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

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by BTGModeratorVI » Thu Dec 03, 2020 2:48 pm
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If xy + z = x(y + z), which of the following must be true?

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

Answer: E
Source: Official guide
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Re: If xy + z = x(y + z), which of the following must be true?

by Scott@TargetTestPrep » Sun Dec 06, 2020 8:58 am
BTGModeratorVI wrote: ↑
Thu Dec 03, 2020 2:48 pm
 If xy + z = x(y + z), which of the following must be true?

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

Answer: E
Source: Official guide
Solution:

Simplifying, we have:

xy + z = xy + xz

z = xz

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1

Answer: E

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