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

[BTGModeratorVI]

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

[Scott@TargetTestPrep]

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