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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
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If xy+z=x(y+z), which of the following must be true? A) x=0 [#permalink] New post 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
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Re: Which of the following must be true? [#permalink] New post 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
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 [#permalink] New post 19 Dec 2005, 19:00
xy+z = xy+xz
z = xz
z(1-x)=0

So either z is 0 or x = 1

Ans: E
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Thanks [#permalink] New post 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
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Re: Which of the following must be true? [#permalink] New post 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
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 [#permalink] New post 20 Dec 2005, 15:35
One more for E,


Same reasoning

XY+Z= XY+XZ

z=xz

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

z= 0 or x=1
  [#permalink] 20 Dec 2005, 15:35
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