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If xy+z=x(y+z), which of the following must be true? 1) [#permalink]
 04 Jul 2006, 03:10
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If xy+z=x(y+z), which of the following must be true?
1) x=0, z=0
2) x=1, y=1
3) y=1, z=0
4) x=1, y=0
5) x=1, z=0
OA will follow.
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Re: PS: xy+z=x(y+z) [#permalink]
04 Jul 2006, 03:55
M8 wrote: If xy+z=x(y+z), which of the following must be true?
1) x=0, z=0
2) x=1, y=1
3) y=1, z=0
4) x=1, y=0
5) x=1, z=0
OA will follow.
4 ?
Am I wrong or does all the values satisfy?
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xy+z=x(y+z) => xy+z=xy+xz => xz - z = 0
=> z(x-1) = 0 => z=0, x=1
Hence 5
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xy + z = xy + xz
xy 's cancel out
z = xz
xz - z = 0
z(x-1) = 0
z = 0, x = 1
(5)
_________________
I am only one; but I am still one. I cannot do everything, but still I can do something. I will not refuse to do the something I can do.
- Helen Keller
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Re: PS: xy+z=x(y+z) [#permalink]
04 Jul 2006, 08:33
M8 wrote: If xy+z=x(y+z), which of the following must be true?
1) x=0, z=0
2) x=1, y=1
3) y=1, z=0
4) x=1, y=0
5) x=1, z=0
OA will follow.
xy + z = x (y + z)
xy + z = xy + xz
z = xz
xz - z = 0
z (x - 1) = 0
z = 0, x = 1
arrived at E.
however any value for x and y with z = 0 satisfy the eq xy + z = x (y + z). therefore, the question is not properly structured. 
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I don't think this question was written accurately.
You can deduce the equation to:
xy+ z = xy + xz --> thus y cancels out and its value doesn't matter
z = xz --> thus it only matters that x must equal 1, if that is true z can have any value
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Director
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OA is 'E'.
But I was really stuck between A and E guys. What do you think about 'A'?
This is GMATPrep question.
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z=xz -> x = 1
z can be anything
let's try x=1, y=1, z=1
xy+z = x(y+z)
(1)(1) + 1 = 1 (1+1)
2=2 .... z doesn't have to equal 0
This question is poorly written!
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xy+z = x(y+z)
xy+z = xy+xz
z-xz = 0
z(1-x) = 0
z = 0, x = 1
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