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Which of the following must be true for an equation?

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by Brent@GMATPrepNow » Wed Aug 07, 2013 8:04 pm
rkbsaggi 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 or y = 0
e. x = 1 or z = 0

Can you please guide me on how to systematically approach such questions?
The key word here is must.
So, for example, consider answer choice A. While it's possible that x = 0 and z = 0, it need not be the case.
For example, x=1, y=1 and z=1 is a solution to the equation. So, this eliminates A.

The solution . . .
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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