OG 2nd ed # 83

[joshua868]

If xy is greater than 0, does (x-1)(y-1)=1?

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

Can someone explain to me why stat 2 is not sufficient? thanks!

[Frankenstein]

Hi,
We need to check: Is (x-1)(y-1)=1 =>xy-x-y+1=1 =>xy=x+y
So, in essence we ened to check: Is xy = x+y?
From(1): It is clear
sufficient
From(2)x=y
So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient

Hence, A

[joshua868]

"So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient "

@Frankenstein I'm still kind of lost
so if x^2=2x does that mean that x=0 or X=2

[djiddish98]

(x-1)(y-1) = 1?

Statement 2 says x=y. However, x and y could be any number (3,20,-1/2), so we're not sure if it's 1.

[Brent@GMATPrepNow]

If xy is greater than 0, does (x-1)(y-1)=1?

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

Can someone explain to me why stat 2 is not sufficient? thanks!

I like how Frankenstein rewrote the target question as "Is xy = x+y?"

Statement 1
When we examine statement 1, it is clear that xy does, indeed, equal x+y

Statement 2
If x=y, then when we replace y with x in the target question, we get "Is x(x) = x+(x)?"
In other words, Is x^2 = 2x?
Well, x^2 could equal 2x if x=2 or x=0
But, x^2 doesn't equal 2x for all other values of x

Since we can't answer the target question with certainty, statement 2 is insufficient.

[Frankenstein]

"So, we need to check if x.x=x+x i.e., x^2=2x?
Not sufficient "

@Frankenstein I'm still kind of lost
so if x^2=2x does that mean that x=0 or X=2

Hi,
To check whether x^2=2x, we need to know the value of x.We do not know the value of x. So, we cannot surely say if that equality holds or not.

[joshua868]

oh okay..Thanks