if xy+z

[bstalling]

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 and y=0
e) x=1 and z=0

OA e

[truplayer256]

xy+z=x(y+z)
xy+z=xy+xz
xy's cancel and you're left with:
z=xz
z-xz=0
z(1-x)=0
z=0 1-x=0
x=1
E

[bstalling]

aghhh! I was soo close!

[sureshbala]

I guess the option must x = 1 or z = 0.

For the given statement to be true it is sufficient it either x =1 or z =0. So this must be true. x = 1, z =0 both these together need not be true.

[Brent@GMATPrepNow]

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 and y=0
e) x=1 and z=0

OA e

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 another 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