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If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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10 Feb 2014, 00:30
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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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10 Feb 2014, 00:30



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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10 Feb 2014, 11:00
Bunuel wrote: If xy > 0, does (x  1)(y  1) = 1?
(1) x + y = xy (2) x = y
]
Sol: given xy> 0 means booths x and y are of same sign.let us solve the given expression we get xy (x+y) +1 St1: x+y=xy so putting these values in the exp we get xyxy+1 or1 so st 1 is sufficient St2 let's put these value in the statement so we get (y1)^2 or y^2+2y1=0 So if y=2 then yes expression equals 1 but if y=2 then no So st1 is sufficient therefore ans A 600 level is okay
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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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10 Feb 2014, 16:49
If xy > 0, does (x  1)(y  1) = 1? (1) x + y = xy (2) x = y xy>0 means that X =0 or y =0 The question ask us if \((x  1)(y  1) = 1\) Lets fix it up: \(xyxy1=1\) or \(xy=x+y\) St(1) is exacty it. Sufficient St tells us that x=y. Not helping us much. ans is A
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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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17 Feb 2014, 01:34



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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 >>> (21)*(21) = 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.



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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)(x2)=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 ? Posted from GMAT ToolKit



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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15 Jun 2015, 04:06



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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)(x2) = 0 so now we need to prove this to prove the question. So when x=2 or when x=0 then (x1)(y1)=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 ? Posted from GMAT ToolKit



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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15 Jun 2015, 04:20



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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15 Jun 2015, 04:36
Ah! Yes that makes more sense than the explanations above. Thanks so much. Posted from GMAT ToolKit



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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15 Jun 2015, 04:37



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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15 Jun 2015, 04:40
Indeed. Thanks again. Posted from GMAT ToolKit



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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16 Jun 2015, 10:18
If xy > 0, does (x  1)(y  1) = 1? One way to think of this is, are (x1) and (y1) reciprocals? If that is true, y  1 = 1/(x  1) (1) x + y = xy x = xy  y => x = y (x  1) => (x/(x1)) = y This can be plugged into the original equation: ( (x/(x1) )  1 = (1/(x  1) ) => multiply 1 by (x  1) to get a common denominator => (x  (x  1) )/ (x  1) =(1/(x1)) (x  x + 1)/(x  1) = (1/(x1)) 1/(x1) = 1/(x1) Sufficient. (2) x = y It's probably easier to try a number. For instance x = y = 8 y  1 = 81 = 7 1/(x  1) = 1/(8  1) = 1/7
But if x = y = 2 y  1 = 2  1 = 1 1/(x  1) = 1 (21) = 1 Not sufficient. A



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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 \((x1)(y1)=1\)? > is \(xyxy+1=1\)? 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 \(x(x2)=0\)? > 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.



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Re: If xy > 0, does (x  1)(y  1) = 1? [#permalink]
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13 Aug 2016, 04:11
asmitap wrote: 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 \((x1)(y1)=1\)? > is \(xyxy+1=1\)? 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 \(x(x2)=0\)? > 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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20 Feb 2018, 17:18
Bunuel wrote: If xy > 0, does (x  1)(y  1) = 1?
(1) x + y = xy (2) x = y
We can reexpress the question as: Does xy  x  y + 1 = 1 ? Does xy = x + y ? Statement One Alone: x + y = xy We see that statement one answers the question. Statement Two Alone: x = y Knowing that x = y, is not sufficient to answer the question. If x = y = 2, then (2  1)(2  1) = 1; however, if x = y = 1, then (1  1)(1  1) does not does equal 1. Answer: A
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