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

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

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New post 02 Oct 2017, 23:52
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A
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C
D
E

Difficulty:

  85% (hard)

Question Stats:

27% (01:00) correct 73% (01:33) wrong based on 30 sessions

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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y [#permalink]

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New post 03 Oct 2017, 00:24
Bunuel wrote:
If xy > 0, does (x – 1)(y – 1) = 2 ?

(1) x + y = –1
(2) x = y


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
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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y [#permalink]

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New post 14 Oct 2017, 20:35
Bunuel wrote:
If xy > 0, does (x – 1)(y – 1) = 2 ?

(1) x + y = –1
(2) x = y


(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

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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y [#permalink]

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New post 14 Oct 2017, 23:49
Bunuel wrote:
If xy > 0, does (x – 1)(y – 1) = 2 ?

(1) x + y = –1
(2) x = y


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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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y [#permalink]

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New post 15 Oct 2017, 20:32
@Bunuel- Again different answers here, could you provide the correct answer?

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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y [#permalink]

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New post 15 Oct 2017, 23:18
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Amerendra wrote:
@Bunuel- Again different answers here, could you provide the correct 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.
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Re: If xy > 0, does (x – 1)(y – 1) = 2 ? (1) x + y = –1 (2) x = y   [#permalink] 15 Oct 2017, 23:18
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