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

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Status: Preparing for GMAT; want to join MBA program in fall 2012
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Location: Sioux Falls, SD, USA
Schools: Tippie School of Management, University of Iowa, Iowa City
If xy > 0, does (x-1)(y-1) = 1? [#permalink]

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03 Dec 2010, 22:47
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If xy > 0, does (x-1)(y-1) = 1?

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

[Reveal] Spoiler:
I choose the answer D, but OG says option 2 is not sufficient. Could you please let me know where I am going wrong?

OG Explanation: (2) Substituting y for x in (x-1)(y-1) = 1 gives (y-1)(y-1) = 1 or thus only that y2-2y+1 = 1; this cannot be solved uniquely for y; NOT sufficient.

I was able to solve this as,
y2-2y+1 = 1
y(y-2)=0 --by subtracting 1 from both sides.

Implies y=0 or y-2 = 0
Given xy > 0, which implies neither x or y not equal to 0. Therefore y = 0 is not possible.
Thus y-2 = 0; y = 2. Thus I think option 2 is sufficient.
[Reveal] Spoiler: OA

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Abel

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Re: Quantitative review - Official guide - DS Question 80 - help [#permalink]

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04 Dec 2010, 02:56
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abelnazareth wrote:
I choose the answer D, but OG says option 2 is not sufficient. Could you please let me know where I am going wrong?

80. If xy > 0, does (x-1)(y-1) = 1?
(1) x + y = xy
(2) x = y

OG Explanation: (2) Substituting y for x in (x-1)(y-1) = 1 gives (y-1)(y-1) = 1 or thus only that y2-2y+1 = 1; this cannot be solved uniquely for y; NOT sufficient.

I was able to solve this as,
y2-2y+1 = 1
y(y-2)=0 --by subtracting 1 from both sides.

Implies y=0 or y-2 = 0
Given xy > 0, which implies neither x or y not equal to 0. Therefore y = 0 is not possible.
Thus y-2 = 0; y = 2. Thus I think option 2 is sufficient.

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

$$xy>0$$ means that either both $$x$$ and $$y$$ are positive or both are negative (so neither of unknowns equals to zero: $$x\neq{0}$$ and $$y\neq{0}$$).

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 $$x=2$$? --> as given that $$x\neq{0}$$, then the question becomes is $$x=2$$? We don't know that (or in other words for $$x=y$$ and $$xy>0$$ equation $$(x-1)(y-1)=1$$ holds true for $$x=y=2$$, but we don't know whether that's true, thus we can answer whether $$(x-1)(y-1)=1$$ holds true), hence this statement is not sufficient.

P.S.
 ! Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/No posting of PS/DS questions is allowed in the main Math forum.

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Re: Quantitative review - Official guide - DS Question 80 - help [#permalink]

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05 Dec 2010, 21:40
Statement 2 says x=y
If x*y>0 & x=y
x*y could be (-2)*(-2)=4 or 2*2=4

x*y=x+y
-2*-2=-2+-2
4 = -4 . so x*y=x+y

if x*y=x+y
2*2=2+2
4=4. so x*y=x+y
two different answers , so statement 2 is insufficient

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

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19 May 2015, 08:01
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Re: If xy > 0, does (x-1)(y-1) = 1? [#permalink]

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19 Sep 2016, 07:17
A is correct. Here's why:

(1) x+y = xy --> Plug into main equation

xy-x-y+1 = 1
xy -x-y = 0
x+y-x-y = 0
0 = 0

SUFFICIENT

(2) x=y --> Rewrite as (y-1)^2 = 1 --> (y-1) = +/- 1

NOT SUFFICIENT

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Re: If xy > 0, does (x-1)(y-1) = 1?   [#permalink] 19 Sep 2016, 07:17
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