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IS |x-z|=|z-y|?

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royaamir
 Post subject: IS |x-z|=|z-y|?
 Post Posted: Fri Apr 08, 2011 11:15 pm 
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Students


Posts: 2
Date efficiency.....

Is |x-z|=|z-y|????
1. x=y
2.|x|-z=|y|-z

I am confused why the answer is A.
Please help!!!
Thanks...
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RonPurewal
 Post subject: Re: IS |x-z|=|z-y|?
 Post Posted: Wed Apr 13, 2011 5:26 am 
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ManhattanGMAT Staff


Posts: 7146
royaamir wrote:
Date efficiency.....

Is |x-z|=|z-y|????
1. x=y
2.|x|-z=|y|-z

I am confused why the answer is A.
Please help!!!
Thanks...


i'll show you how to work with statement (1), since you haven't really requested any help with the other statement.

first approach: ALGEBRA
since x and y are equal, you can substitute x for y, giving
Is |x - z| = |z - x|?
the answer to this question is definitely yes, since the quantities x - z and z - x are opposites, and the absolute values of two opposite quantities will always be the same.

second approach: PLUGGING
just plug in a whole bunch of different sets of x/y/z that satisfy statement (1). i.e., x and y must be the same number, but z can be any number at all (since there are no restrictions on z in the statement).
if you plug in enough sets of numbers, you'll notice the pattern -- the absolute values will always have opposite numbers inside them, and so they will always be the same once the absolute value makes them positive.
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royaamir
 Post subject: Re: IS |x-z|=|z-y|?
 Post Posted: Wed Apr 13, 2011 7:09 am 
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Students


Posts: 2
Thank you Very Much!!!!
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jnelson0612
 Post subject: Re: IS |x-z|=|z-y|?
 Post Posted: Wed Apr 13, 2011 3:02 pm 
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ManhattanGMAT Staff


Posts: 1857
Thanks Ron!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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rachelhong2012
 Post subject: Re: IS |x-z|=|z-y|?
 Post Posted: Mon Feb 13, 2012 12:45 pm 
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Course Students


Posts: 47
rephrase the question:

is X-Z = Z-Y? OR X-Z= Y-Z which can be rephrased as X=Y? (as long as the statement satisfies either condition, it is suff)

1. X=Y suff

2. abs (x) = abs (Y)
could turn out to be:
x=y or x=-y
The first condition satisfies the question, but the second condition doesn't, so it depends on which condition you get. thus it's a maybe to the question, insuff.
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RonPurewal
 Post subject: Re: IS |x-z|=|z-y|?
 Post Posted: Fri Feb 17, 2012 5:53 am 
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ManhattanGMAT Staff


Posts: 7146
rachel, yes.
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