xy+z=x(y+z)

xy+z=xy+xz

z=xz

Sub x=1,z=z or sub z=0,0=0

So x=1 or z=0

Pick 5

akpareek wrote: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=0
4. x=1 or y=0
5. x=1 or z=0

please post the official answer.

selango wrote:xy+z=x(y+z)

xy+z=xy+xz

z=xz

Sub x=1,z=z or sub z=0,0=0

So x=1 or z=0

Pick 5

sup,

i agree that z=xz. but answer choice 1 works for this as well.
0=1*0

so why 5?

Hey Gurpinder,

Great question - and this one comes down to that classic GMAT method of writing questions with very specific language!

Choice 1 does work as a possible solution for this question, but the question asks which "Must Be True".

Choice 1 says that x AND z are both 0, but even if just z (but not necessarily both) is zero this one can hold true. It's not true that both must be 0.

Choice 5 uses "OR" and not "AND". So here, we know that either z is 0 or x is 1. That MUST BE true, so 5 is correct whereas 1 is not. Choice 5 actually disproves choice 1 - if x is 1, then we don't need z to be 0, and obviously x is not 0, so 1 does not have to be the case.

The good news here - you found two answer choices that could be true, so hopefully that encourages you to go back and read the "fine print" on AND vs. OR.

To follow up on Brian's and Selango's posts: for algebra problems such as this, try first to get a pure algebraic solution without having to backsolve. It is generally faster (but not always!) and will eliminate some of the confusion that you had with answer choice #1, which Brian explained perfectly in his post.

After simplifying the equation to z=xz continue with your algebraic manipulation by subtracting xz from both sides to get z-xz = 0. Then factor out the z to see that z(1-x) = 0. By equating each term in the product to 0 it is clear that either z = 0 or x = 1. As only 5 matches your solution it must be correct and there is no need to test the others. Hope this helps...