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## Comment on

Basic Equation Solving## Hi Brent,

In your solution to this question

https://gmatclub.com/forum/if-x-y-2-x-2-y-2-then-which-one-of-the-following-statements-241756.html

Given: (x − y)² = x² + y²

(x − y) (x − y) = x² -xy -xy +y² --> x² -2xy +y² = x² + y²

How you got it x² - xy + y² = x² + y²

where is the 2 in -2xy, although it will disappear in the next steps when we divide by -2, but I am just curious why it disappeared before, or maybe I am missing something..

Thank you.

## Good catch - thanks!!

Good catch - thanks!!

I have edited my solution here: https://gmatclub.com/forum/if-x-y-2-x-2-y-2-then-which-one-of-the-follow...

Cheers,

Brent

## Hi Brent, I have a question

Target question: is x>0

1. xy + y = y

I rearrange statement one to be x = (y-y)/y

Since any number minus itself is zero and since zero divided by any number is zero, the statement should never be greater than zero so I would conclude that statement one is sufficient. Why does this not work? I understand how you get two different answers by plugging in

(Case a: x = 1 and y = 0, x > 0

Case b: x = -1 and y = 0, x < 0 )

but I wouldn't have thought to plug in numbers for statement one if I would have first rearranged to get x = (y-y)/y

Thanks for your help,

Josh

## Great question, Josh!!

Great question, Josh!!

Question link: http://www.beatthegmat.com/kaplan-is-x-0-t288237.html

It all comes down to your statement "zero divided by any number is zero"

This is not entirely true. 0/0 does not equal zero. 0/0 is undefined.

So, when we take xy + y = y and subtract y from both sides to get xy = 0, we must be very careful about our next step.

Our next step CANNOT be to divide both sides by y, because we may be inadvertently dividing by 0 (if it's the case that y = 0).

So, at this point (xy = 0), we must make the conclusion that either x = 0 or y = 0.

Does that help?

Cheers,

Brent

## Thanks Brent, that clears it

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