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by theCodeToGMAT » Fri Oct 18, 2013 11:00 am
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

[spoiler]{E}[/spoiler]
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by Brent@GMATPrepNow » Fri Oct 18, 2013 11:24 am
theCodeToGMAT wrote: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

[spoiler]{E}[/spoiler]
The key word here is must.

Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0

This tells us that z = 0 or x = 1
Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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