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.
_________________

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,

x= y + 6 stmt1

x= -y -> !x! = !y! so stmt1 is the answer B is the choice

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.

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.

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|.
_________________

Ahhh! That makes sense! I am assuming |x| = |y| when I am trying to verify if it does or does not. Thanks!

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.

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

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

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.

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.
_________________

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