NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 11:07 It is currently 24 Apr 2024, 11:07
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
catennacio
Intern
Intern
Joined: 15 Apr 2010
Posts: 35
Own Kudos [?]: 99 [41]
Given Kudos: 11
Send PM
Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   Updated on: 11 Dec 2018, 23:28
10
Kudos
31
Bookmarks
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

73% (00:57) correct 27% (01:05) wrong based on 1421 sessions
Hide Show timer Statistics
Is |x| = |y| ?

(1) x - y = 6
(2) x + y = 0
ShowHide Answer
Official Answer
B

Originally posted by catennacio on 02 Jul 2012, 21:25.
Last edited by Bunuel on 11 Dec 2018, 23:28, edited 1 time in total.
Renamed the topic and edited the question.
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618785 [10]
Given Kudos: 81588
Send PM
CAT Tests Forum Quiz Mode
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   02 Jul 2012, 23:38
2
Kudos
8
Bookmarks
Expert Reply
Is │x│=│y│?

Is \(|x|=|y|\)? The question basically asks whether \(x=y\) or \(x=-y\)

(1) x - y = 6. If \(x=3\) and \(y=-3\) then the answer is YES but if \(x\) and \(y\) are some other values then the answer is NO.

(2) x + y = 0. Rearrange: \(x=-y\). Sufficient.

Answer: B.
General Discussion
User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 29 Mar 2012
Posts: 267
Own Kudos [?]: 1492 [3]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Send PM
GMAT ToolKit User
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   02 Jul 2012, 21:38
2
Kudos
1
Bookmarks
Hi,

Using (1),
x-y=6
x=3, y=-3
then, |x|=|y|
but when x=9, y=3
\(|x| \neq |y|\). Insufficient.

Using (2),
x+y=0
or x = -y, when y=1, x=-1
and |x|=|y|, Sufficient.

Thus, Answer (B)

Regards,
avatar
krrish
Intern
Intern
Joined: 04 Mar 2013
Posts: 47
Own Kudos [?]: 13 [0]
Given Kudos: 6
Location: India
Concentration: General Management, Marketing
Schools: Booth '16 Kellogg '14 Stanford '14 Sloan '14
GPA: 3.49
WE:Web Development (Computer Software)
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   16 May 2013, 09:34
catennacio wrote:
Is │x│=│y│?

(1) x - y = 6
(2) x + y = 0




x= y + 6 stmt1

x= -y -> !x! = !y! so stmt1 is the answer B is the choice :)
User avatar
WholeLottaLove
Senior Manager
Senior Manager
Joined: 13 May 2013
Posts: 314
Own Kudos [?]: 565 [0]
Given Kudos: 134
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:07
My first instinct was to manipulate |x|=|y|

x=y
OR
x=-y

1.) says that x-y=6 which means we can get values for x and y

x=6+y
y=x-6

So, for x=y

6+y=y
6=0 (Invalid)

x=x-6
0=6 (Invalid)

So, for x=-y

6+y=-y
y=-3

x=-x+6
x=3

Why wouldn't we use that methodology on this problem?
User avatar
Zarrolou
Director
Director
Joined: 02 Sep 2012
Status:Far, far away!
Posts: 859
Own Kudos [?]: 4890 [1]
Given Kudos: 219
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Send PM
GMAT ToolKit User
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:27
1
Kudos
WholeLottaLove wrote:
My first instinct was to manipulate |x|=|y|

x=y
OR
x=-y

1.) says that x-y=6 which means we can get values for x and y

x=6+y
y=x-6

So, for x=y

6+y=y
6=0 (Invalid)

x=x-6
0=6 (Invalid)

So, for x=-y

6+y=-y
y=-3

x=-x+6
x=3

Why wouldn't we use that methodology on this problem?


Are you saying that A is sufficient?

In the case \(x=3\) and \(y=-3\) => \(|x|=|y|\).

But if \(x=90\) and \(y=84\) then x - y = 6 but \(|x|\neq{|y|}\).

The question asks you if x=y OR x=-y, you cannot assume that it's true in your solution to find the values of x,y for which it holds ture.
User avatar
WholeLottaLove
Senior Manager
Senior Manager
Joined: 13 May 2013
Posts: 314
Own Kudos [?]: 565 [0]
Given Kudos: 134
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:43
I should have worded that better.

I guess that solving the problem they way I did, I would say A is correct.

I see that for x-y=6 there could be many values for x and y, however, it seems like many similar problems are solved by manipulating statements (i.e. x-y=6) and plugging into x=y or x=-y.

I understand how this problem was solved, but I want to understand WHY it was solved the way it was.

As always, thank you for for help.


Zarrolou wrote:
WholeLottaLove wrote:
My first instinct was to manipulate |x|=|y|

x=y
OR
x=-y

1.) says that x-y=6 which means we can get values for x and y

x=6+y
y=x-6

So, for x=y

6+y=y
6=0 (Invalid)

x=x-6
0=6 (Invalid)

So, for x=-y

6+y=-y
y=-3

x=-x+6
x=3

Why wouldn't we use that methodology on this problem?


Are you saying that A is sufficient?

In the case \(x=3\) and \(y=-3\) => \(|x|=|y|\).

But if \(x=90\) and \(y=84\) then x - y = 6 but \(|x|\neq{|y|}\).

The question asks you if x=y OR x=-y, you cannot assume that it's true in your solution to find the values of x,y for which it holds ture.
User avatar
B
mau5
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 485
Own Kudos [?]: 3092 [1]
Given Kudos: 141
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:48
1
Kudos
WholeLottaLove wrote:
My first instinct was to manipulate |x|=|y|

x=y
OR
x=-y

1.) says that x-y=6 which means we can get values for x and y

x=6+y
y=x-6

So, for x=y

6+y=y
6=0 (Invalid)

x=x-6
0=6 (Invalid)

So, for x=-y

6+y=-y
y=-3

x=-x+6
x=3

Why wouldn't we use that methodology on this problem?


When you assume that x=y and solve the equation [x-y = 6], you WILL get invalid solutions as you got because you have anyways assumed that x=y-->
x-y = 0;which contradicts the given fact.

However, when you assume that x=-y-->x+y=0, you have inherently assumed that |x| IS equal to |y| and now you are just solving for the values of x and y. Thus, the equation [x-y=6] would really not make any difference for this method.( x-y) could equal anything and you would still get |x| = |y|.
User avatar
WholeLottaLove
Senior Manager
Senior Manager
Joined: 13 May 2013
Posts: 314
Own Kudos [?]: 565 [0]
Given Kudos: 134
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:52
Ahhh! That makes sense! I am assuming |x| = |y| when I am trying to verify if it does or does not. Thanks!

vinaymimani wrote:
WholeLottaLove wrote:
My first instinct was to manipulate |x|=|y|

x=y
OR
x=-y

1.) says that x-y=6 which means we can get values for x and y

x=6+y
y=x-6

So, for x=y

6+y=y
6=0 (Invalid)

x=x-6
0=6 (Invalid)

So, for x=-y

6+y=-y
y=-3

x=-x+6
x=3

Why wouldn't we use that methodology on this problem?


When you assume that x=y and solve the equation [x-y = 6], you WILL get invalid solutions as you got because you have anyways assumed that x=y-->
x-y = 0;which contradicts the given fact.

However, when you assume that x=-y-->x+y=0, you have inherently assumed that |x| IS equal to |y| and now you are just solving for the values of x and y. Thus, the equation [x-y=6] would really not make any difference for this method.( x-y) could equal anything and you would still get |x| = |y|.
User avatar
Zarrolou
Director
Director
Joined: 02 Sep 2012
Status:Far, far away!
Posts: 859
Own Kudos [?]: 4890 [1]
Given Kudos: 219
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Send PM
GMAT ToolKit User
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   12 Jun 2013, 12:53
1
Kudos
Yes Wotta you should manipolate the statement to understand the question better.

Is \(|x|=|y|\)? it s like saying is x=y or x=-y?

But once you start analyzing the statement you cannot use that info.
User avatar
B
AmritaSarkar89
Manager
Manager
Joined: 22 Feb 2016
Posts: 67
Own Kudos [?]: 52 [0]
Given Kudos: 208
Location: India
Concentration: Economics, Healthcare
Schools: ISB '18 Kellogg '19 (I) Yale '19 (S) Tuck '19 (S)
GMAT 1: 690 Q42 V47
GMAT 2: 710 Q47 V39
GPA: 3.57
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   01 Oct 2016, 20:22
Look into the question as - we need to find out if the numeric value of A and B are equal or not.
Statement1: Case 1
A=12 B=6
A-B=6
or
A=-3 and B=3
A-B=6
NOT SUFFICIENT

Statement2:
A+B=0
This condition is only possible when both A and B are of same numeric values however their signs are opposite or A and B are both 0. In both the case Mod A= Mod B

Hope this helps
User avatar
S
KrishnakumarKA1
Senior Manager
Senior Manager
Joined: 05 Jan 2017
Posts: 416
Own Kudos [?]: 284 [0]
Given Kudos: 15
Location: India
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   24 Feb 2017, 03:55
Prompt analysis
x and y are real numbers


Superset
The answer to this question will be either yes or no.

Translation
In order to find the answer, we need:
1# exact value of x and y.
2# 2 equation in x and y to find their exact value
3# any other specific equation or properties to determine if the condition holds true.

Statement analysis
St 1: x-y = 6. We take two values for (x,y) i.e. (4,-2) and (3,-3)for former it doesn't hold true and for latter it holds true. INSUFFICIENT

St 2: x +y = 0 or x = -y. Taking mod on both side we can say that |x| = |y|. Answer

Option B
avatar
B
vaibhavi21
Intern
Intern
Joined: 25 Nov 2018
Posts: 3
Own Kudos [?]: 1 [0]
Given Kudos: 3
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   11 Dec 2018, 10:31
Hi,,, can I know for statement B , can't be the case where both variables are 0 & then we can get x+y=0.

Kindly help.
User avatar
S
KrishnakumarKA1
Senior Manager
Senior Manager
Joined: 05 Jan 2017
Posts: 416
Own Kudos [?]: 284 [1]
Given Kudos: 15
Location: India
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   11 Dec 2018, 22:23
1
Kudos
vaibhavi21 wrote:
Hi,,, can I know for statement B , can't be the case where both variables are 0 & then we can get x+y=0.

Kindly help.


Yes. Both "x" and "y" can be zero.

Even in that case, |x| = |y|.

So statement B is sufficient.
User avatar
P
Showmeyaa
Senior Manager
Senior Manager
Joined: 24 Jun 2019
Posts: 432
Own Kudos [?]: 437 [0]
Given Kudos: 117
Location: India
Concentration: Marketing, Strategy
Send PM
Reviews Badge
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   30 Apr 2021, 14:47
catennacio wrote:
Is |x| = |y| ?

(1) x - y = 6
(2) x + y = 0


Asked: If |x| = |y|?
Modifying the question stem as:
if x^2 = y^2?
if x^2 - y^2 = 0
if (x + y)(x-y) = 0

1) x - y = 6. We need the value of x+y to confirm
2) x + y = 0. If x+y = 0, then the whole equation becomes 0. Sufficient.
User avatar
S
Kimberly77
Senior Manager
Senior Manager
Joined: 16 Nov 2021
Posts: 476
Own Kudos [?]: 27 [0]
Given Kudos: 5900
Location: United Kingdom
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   08 Apr 2022, 03:40
Hi brunel, Is |x|=|y||x|=|y|? you mentioned x=y or x=−y , why there is no -x here when || is removed from x?
Am I missing something? Thanks
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32650
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink] New post   09 Jul 2023, 20:34
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.
GMAT Club Bot
gmatclubot
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0 [#permalink]
09 Jul 2023, 20:34
Moderator:
Bunuel
Math Expert
92902 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions