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If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
 23 May 2012, 01:57
Question Stats:
36% (02:42) correct
63% (01:26) wrong based on 49 sessions
If x and y are integers and 4xy = x^2*y+4y, what is the value of xy? (1) y-x = 2 (2) x^3 <0 what I did : 4xy = x^2y+4y 4x = x^2+4 x^2-4x+4 = 0 (x-2)^2=0 x = 2 is this wrong?
Last edited by Bunuel on 23 May 2012, 02:15, edited 1 time in total.
Edited the OA
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
23 May 2012, 02:14
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kashishh wrote: If x and y are integers and 4xy = x^2*y+4y, what is the value of xy?
(1) y-x = 2
(2) x^3 <0
what I did : 4xy = x^2y+4y
4x = x^2+4
x^2-4x+4 = 0
(x-2)^2=0
x = 2
is this wrong? You cannot divide 4xy=x^2y+4y by y and write 4x=x^2+4, because y can be zero and division be zero is not allowed. Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero. So when you divide by y you assume, with no ground for it, that y does not equal to zero thus exclude a possible solution. If x and y are integers and 4xy = x^2*y+4y, what is the value of xy?4xy=x^2*y+4y --> x^2*y-4xy+4y=0 --> y(x^2-4x+4)=0 --> y(x-2)^2=0 --> either x=2 or y=0 (or both). (1) y-x = 2 --> if x=2 then y=4 and xy=8 but if y=0 then x=-2 and xy = 0. Not sufficient. (2) x^3<0 --> x<0, so x\neq{2} which means that y must equal to zero --> xy=0. Sufficient. Answer: B. Hope it's clear.
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
25 May 2012, 19:15
thanks bunuel. Its a common error to 'cancel' y on both sides. I fell prey to the same mistake.
However, just to clarify, basically when x = 2 then y can take any value and when y=0 x can take any value. In either case xy=0?
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
26 May 2012, 02:42
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
26 May 2012, 07:09
Bunuel wrote:
If x=2 then y can take any value - TRUE. In this case xy=0 only if y=0 but for any other possible value of y xy does not equal to zero (for example consider x=2 and y=1).
Just by looking at this equation y(x^2 -4x+4) = 0 either the quadratic term has to equal 0, in which case x=2, or y has to equal to zero. In which scenario will y =1 and x=2 occur?
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
28 May 2012, 05:26
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Re: If x and y are integers and 4xy = x^2*y+4y, what is the [#permalink]
31 May 2012, 20:55
Made silly mistake.... I thought using stmt 1 - xy always comes to be 0...
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If x and y are integers and 4xy = x^2y + 4y, what is the value of xy?
(1) y–x = 2
(2) x3 < 0
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