GMAT TIGER wrote:
If xy + z = x (y + z), which of the following must be true?
a. x=0 & z=0
b. x=1 & y=1
c. y=1 & z=0
d. x=1 or y=0
e. x=1 or z=0
I am missing something in this problem..
Please, help to figure out the point here..Thank you
I know E is correct but I find A is also a correct one.
xy + z = x (y + z)
xy + z = xy + xz
z = xz
z - xz = 0
z (1 - x) = 0
therefore, z = 0 and x = 1.
but how to prove that A is also correct?
Actually, you can see that xz=z or x=1. so you can eliminate the choices where x is zero first.
I got the question.. thank you
I was thinking in a different way.
Anyway, x should be 1 to met the condition for xz = z, and y can be any for the given equation OR x can be any unless z = 0.
The only choice that points this is E. In A, x not necessarily must be 0 when z is 0 and vice versa.