If xy 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y

Question

If xy > 0, does (x – 1)(y – 1) = 2 ? 
 
(1) x + y = –1
(2) x = y

Bunuel · Accepted Answer

The OA is under the spoiler in the original post and it's A.

If xy > 0, does (x – 1)(y – 1) = 2 ?

Does (x – 1)(y – 1) = 2 ?
Does xy - x - y + 1 = 2?
Does xy - x - y = 1?
Does xy - (x + y) = 1?

(1) x + y = –1. Substitute into the question: does xy + 1 = 1? Or: does xy = 0? We are given that xy > 0, so the answer to the question is NO. Sufficient.

(2) x = y. Substitute into the original question: does (x – 1)^2 = 2 ? Does  x – 1=+/-\sqrt{2} ? Does  x=1+/-\sqrt{2} ? We don't know that. Not sufficient.

Answer: A.

GMATinsight · Answer

Question  : does (x – 1)(y – 1) = 2 ?   
   Question  : does xy - (x+y) +1 = 2 ?   
   Question  : does xy - (x+y) = 1 ?

Statement 1 : x+y = -1

but we dont know about xy hence
NOT SUFFICIENT

Statement 2 : x = y 
but we dont know about value of x hence
NOT SUFFICIENT

Combining the two statements
x = y = -1/2
SUFFICIENT

Answer: Option C

elainetianfong · Answer

(x – 1)(y – 1) = 2
=> xy - x - y -1 = 0
=> xy = 1 +x +y
So the question basically is whether xy = 1 +x +y
 
(1) x + y = –1 
=> xy = 0 (which will not happen as xy >0)
Sufficient
 
(2) x = y 
=> x^2 = 1 + 2x
=> x^2 - 2x -1 = 0
=> We surely can find 2 values of x that satisfies above equation.
So, it depends on x and y that the condition is met or not.
Insufficient.

So A is the answer

RicAssassin · Answer

D

Not sure if the solution is correct, but here is how I did it:

(1) Solving for the equation:
1 + xy - (x+y) = 2, this comes out to be xy=0 which doesn't confirm with the given situation. Hence,

SUFFICIENT

2) putting x=y in the given, we get x=y= 1+ sqrt 2 or 1-sqrt 2. Both give you 2 as an answer.

SUFFICIENT

Hence, D.

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Amirfunc · Answer

@Bunuel- Again different answers here, could you provide the correct answer?

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If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y

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