Why It's E?! Please Explain.

[Haitham]

Hi all!

I need help understanding this question and its answer:

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 or y=0
E) x=1 or z=0

The correct answer is E, but why? (my first choice was A)

Thanks,
Haitham

[cramya]

Haitham,
Refer to https://www.beatthegmat.com/gmatprep-xy- ... 18211.html

Stuart provided a nice solution with explanation which may answer your question.

Let us know if u still have questions.

[Ossa]

Hi Haitham,

I think this is the shortest way to do it:

If xy+z=x(y+z), then
xy+z=xy+xz, which means that xz=z, and this can only happen if x=1, or if z=0.

Hi all!

I need help understanding this question and its answer:

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 or y=0
E) x=1 or z=0

The correct answer is E, but why? (my first choice was A)

Thanks you,
Haitham

[Haitham]

Thank you guys! It's all clear to me now