Are we really sure? XY>0 issue

[matteomasciotti]

Hi guys,
I came across this easy DS problem on the Official Gmat Quant. Review, #80.
it states the following:

if xy>0 is (x-1)(y-1)=1?

1)x+y=xy
2)x=y

I'am not going to go through the first statement,but rather, I would like to draw your attention towards statement number 2.

if x=y , then the expression (x-1)(y-1)=1 can be written in this way:
xy-y-x+1=1
substituing x with y we get:
y^2-2y=0 (which is the same result showed at the end of the book)

Now, the solution at the back tells us that, since y^2-2y=0 has not gotten only one solution we can't tell whether (x-1)(y-1) is equal to 1. but ...are we really sure?
If we solve for y the equation y^2-2y=0 we can have two solutions, either y is 0 or y is 2.
Fine..but the initial statement tells us that XY>0 which means that y could not be 0, and therefore, in my humple opinion, y can only be 2, hence, if y=2 then (x-1)(y-1) is actually equal to 1.
But ..unfortunately this is not the case...why is my assumption flawed?

[Jim@StratusPrep]

Take a step back. You are using the question. To prove itself right. If x=y they can be any set of values, all of which. (Except 2) do not give you 1 for the statement in question.

[hemant_rajput]

Sometimes substituting the number into the equation is the quick and easy way to verify your approach. It so happen in GMAT question that you come to a conclusion after some deduction and inferences, but if we go the beginning and take other approach now our conclusion will be false.

for ex :- if we put 3 for both x and y , we'll find that it is not equal to 2. here we got one more answer so we can not say for sure about this approach.

Hope it make it more clear.

[matteomasciotti]

Yeah sorry...I made it too complicated

[ceilidh.erickson]

On any DS question, the best approach is to simplify the question as much as possible before looking at the statements.

(x - 1)(y - 1) = 1 ?
xy - x - y + 1 = 1 ?
xy - x - y = 0 ?
xy = x + y ?

This is the most simplified version of our question - does xy equal x + y? If we simplify the question, we can see that statement (1) answers it exactly, so that's sufficient.

With statement (2), does knowing that x and y are equal tell us whether xy equals x + y? Well, does x^2 always equal 2x? Only if x (and therefore y) is equal to 2 or 0. You were doing the right math, but not asking yourself the right question! It's a really common mistake to treat the question as the thing you know, rather than the thing you're wondering.

This may seem overly simplistic, but I find that it's really helpful to keep a question mark attached to the question in your own notes. That way it's clear that it's something you're wondering, not something you know! Simplifying the question as much as possible will make it all the more clear.

[matteomasciotti]

Thanks a lot Ceilidh. I found your suggestion very helpful. It is a very common mistake I make, I take the question as an answer...

[Brent@GMATPrepNow]

On any DS question, the best approach is to simplify the question as much as possible before looking at the statements.

I wholeheartedly agree!

If anyone would like to learn more about rephrasing the target question, we have a free video on this topic: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100

Cheers,
Brent