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Director
Joined: 29 Aug 2005
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Intuitive approaches are welcome: [#permalink]  21 Jul 2009, 12:13
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Manager
Joined: 03 Jul 2009
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Location: Brazil
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Kudos [?]: 58 [0], given: 13

Re: GMATPrep2: number prop - absolutes [#permalink]  21 Jul 2009, 13:47
Seofah, what is the answer? Just to guarantee you the explanation.
Current Student
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Re: GMATPrep2: number prop - absolutes [#permalink]  21 Jul 2009, 14:35
IS the answer E ? please confirm before I give an explanation ... as this was quite a confusing one and tough one
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Re: GMATPrep2: number prop - absolutes [#permalink]  21 Jul 2009, 17:05
3
KUDOS
First analyzing the information provided:

If zy < xy < 0, there are two possibilities: y is positive, or y is negative:

Case 1: If y is negative, then (dividing by y in the inequality above, and reversing it), we find that 0 < x < z

Case 2: If y is positive, then (dividing by y in the inequality above), we find that z < x < 0

Now to understand the question. Recall that |x - z| is just the distance from x to z on the number line, and |x| is the distance from x to zero. So the question "Is |x - z| + |x| = |z|?" is really just asking "Is the distance from x to z, plus the distance from x to zero, equal to the distance from z to zero?"

Let's draw a number line for Case 1 above:

------0------x--------z------

Here, if you add the distance from z to x and the distance from x to zero, you clearly get the entire distance from z to zero.

And the number line for Case 2:

----z------x--------0-------

Again, if you add the distance from z to x, and the distance from x to zero, you clearly get the entire distance from z to zero.

So in each possible case above, the answer to the question is 'yes'. We don't even need the Statements.

I suppose that makes the answer D, but it's the only real GMAT question I've ever encountered where you don't need either statement to answer the question. It's odd, to be sure, and makes me wonder if there was an error in the question design.
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Current Student
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Re: GMATPrep2: number prop - absolutes [#permalink]  21 Jul 2009, 17:17
Ian superb explanation

Kudos to you
Manager
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Re: GMATPrep2: number prop - absolutes [#permalink]  21 Jul 2009, 18:33
Wow, Have never seen such great explaination to a problem this challenging. +5
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Re: GMATPrep2: number prop - absolutes [#permalink]  22 Jul 2009, 05:27
Ian, thanks for the great explanation!

Needless to say, OA D.
Re: GMATPrep2: number prop - absolutes   [#permalink] 22 Jul 2009, 05:27
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