Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 23 Mar 2017, 21:43

### 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

# Is |x| + |y| = 0?

Author Message
TAGS:

### Hide Tags

Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 247
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)
Followers: 5

Kudos [?]: 79 [0], given: 46

Is |x| + |y| = 0 [#permalink]

### Show Tags

01 May 2011, 10:37
3
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:13) correct 45% (01:12) wrong based on 351 sessions

### HideShow timer Statistics

Is |x| + |y| = 0

(1) x + 2|y| = 0
(2) y + 2|x| = 0
[Reveal] Spoiler: OA

_________________

WarLocK
_____________________________________________________________________________
The War is oNNNNNNNNNNNNN for 720+
see my Test exp here http://gmatclub.com/forum/my-test-experience-111610.html
do not hesitate me giving kudos if you like my post.

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.
VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1346
Followers: 17

Kudos [?]: 249 [0], given: 10

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
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

SVP
Joined: 16 Nov 2010
Posts: 1671
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 528 [0], given: 36

Re: Is |x| + |y| = 0 [#permalink]

### Show Tags

02 May 2011, 19:30
(1)
-2 + 2|-1| = 0

-2 + 2|1| = 0

0 + |0| = 0

(2)

-2 + 2|-1| = 0

-2 + 2|1| = 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: 334
Location: India
Followers: 1

Kudos [?]: 215 [0], given: 33

Re: Is |x| + |y| = 0 [#permalink]

### Show Tags

04 May 2011, 21:51
Warlock007 wrote:
Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 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: 28
Followers: 0

Kudos [?]: 7 [0], given: 3

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

_________________

http://www.hannibalprep.com

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7244
Location: Pune, India
Followers: 2200

Kudos [?]: 14314 [1] , given: 222

Re: Is |x| + |y| = 0 [#permalink]

### Show Tags

05 May 2011, 18:47
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
Warlock007 wrote:
Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 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 + 2|y| = 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 + 2|x| = 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 = -2|y| and y = -2|x| 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
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Intern
Joined: 18 Feb 2010
Posts: 28
Followers: 1

Kudos [?]: 63 [1] , given: 5

Is |x| + |y| = 0? [#permalink]

### Show Tags

21 Jun 2012, 19:48
1
KUDOS
2
This post was
BOOKMARKED
Is |x| + |y| = 0?

(1) x + 2|y| = 0
(2) y + 2|x| = 0
Joined: 29 Mar 2012
Posts: 325
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 29

Kudos [?]: 415 [0], given: 23

### Show Tags

21 Jun 2012, 21:54
Is |x| + |y| = 0?

1. x + 2|y| = 0
2. y + 2|x| = 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.

Regards,
Math Expert
Joined: 02 Sep 2009
Posts: 37560
Followers: 7393

Kudos [?]: 99302 [2] , given: 11010

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

22 Jun 2012, 01:35
2
KUDOS
Expert's post
Is |x| + |y| = 0?

Since absolute value is non-negative the from $$|x| + |y| = 0$$ we have that the sum of two non-negative 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 + 2|y| = 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 non-negative value ($$|y|$$), so $$-\frac{x}{2}\geq{0}$$ --> $$x\leq{0}$$.

(2) y + 2|x| = 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 non-negative 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: $$x-2y=0$$ and $$y-2x=0$$. Solving gives $$x=y=0$$. Sufficient.

Hope it's clear.

_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 101

Kudos [?]: 920 [1] , given: 43

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

24 Jun 2012, 13:38
1
KUDOS
Is |x| + |y| = 0?

(1) x + 2|y| = 0
(2) y + 2|x| = 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 side-by-side and obtain x + 2|y| + y + 2|x| = 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.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
Joined: 02 Sep 2009
Posts: 37560
Followers: 7393

Kudos [?]: 99302 [0], given: 11010

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

Theory on Abolute Values: math-absolute-value-modulus-86462.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

_________________
Director
Joined: 25 Apr 2012
Posts: 728
Location: India
GPA: 3.21
Followers: 43

Kudos [?]: 716 [1] , given: 723

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

04 Jul 2013, 04:58
1
KUDOS
Is |x| + |y| = 0?

(1) x + 2|y| = 0
(2) y + 2|x| = 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+2|y|=0
Now if y is less than equal to 0 than we have x-2y=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+2|x|=0
If x is less than or equal to zero than y-2x=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: 472
Followers: 3

Kudos [?]: 165 [0], given: 134

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

04 Jul 2013, 13:02
Is |x| + |y| = 0?

(1) x + 2|y| = 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 + 2|y| = 0
2|y| = -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 + 2|x| = 0
This is a similar statement to the above one, except we have the absolute value of x instead of y.
y + 2|x| = 0
2|x| = -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 + 2|y| = 0
x-2y = 0

y + 2|x| = 0
y - 2x = 0

y-2x=x-2y
3y=3x
y=x=0
SUFFICIENT
(C)
Intern
Joined: 15 Sep 2013
Posts: 11
Schools: Sloan '19 (A)
GMAT 1: 700 Q46 V40
Followers: 0

Kudos [?]: 6 [0], given: 19

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

13 Oct 2013, 03:05
Bunuel wrote:
Is |x| + |y| = 0?

Since absolute value is non-negative the from $$|x| + |y| = 0$$ we have that the sum of two non-negative 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 + 2|y| = 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 non-negative value ($$|y|$$), so $$-\frac{x}{2}\geq{0}$$ --> $$x\leq{0}$$.

(2) y + 2|x| = 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 non-negative 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: $$x-2y=0$$ and $$y-2x=0$$. Solving gives $$x=y=0$$. Sufficient.

Hope it's clear.

Hi Bunuel, why do the "equations from the statements transform to: $$x-2y=0$$ and $$y-2x=0$$"? Shouldn't it be -x + 2y = 0 and -y +2x = 0? Hope you can help clarify.
Math Expert
Joined: 02 Sep 2009
Posts: 37560
Followers: 7393

Kudos [?]: 99302 [0], given: 11010

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 non-negative the from $$|x| + |y| = 0$$ we have that the sum of two non-negative 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 + 2|y| = 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 non-negative value ($$|y|$$), so $$-\frac{x}{2}\geq{0}$$ --> $$x\leq{0}$$.

(2) y + 2|x| = 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 non-negative 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: $$x-2y=0$$ and $$y-2x=0$$. Solving gives $$x=y=0$$. Sufficient.

Hope it's clear.

Hi Bunuel, why do the "equations from the statements transform to: $$x-2y=0$$ and $$y-2x=0$$"? 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 $$x + 2|y| = 0$$ becomes $$x-2y=0$$ and $$y + 2|x| = 0$$ becomes $$y-2x=0$$.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14377
Followers: 602

Kudos [?]: 174 [0], given: 0

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

28 Oct 2015, 15:04
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.
_________________
Manager
Joined: 25 Sep 2015
Posts: 148
Location: United States
GMAT 1: 700 Q V
Followers: 0

Kudos [?]: 31 [0], given: 72

Re: Is |x| + |y| = 0? [#permalink]

### Show Tags

12 Dec 2015, 22:21
Bunuel wrote:
Is |x| + |y| = 0?

Since absolute value is non-negative the from $$|x| + |y| = 0$$ we have that the sum of two non-negative 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 + 2|y| = 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 non-negative value ($$|y|$$), so $$-\frac{x}{2}\geq{0}$$ --> $$x\leq{0}$$.

(2) y + 2|x| = 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 non-negative 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: $$x-2y=0$$ and $$y-2x=0$$. Solving gives $$x=y=0$$. Sufficient.

Hope it's clear.

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: 73
Location: United States
Concentration: General Management, Strategy
WE: Design (Manufacturing)
Followers: 0

Kudos [?]: 8 [0], given: 21

Re: Is |x| + |y| = 0 [#permalink]

### Show Tags

28 Jul 2016, 11:58
Warlock007 wrote:
Is |x| + |y| = 0
1)x + 2|y| = 0
2)y + 2|x| = 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: 376
Schools: Schulich '16
Followers: 4

Kudos [?]: 66 [0], given: 4

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
Re: Is |x| + |y| = 0?   [#permalink] 29 Jul 2016, 01:16
Similar topics Replies Last post
Similar
Topics:
2 Is x + y > 0 ? 11 15 Jul 2014, 13:58
Is x + y > 0 ? 1 26 Nov 2012, 00:24
20 If y is an integer and y = |x| + x, is y = 0? 8 21 Feb 2012, 22:07
12 Is x + y > 0 ? 18 26 Dec 2010, 08:31
7 If y is an integer and y=|x|+x, is y=0? 19 14 Dec 2010, 22:03
Display posts from previous: Sort by