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

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Manager
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If xy + z = x(y+z), which of the following must be true? A. [#permalink] New post 23 Dec 2007, 20:47
If xy + z = x(y+z), which of the following must be true?

A. x = 0, z = 0
B. x = 1, y = 1
C. y = 1, z = 0
D. x = 1, y = 0
E. x = 1, z = 0

What I did was:

Step 1: xy + z = xy + xz

Step 2: Substitute the values in the answer options to see which one gives equal values. But the problem was, i found 3 such answers!

B: 1 + z = 1 + z
D: z = z
E: y = y

The OA is E. Can you guys please help to explain this?

Thanks.
Manager
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 [#permalink] New post 23 Dec 2007, 20:53
hi there

xy+z=xy+xz =>

z = xz

z- xz=0
z(1-x)=0
z=0, x=1
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 [#permalink] New post 25 Dec 2007, 09:16
expand and rearranging the given equation gives you:

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

the only way for that to be true is for one of the terms to be zero, namely, either z=0 or 1-x=0, i.e. x=1.

Option E states this
  [#permalink] 25 Dec 2007, 09:16
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If xy + z = x(y+z), which of the following must be true? A.

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