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kindly explain the ans

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by selango » Mon Aug 09, 2010 9:29 am
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
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by Gurpinder » Mon Aug 09, 2010 9:34 am
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.
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by Gurpinder » Mon Aug 09, 2010 9:37 am
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?
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by Brian@VeritasPrep » Mon Aug 09, 2010 9:46 am
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.
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by chris@veritasprep » Mon Aug 09, 2010 10:07 am
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...
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