If XY+Z = X(Y+Z), which of the following is true:

[a123]

Question on GMAT Prep Math:

If XY+Z = X(Y+Z), which of the following is true:
a). x=0, z=0
b). x=1, y=1
c). y=1, z=0
d). x=1, y=0
e). x=1, z=0

The answer is E.

I'm not sure why (E) is true since it shows: Y = Y
But (A) gives you 0=0 which is also true
and (D) shows Z = Z

[george.kourdin]

is this exactly how the question was posted? if so - i am also not sure. think there is a typo somewhere/conditions missing.

looked around and one explanation for E is:

xy+z = x(y+z)
xy + z = xy+zx
z = zx
z-zx = 0
z (1-x)=0
z = 0 1-x = 0
1=x

this still doesn't explain why other answer choices are wrong since they satisfy the inequality, but its a start....can you double check the question?

[RonPurewal]

for whatever reason, the original poster left the "and"s and "or"s out of the problem. needless to say, those are crucial.

here's another thread with the problem transcribed correctly:
if-xy-z-x-y-z-which-of-the-following-must-be-true-t6468.html

there's now no need for this thread, so i'm going to lock it.