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Algebra

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by BTGmoderatorRO » Fri Dec 29, 2017 8:45 am
If XY + Z = X(Y+Z), then 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
OA is E

Can the value of X and Z be Zero? An Expert should pls analyse the correct answer. Thanks in anticipation.
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by Brent@GMATPrepNow » Fri Dec 29, 2017 8:48 am
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
B. y = 1 and z = 0
D. x = 1 or y = 0
E. x = 1 or Z = 0
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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by Scott@TargetTestPrep » Mon Sep 02, 2019 6:31 pm
BTGmoderatorRO wrote:If XY + Z = X(Y+Z), then 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
OA is E

Can the value of X and Z be Zero? An Expert should pls analyse the correct answer. Thanks in anticipation.
Simplifying, we have:

XY + Z = XY + XZ

Z = XZ

XZ - Z = 0

Z(X - 1) = 0

Z = 0 or X = 1

Answer: E

Scott Woodbury-Stewart
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