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# If xy+z=x(y+z), which of the following must be true? 1)

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Senior Manager
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If xy+z=x(y+z), which of the following must be true? 1) [#permalink]

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04 Jul 2006, 02:10
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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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SVP
Joined: 30 Mar 2006
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04 Jul 2006, 02:55
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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Manager
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04 Jul 2006, 04:56
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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Intern
Joined: 05 Nov 2005
Posts: 33

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Location: London

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04 Jul 2006, 05:02
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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VP
Joined: 25 Nov 2004
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04 Jul 2006, 07:33
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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Intern
Joined: 23 Jun 2006
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04 Jul 2006, 09:12
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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Senior Manager
Joined: 08 Jun 2004
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04 Jul 2006, 23:49
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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Intern
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13 Jul 2006, 22:22
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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GMAT Club Legend
Joined: 07 Jul 2004
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13 Jul 2006, 23:34
xy+z = x(y+z)
xy+z = xy+xz
z-xz = 0
z(1-x) = 0

z = 0, x = 1

Kudos [?]: 457 [0], given: 0

13 Jul 2006, 23:34
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