Problem Solving

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
B. y = 1 and z = 0
D. x = 1 or y = 0
E. x = 1 or Z = 0

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 a 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

Hi lucas211,

There's a discussion of this question here:

https://www.beatthegmat.com/must-be-true-qs-t278003.html

GMAT assassins aren't born, they're made,
Rich

danielle07 wrote:Hi, How did you come up for the word "must"? Thanks

It's written in the question: "which of the following MUST be true?" With such a question, we can eliminate any answer that does not HAVE to be true.

lucas211 wrote: ↑

Thu May 26, 2016 6:36 am

Hello BTG

Would like to know if my approach to the following question is correct:




1) we multiply out the right side to get the equation: xy+z = xy + xz
2) we subtract xy from both sides to get z = xz
3) from here we see, that z = xz, either x have to be one or z have to be "0".

Is this the correct approach?

Thanks in advance

Simplifying, we have:

xy + z = xy + xz

z = xz

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1

Answer: E