If xy + z = x(y + z), which of the following must be true?

[brandon.sitz]

I recently took a GMAT Prep practice exam and came across the following problem:

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

I chose answer choice (a) which was incorrect. I do not understand why (a) would not be a valid answer because if you plug in 0 for both "x" AND "z", the equation would result in 0=0 which is a true statement. Can someone please let me know what I'm doing wrong?

[gokul_nair1984]

Given: xy + z = xy + xz

Cancelling xy on both sides, we get,
z = xz
or z-xz = 0
or z(1-x) = 0

This implies that either z=0 or x=1.. Thus (E) has to be the answer.

I chose answer choice (a) which was incorrect. I do not understand why (a) would not be a valid answer because if you plug in 0 for both "x" AND "z", the equation would result in 0=0 which is a true statement. Can someone please let me know what I'm doing wrong?

This can be true but need not necessarily be true for the given condition to hold good as we could also substitute other values that might suffice the given condition. The question stem clearly indicates which of the following must be true . As per your justification options( A,B,C) will also satisfy both sides of the given conditions. Try these options and you will find out.. However only option E is mandatory for the condition to hold good under any given conditional circumstance.

I hope I could help

[RonPurewal]

Given: xy + z = xy + xz

Cancelling xy on both sides, we get,
z = xz
or z-xz = 0
or z(1-x) = 0

This implies that either z=0 or x=1.. Thus (E) has to be the answer.

I chose answer choice (a) which was incorrect. I do not understand why (a) would not be a valid answer because if you plug in 0 for both "x" AND "z", the equation would result in 0=0 which is a true statement. Can someone please let me know what I'm doing wrong?

This can be true but need not necessarily be true for the given condition to hold good as we could also substitute other values that might suffice the given condition. The question stem clearly indicates which of the following must be true . As per your justification options( A,B,C) will also satisfy both sides of the given conditions. Try these options and you will find out.. However only option E is mandatory for the condition to hold good under any given conditional circumstance.

I hope I could help

this is a nice summary.

another way of looking at it: the original poster has given an answer to "which of the following COULD be true?", but, unfortunately, the question is "which of the following MUST be true?"