Question in the attachment

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

eitijan wrote:Source: GMATPrep

Why option A and B are wrong?

A and B COULD be true, but they don't necessarily have to be true.
The question asks, what MUST be true.

Cheers,
Brent

eitijan wrote:Does'nt option A and B gives the valu for x and z which means would be the solution for this case?

Not able to get convinced.

If particular values are satisfying the eqn where it is mentioned 'and' i.e. values of x and z are given for the same case.

Please correct my understanding.

A) It COULD be true that x = 0, y = 0 and z = 0
But it COULD also be true that x = 1, y = 1 and z = 1
So A need not be true.

B) It COULD be true that x = 1, y = 1 and z = 1
But it COULD also be true that x = 0, y = 0 and z = 0
So B need not be true.

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We want to know what MUST be true

Hi eitijan,

When a question asks what "MUST" be true, that really means "which of these 5 answers is ALWAYS TRUE no matter what variations you consider?"

Answers A and B both use the word "and", meaning that both values have to happen at the same time. However...

In Answer A, if Z=0, then it wouldn't matter what X equaled (so X doesn't have to equal 1)

In Answer B, if X=1, then it wouldn't matter what Y equaled (so Y doesn't have to equal 1)

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