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Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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 02 Jul 2012, 21:25
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Is │x│=│y│? (1) x - y = 6 (2) x + y = 0
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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02 Jul 2012, 21:38
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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,
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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02 Jul 2012, 23:38
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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 
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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?
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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12 Jun 2013, 12:27
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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.
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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. |
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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12 Jun 2013, 12:48
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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|.
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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|. |
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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12 Jun 2013, 12:53
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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.
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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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
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0 [#permalink]
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Re: Is │x│=│y│? (1) x - y = 6 (2) x + y = 0
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13 May 2018, 10:26
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