Data Sufficiency

Castor.kim wrote:Is |x| = |y| ?

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

Target question: Is |x| = |y| ?

Statement 1: x - y = 6
This essentially tells us that x is 6 greater than y. This yields several possible cases. Here are two:
case a: x = 7 and y = 1, in which case |x| does not equal |y|
case b: x = 3 and y = -3, in which case |x| equals |y|
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x + y = 0
Rearrange to get: x = -y
This means that the magnitude of x is equal to the magnitude of y (i.e., they're both the same distance from 0 on the number line).
If x and y are the same distance from 0 on the number line, then |x| definitely equals |y|
As such, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

Castor.kim wrote:Is |x| = |y| ?

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

let the given question to x^2 = y^2
it can be (x+y)(x-y) = 0
(actually I can't convinced that is right way...)

option1) x-y=6, so x+y=0, x=y SUFFICIENT
option2) x+y=0, so x-y=any number INSUFFICIENT

but OA is B
anyone help the process of solving?

Hi Castor.kim!

I like your train of thought for writing the x^2=y^2. This is actually true because the technical definition of |x| = sqrt(x^2). So you could actually write that sqrt(x^2) = sqrt(y^2) and then square both sides (which wouldn't impact the signs.

So let's go back to your logic and I'm going to throw in a ?? to remind us of what we DON'T know:

x^2 = y^2 ?? ...subtract y^2 from both sides...
x^2 - y^2 = 0 ?? ...factor...
(x-y)(x+y)=0 ??

Ok, so the rephrased questions is
"Does (x-y)(x+y) = 0 ??"

Statement (1): x - y = 6
Plug in (x-y)=6 into the question...

(6)(x+y)=0 ?? ...divide both sides by 6...
(x+y)=0 ??

Well, I don't know if (x+y) = 0 so I can't answer yet...NOT Sufficient.


Statement (2): x + y = 0
Plug in (x+y)=0 into the question...

(x-y)(0)=0 ??

Well, anything times a 0 will equal 0, right? So then the left hand side of my equation (x-y)(0) is going to turn into 0, and 0=0, so I KNOW that it is true...cause 0 always equals 0!! SUFFICIENT.

That means my answer is B!

Hope this helps!

Whit

Castor.kim wrote:Is |x| = |y| ?

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

let the given question to x^2 = y^2
it can be (x+y)(x-y) = 0
(actually I can't convinced that is right way...)

option1) x-y=6, so x+y=0, x=y SUFFICIENT
option2) x+y=0, so x-y=any number INSUFFICIENT

but OA is B
anyone help the process of solving?

And one more note - I might be wrong, but I'm thinking that where you went wrong was assuming that (x+y)(x-y)=0 was something we KNEW to be true, when in fact it was the question we were asking!! So we didn't know if x+y would actually =0 from statement 1!

Sorry if I didn't make that clear in my earlier post!!

Whit