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

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Manager
Joined: 21 Sep 2006
Posts: 110

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Location: Where you mind is
If xy + z = x(y+z), which of the following must be true? A. [#permalink]

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23 Dec 2007, 21:47
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

Thanks.

Kudos [?]: 21 [0], given: 0

Manager
Joined: 01 Sep 2007
Posts: 98

Kudos [?]: 32 [0], given: 0

Location: Astana

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23 Dec 2007, 21:53
hi there

xy+z=xy+xz =>

z = xz

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

Kudos [?]: 32 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1545

Kudos [?]: 179 [0], given: 2

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25 Dec 2007, 10:16
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

Kudos [?]: 179 [0], given: 2

25 Dec 2007, 10:16
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