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 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

Hi ash4gmat,

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

ash4gmat wrote:If xy+z=x(y+z), which of the following must be true.
1.x=0 and z=0
2.x=1 and y=1
3.y=1 and z=1
4.x=1 or y=0
5.x=1 or z=0
OA is E

We are given the following equation, which we can simplify:

xy + z = x(y + z)

xy + z = xy + xz

z = xz

z - xz = 0

z(1 - x) = 0

z = 0

or

1 - x = 0

x = 1

So x = 1 or z = 0

Answer:E