure if I am right or it was just a fluke). Please provide input. x + y = 0, means both value of x&y needs to be known (preferably zero) Each statement talks about two variables at the same time Both Insufficient So either C or E Now, Statement 1 is in form of y=mx+c (m=0.5/+0.5  slope) & Statement 2 is in form of y=mx+c (m=2/+2  slope) Since any of the possibilities do not overlap each other, these lines will intersect each other at one point  and thus a solution is possible with the help of both the statements. Thus C



Manager
Joined: 20 Mar 2015
Posts: 56
Location: United States
Concentration: General Management, Strategy
WE: Design (Manufacturing)

Re: Is x + y = 0
[#permalink]
Show Tags
28 Jul 2016, 11:58
Warlock007 wrote: Is x + y = 0 1)x + 2y = 0 2)y + 2x = 0 I know its an easy one even i got answer in seconds but still need more perfection in fundamentals of mod questions m looking forward to a basic fundamental explanation of the same addition of two positive values will only result in zero if both the numbers are 0. niether 1 nor 2 sufficiently states that. But if we combine both of them, we have x=y=0 , the only case which satisfies the equations. hence C. The OA is wrong!



Senior Manager
Joined: 02 Mar 2012
Posts: 273

Re: Is x + y = 0?
[#permalink]
Show Tags
29 Jul 2016, 01:16
only when x and y both =0 this will be true
1)may possibilities including one with 0+ 0
2)many possibilities including one with 0+0
1+2,
commn is x=y=0
so C



NonHuman User
Joined: 09 Sep 2013
Posts: 13244

Re: Is x + y = 0?
[#permalink]
Show Tags
17 Oct 2019, 01:39
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: Is x + y = 0?
[#permalink]
17 Oct 2019, 01:39






