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

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Senior Manager
Joined: 08 Jun 2004
Posts: 499
Location: Europe
Followers: 1

Kudos [?]: 20 [0], given: 0

If xy+z=x(y+z), which of the following must be true? 1) [#permalink]  04 Jul 2006, 02:10
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 3 sessions
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.
SVP
Joined: 30 Mar 2006
Posts: 1739
Followers: 1

Kudos [?]: 45 [0], given: 0

Re: PS: xy+z=x(y+z) [#permalink]  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?
Manager
Joined: 12 Apr 2006
Posts: 218
Location: India
Followers: 1

Kudos [?]: 24 [0], given: 17

xy+z=x(y+z) => xy+z=xy+xz => xz - z = 0

=> z(x-1) = 0 => z=0, x=1

Hence 5
Intern
Joined: 05 Nov 2005
Posts: 33
Location: London
Followers: 0

Kudos [?]: 1 [0], given: 0

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

VP
Joined: 25 Nov 2004
Posts: 1495
Followers: 6

Kudos [?]: 38 [0], given: 0

Re: PS: xy+z=x(y+z) [#permalink]  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.
Intern
Joined: 23 Jun 2006
Posts: 26
Followers: 0

Kudos [?]: 3 [0], given: 0

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
Senior Manager
Joined: 08 Jun 2004
Posts: 499
Location: Europe
Followers: 1

Kudos [?]: 20 [0], given: 0

OA is 'E'.
But I was really stuck between A and E guys. What do you think about 'A'?
This is GMATPrep question.
Intern
Joined: 13 Jul 2006
Posts: 1
Followers: 0

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

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!
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5078
Location: Singapore
Followers: 22

Kudos [?]: 184 [0], given: 0

xy+z = x(y+z)
xy+z = xy+xz
z-xz = 0
z(1-x) = 0

z = 0, x = 1
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