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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]

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19 Aug 2007, 08:45
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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=0
d. x=1 and y=0
e. x=1 and z=0
Senior Manager
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19 Aug 2007, 08:51
well, xy+z=x(y+z)
xy+z=xy+xz
z-xz=0
z(1-x)=0
z=0; x=1

VP
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19 Aug 2007, 09:00
Piter 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=0
d. x=1 and y=0
e. x=1 and z=0

It looks complicated, only thing u need is simplifying the equation.
xy+z=x(y+z)
xy+z=xy+xz
xy+z-xy-xz=0
z-xz=0
z(1-x)=0
z=0 and x=1

E
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19 Aug 2007, 09:55
I believe this question is worded incorrectly... some of the answer choices should say OR not AND.

But, yes, straight E on this one.
19 Aug 2007, 09:55
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# if xy+z=x(y+z), which of the following must be true? a.

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