gmatusa2010 wrote:If xy > o, does (x-1)(y-1) = 1?
1. x+y = xy
2. x = y
Is there a way to do this without expanding (x-1)(y-1)?
I didn't immediately see that x+y=xy is the same thing. I was actually distracted by xy>0. Is there a way to use xy>0?
In this question, statement 1 is more than sufficient. If we have statement 1 available, we don't need any extra information to say that (x - 1)(y - 1) = 1. Because,
.... x + y = xy
=> xy - x - y = 0
=> xy - x - y + 1 = 1
=> (x - 1)(y - 1) = 1
Thus if (x + y) = xy, it implies that (x - 1)(y - 1) is always equal to 1. Even for x = 0, y = 0. As the question doesn't ask for the possible values of x and y, the information xy > 0 is useless for statement 1.
shovan85 wrote:1. x+y = xy
This will happen only when x = y = 0 OR x = y = 2
The reason xy>0 is given so that you can not select x = y = 0
Nowhere it is mentioned x and y are integers.
Take x = 3 and y = 3/2 => (x + y) = xy
Take x = 4 and y = 4/3 => (x + y) = xy
Take x = 10 and y = 10/9 => (x + y) = xy
In fact if (x + y) = xy, then rearranging terms results y = x/(x - 1). For any value of x (except x = 1), there exists a value y for which statement 2 satisfies.
And another point the question doesn't ask for possible value of x and y. Thus there is no point whether we can select x = y = 0 or not.
