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

komati_anusha wrote:I solved it by simplifying or rephrasing question.
xy + z = xy + xz
z = xz
z/z = x
x = 1
Eliminate AC
Next I cannot able to eliminate.

Once we know that z = xz, we cannot divide both sides by z, because it COULD be the case that z equals zero, and we should never divide by zero.

Here's why:
We know that (2)(0) = (1)(0)
However, if we try to divide by both sides by 0, we may believe that we get: 2 = 1, which of course is not true.

Cheers,
Brent

Hi komati_anusha,

There's a discussion of this questions here:

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

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