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

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Intern
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 129 [0], given: 6

If xy > 0, does (x – 1)(y – 1) = 1? (1) x + y = xy (2) x = y [#permalink]  23 Feb 2012, 23:33
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Difficulty:

45% (medium)

Question Stats:

65% (01:35) correct 35% (00:46) wrong based on 23 sessions
If xy > 0, does (x – 1)(y – 1) = 1?

(1) x + y = xy

(2) x = y
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27237
Followers: 4236

Kudos [?]: 41138 [1] , given: 5672

Re: does (x – 1)(y – 1) = 1? [#permalink]  23 Feb 2012, 23:38
1
This post received
KUDOS
Expert's post
BANON wrote:
If xy > 0, does (x – 1)(y – 1) = 1?

(1) x + y = xy

(2) x = y

If $$xy>0$$ does $$(x-1)(y-1)=1$$?

Question: is $$(x-1)(y-1)=1$$? --> is $$xy-x-y+1=1$$? is $$x+y=xy$$?

(1) $$x+y=xy$$ --> directly gives us the answer YES. Sufficient.

(2) $$x=y$$ --> question becomes: is $$x+x=x^2$$? --> is $$x(x-2)=0$$? --> is $$x=0$$ or $$x=2$$? --> since given that $$xy>0$$, then $$x\neq{0}$$, so the question becomes is $$x=2$$? We don't know that, hence this statement is not sufficient.

Answer: A.

Hope it's clear.
_________________
Intern
Joined: 20 Feb 2012
Posts: 41
Followers: 1

Kudos [?]: 129 [0], given: 6

Re: does (x – 1)(y – 1) = 1? [#permalink]  24 Feb 2012, 00:03
thank u BUNUEL for ur instant reply's

after ur explanation's they all seem like sub par questions.
Re: does (x – 1)(y – 1) = 1?   [#permalink] 24 Feb 2012, 00:03
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# If xy > 0, does (x – 1)(y – 1) = 1? (1) x + y = xy (2) x = y

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