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# If xy+z=x(y+z), which of the following must be true? A) x=0

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Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 4 [0], given: 0

If xy+z=x(y+z), which of the following must be true? A) x=0 [#permalink]  19 Dec 2005, 16:06
If xy+z=x(y+z), which of the following must be true?

A) x=0 and z=0
B) x=1 and y=1
C) y=1 and z=1
D) x=1 or y=0
E) x=1 or z=0

From the equation...I feel we have the following possibilities:

x=0, y=0, z=0
x=1, y=1, z=1
x=1, y=0, z=1
x=1, y=1, z=0

Why is E right and D is wrong?
Senior Manager
Joined: 05 Oct 2005
Posts: 485
Followers: 1

Kudos [?]: 2 [0], given: 0

Re: Which of the following must be true? [#permalink]  19 Dec 2005, 16:11
ellisje22 wrote:
If xy+z=x(y+z), which of the following must be true?

A) x=0 and z=0
B) x=1 and y=1
C) y=1 and z=1
D) x=1 or y=0
E) x=1 or z=0

From the equation...I feel we have the following possibilities:

x=0, y=0, z=0
x=1, y=1, z=1
x=1, y=0, z=1
x=1, y=1, z=0

Why is E right and D is wrong?

xy+z = x(y+z)..... xy+z = xy+xz..... the xy's cancel each other..... z=xz ..... x=1 makes this true (z=z) for any value of z, and z=0 makes this true for any value of x (0=0).
Hence, E.

Hope this helps
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5077
Location: Singapore
Followers: 22

Kudos [?]: 186 [0], given: 0

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

So either z is 0 or x = 1

Ans: E
Manager
Joined: 13 Dec 2005
Posts: 64
Followers: 1

Kudos [?]: 4 [0], given: 0

Thanks [#permalink]  19 Dec 2005, 19:25
Thanks! I wasn't sure what the question was really asking but now I get it. Basically they are saying for EVERY single value you could plug into the third variable, which of the values for the first two (which they give in the answer) will ALWAYS hold true.
Senior Manager
Joined: 14 Apr 2005
Posts: 418
Location: India, Chennai
Followers: 1

Kudos [?]: 6 [0], given: 0

Re: Which of the following must be true? [#permalink]  20 Dec 2005, 04:10
ellisje22 wrote:
If xy+z=x(y+z), which of the following must be true?

A) x=0 and z=0
B) x=1 and y=1
C) y=1 and z=1
D) x=1 or y=0
E) x=1 or z=0

Why is E right and D is wrong?

xy +z = xy + xz
z = xz
or z - xz = 0
or z(1-X) = 0 => Z = 0 or 1-X = 0
=> Z = 0 or X = 1 Which is E.
Senior Manager
Joined: 11 Nov 2005
Posts: 330
Location: London
Followers: 1

Kudos [?]: 8 [0], given: 0

One more for E,

Same reasoning

XY+Z= XY+XZ

z=xz

z-xz = 0
z(1-x) =0

z= 0 or x=1
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