is x^2 = XY?

1) (X^2)-(Y^2)= (X + 5)(Y - 5)

Is this sufficient or not?

My problem is:
to set the equation on the right to zero, x= -5 OR y = 5

* X can be -5. If X = -5 then the right side of the equation is 0, but X^2 must equal Y^2.

so this means while X = -5, Y can be either 5 or -5 and equations on the left and right would = 0. Correct?

* Y can be 5. If Y = 5, then the right side of the equation is 0, but X^2 must equal Y^2 to make the left side of the equation = 0.
so this means while Y= 5, X can be either 5 or -5. correct?

My problem is:
is my reasoning correct in that the above scenarios? because of the different possibilities for Y and X respectively?

I'll walk you through your reasoning. I think you're not necessarily wrong here - but you've gone too far on a data sufficiency problem in the "what might be the case" scenarios, which isn't really an efficient use of your time here.

to set the equation on the right to zero, x= -5 OR y = 5
* X can be -5. If X = -5 then the right side of the equation is 0, but X^2 must equal Y^2.
so this means while X = -5, Y can be either 5 or -5 and equations on the left and right would = 0. Correct?
Yes -- IF x is -5, AND y is either 5 or -5, THEN the equation works. If this isn't the case, though, the equation doesn't work. Since we don't know whether this very specific case is the scenario, we don't have enough information. Basically, we have 1 equation and 2 unknowns, so we have insufficient information.

* Y can be 5. If Y = 5, then the right side of the equation is 0, but X^2 must equal Y^2 to make the left side of the equation = 0.
so this means while Y= 5, X can be either 5 or -5. correct?
Same issue here -- You've presented one other scenario where we MIGHT have a situation that makes the equation work, but we don't have any information that leads us to believe that this might actually be the case.

Thus, your reasoning is sound, but unnecessary in this situation.

Hope this helps,

Veritas Help

Hi VP HELP
I thought I took the problem to the extent necessary to solve?

if statement 1) says x^2-Y^2 = (X+5)(Y-5) then we must find all values which make this equation true, correct?

Here are my pairs (-5,5) (-5,-5) (-5,5) (5,5). all of these pairs make statement 1) true.

Now I have to see if the pairs sufficiently answer the initial quesiton x^2=xy with a definite yes or definite no.

using the first pair 25=-25 no
using the second pair 25=25 yes

because i have both a yes and a no answer, statement 1 is insufficient.

I maybe overthinking it, can you tell me what you would do to solve it quickly?

Sure.
Quickest way to solve this one quickly...

statement 1) says x^2-Y^2 = (X+5)(Y-5)
x^2-Y^2 is the same as (x+y)(x-y)
Since this is NOT the same as (x+5)(y-5) we know we don't have enough information, and we cannot solve it. (They've given us something that looks similar in format to make it seem confusing, but since it is indeed different, there is nothing we can do with these two sides to solve...)

Veritas Help