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

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If xy > 0, does (x-1)(y-1) = 1? (1) x + y = xy (2) x = y [#permalink]  14 Apr 2008, 12:47
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If xy > 0, does (x-1)(y-1) = 1?

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

So I got this one wrong, but would like to find out where I went wrong. I'll give you folks some time to show your approaches.
Manager
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Re: OG 11 Quant Review DS 80 [#permalink]  14 Apr 2008, 15:21
The answer I got is A.

(x-1)(y-1) = xy-(x+y)+1. Since from stat 1 x+y = xy, then (x-1)(x+1)=1
Senior Manager
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Re: OG 11 Quant Review DS 80 [#permalink]  14 Apr 2008, 16:01
Did same approach mentioned above.

plugged some numeric values for stmt 2

xy - (x+y) +1 = 1 for x = y = 2
while it does not hold for 3.
Manager
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Re: OG 11 Quant Review DS 80 [#permalink]  14 Apr 2008, 16:03
Stat1: xy - (x+y) + 1 = xy - xy + 1 = 1

Stat2: (x-1)*(y-1) becomes (x-1)*(x-1) so x (and y) can be any number other than 0 and satisfy the xy>0 statement, but only 2 (and 0, which we just counted out) satisfy (x-1)*(y-1)=1... thus, Stat2 is out.

Stat1 [A]
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SVP
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Re: OG 11 Quant Review DS 80 [#permalink]  14 Apr 2008, 16:29
ok, cool. youre all on the right track so far. but here is my question:

i simplified the stem down to asking if xy-x-y=0

i see from statement 1 that its suffcient.

now, for statement 2, i subbed in x=y to get y^2-2y=0 --> y(y-2)=0

so for that to be true, either y is 0 or y is 2. now we are told that xy>0, so y cannot be 0. Therefore, y must be 2, and (x-1)(y-1) = (2-1)(2-1) = 1*1 = 1

why isnt that approach for statement 2 correct ?
Senior Manager
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Re: OG 11 Quant Review DS 80 [#permalink]  14 Apr 2008, 17:33
pmenon,

your approach did confuse me at first.

the answer is....you are restricting value of x to be 0 or 2 to satisfy the equality of question stem, one they are asking if can be true.

stem 2 says x=y doesnt restrict valu of x in any way..

Not sure above makes sense...there sure is easier explanation
SVP
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Re: OG 11 Quant Review DS 80 [#permalink]  15 Apr 2008, 02:22
well according to the question, xy>0, so we have to take into account when both the variables are negative and when both the variables are positive for statement 2:

xy = x + y

if both x and y are positive, then:

x^2 = 2x

x^2 - 2x = 0

x(x-2) = 0

so x could be 0 or 2, but because none of the variables is suppose to be 0, then x is 2

if both x and y are negative, then:

x^2 = -2x

x^2 + 2x = 0

x(x+2) = 0

so x could be 0 or -2, but because none of the variables is suppose to be 0, then x is -2.

so statement 2 is not suff. Also, because we already found statement 1 to be suff., the answer should be A.
CEO
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Re: OG 11 Quant Review DS 80 [#permalink]  16 Apr 2008, 21:11
Agree with A - similar method to first poster.
Re: OG 11 Quant Review DS 80   [#permalink] 16 Apr 2008, 21:11
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