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

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Math Expert
Joined: 02 Sep 2009
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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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02 Oct 2017, 22:52
Expert's post
3
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Difficulty:

85% (hard)

Question Stats:

24% (00:59) correct 76% (01:54) wrong based on 38 sessions

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If xy > 0, does (x – 1)(y – 1) = 2 ?

(1) x + y = –1
(2) x = y
[Reveal] Spoiler: OA

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Kudos [?]: 135771 [0], given: 12708

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Joined: 08 Jul 2010
Posts: 1857

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

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02 Oct 2017, 23:24
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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

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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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14 Oct 2017, 19:35
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.

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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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14 Oct 2017, 22:49
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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15 Oct 2017, 19:32

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Math Expert
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Posts: 42618

Kudos [?]: 135771 [1], given: 12708

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

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15 Oct 2017, 22:18
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Expert's post
Amerendra wrote:

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.

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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, 22:18
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