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

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Luci
 Post subject: If xy + z = x(y + z) which must be true?
 Post Posted: Sun Aug 05, 2007 11:49 am 
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
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GMAT 2007
 Post subject:
 Post Posted: Sun Aug 05, 2007 12:42 pm 
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
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Luci
 Post subject:
 Post Posted: Sun Aug 05, 2007 6:00 pm 
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
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pizzadead
 Post subject: Revisit: xy + z = x(y+z)
 Post Posted: Wed Oct 08, 2008 3:39 pm 
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
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RonPurewal
 Post subject:
 Post Posted: Fri Oct 24, 2008 5:03 am 
Offline
ManhattanGMAT Staff


Posts: 7146
GMAT 2007 wrote:
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.
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