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Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

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\(xy>0\) 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 YES answer to the question. 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, hence this statement is not sufficient.

\(xy>0\) 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 YES answer to the question. 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, hence this statement is not sufficient.

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

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14 Jan 2015, 05:13

stm11: x+y=xy; substitute x and y as 2 & 2 ; then the equation satisfies the stmt1 ------>>>2+2=2*2; and also the main equation -------->>> (2-1)*(2-1) = 1; Hence Sufficient;

Stmt2: there are many values that satisfy the equation X=Y , but do not satisfy the equation (x - 1)(y - 1) = 1. Hence Insufficient.

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

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15 Jun 2015, 04:02

Statement one is easy enough

However statement two results in (X)(x-2)=0 so x=0 or x=2. However x cannot be zero due to the xy>0 statement. Why is statement two not sufficient then ?

However statement two results in (X)(x-2)=0 so x=0 or x=2. However x cannot be zero due to the xy>0 statement. Why is statement two not sufficient then ?

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

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15 Jun 2015, 04:15

Yes so you got x^2=2x -> (x)(x-2) = 0 so now we need to prove this to prove the question. So when x=2 or when x=0 then (x-1)(y-1)=1 ... However we have two results and it is on this ground that it is eliminated as not sufficient. I am asking whether the statement xy>0 does not eliminate x=0 as a possible answe leaving only x=2 and this making statement two sufficient ?

Yes so you got x^2=2x -> (x)(x-2) = 0 so now we need to prove this to prove the question. So when x=2 or when x=0 then (x-1)(y-1)=1 ... However we have two results and it is on this ground that it is eliminated as not sufficient. I am asking whether the statement xy>0 does not eliminate x=0 as a possible answe leaving only x=2 and this making statement two 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, hence this statement is not sufficient.
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Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

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16 Jun 2015, 10:18

1

This post received KUDOS

If xy > 0, does (x - 1)(y - 1) = 1? One way to think of this is, are (x-1) and (y-1) reciprocals? If that is true, y - 1 = 1/(x - 1) (1) x + y = xy x = xy - y => x = y (x - 1) => (x/(x-1)) = y This can be plugged into the original equation: ( (x/(x-1) ) - 1 = (1/(x - 1) ) => multiply 1 by (x - 1) to get a common denominator => (x - (x - 1) )/ (x - 1) =(1/(x-1)) (x - x + 1)/(x - 1) = (1/(x-1)) 1/(x-1) = 1/(x-1) Sufficient. (2) x = y It's probably easier to try a number. For instance x = y = 8 y - 1 = 8-1 = 7 1/(x - 1) = 1/(8 - 1) = 1/7

But if x = y = 2 y - 1 = 2 - 1 = 1 1/(x - 1) = 1 (2-1) = 1 Not sufficient. A

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

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12 Aug 2016, 02:25

Hello from the GMAT Club BumpBot!

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

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13 Aug 2016, 04:08

Bunuel wrote:

SOLUTION

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

\(xy>0\) 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 YES answer to the question. 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, hence this statement is not sufficient.

Answer: A.

hi Bunnel. i don't understand why statement 2 is not sufficient. From x^2 = 2x we get x=2. Why are we considering x=0 or x=2? On substituting x=2, it satisfies the question stem. Please help.

\(xy>0\) 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 YES answer to the question. 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, hence this statement is not sufficient.

Answer: A.

hi Bunnel. i don't understand why statement 2 is not sufficient. From x^2 = 2x we get x=2. Why are we considering x=0 or x=2? On substituting x=2, it satisfies the question stem. Please help.

Two solutions satisfy x^2 = 2x, x=0 and x=2.
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Re: If xy > 0, does (x - 1)(y - 1) = 1? [#permalink]

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01 Sep 2017, 08:13

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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