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Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
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12 Jun 2013, 11:27
1
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.
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
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12 Jun 2013, 11:43
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.
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
[#permalink]
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12 Jun 2013, 11:48
1
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|.
_________________
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
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12 Jun 2013, 11:52
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|.
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
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01 Oct 2016, 19:22
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
Re: Is |x| = |y| ? (1) x - y = 6 (2) x + y = 0
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24 Feb 2017, 02:55
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
close
70% (00:36) correct 
