If xy + z = x(y + z) which must be true?

[Luci]

If xy+z=x(y+z) wich must be true?

1-X=0,Z=0
2-X=1,Y=1
3-Y=1,Z=0
4-X=1,Y=0
5-X=1,Z=0

Correct answer is E) X=1 and Z=0 which leaves y+0=y+0
I fortunately did it right in the GMATPrep and it was question number 2 but It should be much easier or do I need a rest right now because I cannot see anything?

1- If X=0,Z=0 this yield--> 0*y+0=0*y+0*0--> 0=0
2- If X=1,Y=1 this yield--> 1*1+z=1*1+1*z--> 1+z=1+z
3- If Y=1,Z=0 this yield--> x*1+0=x*1+x*0--> x=x
4- If X=1,Y=0 this yield--> 1*0+z=1*0+1*z--> z=z
5- If X=1,Z=0 this yield--> 1*y+0=1*y+1*0--> y=y

Obviously I´m missing something, it couldn´t be so difficult. I´m quite tired after working, so maibe tomorrow I´ll see it clear. Why is 5 right and not the rest?

Thanks

Luci

Thanks

[GMAT 2007]

There is an easy approach to solve the problem, here it goes: -

We know from the question xy + z = x(y+z)

xy + z = xy + xz

z = xz
or z-xz = 0
or z(1-x) = 0

If you look above, the solution of the above equation is 1-x =0 or z=0

So the answer is (A)

Hope it helps

GMAT 2007

[Luci]

Thanks GMAT 2007, it helps and you are right with your explantion and your answer, but I still dont know why the other solutions seems to make sens as well...

If we work in the question we get the correct result as GMAT 2007 did, but if we simply substitute values all of them seems to by a possible solution.

Any explanation?

Thanks

[pizzadead]

Can someone revisit this question? Both
"Guest" and "GMAT 2007" came up w different answers--the former with "E" and the latter with "A"

Thanks

[RonPurewal]

There is an easy approach to solve the problem, here it goes: -

We know from the question xy + z = x(y+z)

xy + z = xy + xz

z = xz
or z-xz = 0
or z(1-x) = 0

If you look above, the solution of the above equation is 1-x =0 or z=0

So the answer is (A)

Hope it helps

GMAT 2007

this is right up to the next-to-last line. in other words, the derivation of "1 - x = 0 OR z = 0" is spot on.

however, that's when things start to go south. you have to actually solve these equations; doing so yields x = 1 (NOT x = 0) and z = 0, respectively.
therefore, the solution is x = 1 OR z = 0, so, (e).

by the way, i do believe that the original problem statement contains certain "and"s and "or"s, which are definitely significant. it appears that the original poster has excised these "and"s and "or"s, replacing them with commas. please copy problems EXACTLY.

[rustom.hakimiyan]

There is an easy approach to solve the problem, here it goes: -

We know from the question xy + z = x(y+z)

xy + z = xy + xz

z = xz
or z-xz = 0
or z(1-x) = 0

If you look above, the solution of the above equation is 1-x =0 or z=0

So the answer is (A)

Hope it helps

GMAT 2007

this is right up to the next-to-last line. in other words, the derivation of "1 - x = 0 OR z = 0" is spot on.

however, that's when things start to go south. you have to actually solve these equations; doing so yields x = 1 (NOT x = 0) and z = 0, respectively.
therefore, the solution is x = 1 OR z = 0, so, (e).

by the way, i do believe that the original problem statement contains certain "and"s and "or"s, which are definitely significant. it appears that the original poster has excised these "and"s and "or"s, replacing them with commas. please copy problems EXACTLY.

Bumping an old thread:

To correct the OP's mistake in the answer choices, the choices are as follows:
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 plugged in the numbers into the original stem and received multiple satisfactory answers. Why is that the wrong approach in this problem?

[RonPurewal]

The problem says, "Which MUST be true?"

If you plug in the choices, you're finding things that CAN be true, but you're not showing that they are necessarily true.

E.g.,
If I told you I was born in the 1970's, which of the following MUST be true? (Right now it's June 2014, in case anyone comes back and reads this thread after more than a year.)
(a) 34 years ≤ my age ≤ 44 years
(b) I'm 39 years old.

If you "plug in" (b), then it will work (you'll figure out that I was born between June 1974 and June 1975). But it clearly doesn't HAVE to be true.

(a) encompasses the entire range of possible ages, so it indeed MUST be true.