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If a<y<z<b;

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Shobuj40
 Post subject: If a<y<z<b;
 Post Posted: Fri Jan 30, 2009 2:24 pm 
If a<y<z<b; is ! y-a! < !y-b!
a. !z-a!<!z-b!
b. !y-a!<!z-b!
Ans : D
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RonPurewal
 Post subject: Re: If a<y<z<b;
 Post Posted: Wed Feb 11, 2009 10:00 am 
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ManhattanGMAT Staff


Posts: 7146
the first thing you should do here is rephrase the question.
big takeaway:
if you see the ABSOLUTE VALUE OF A DIFFERENCE, you should recast it as the DISTANCE BETWEEN THE TWO THINGS on the number line.

therefore, |y - a| is the distance between y and a, and so on.

hence:

QUESTION: is y closer to a than to b ?
(1) z is closer to a than to b
(2) y is closer to a than z is to b

statement (1):
note that the distance y-a is less than the distance z-a, because y is placed between a and z.
also, note that the distance y-b is greater than the distance z-b, since z lies between y and b.
therefore:
distance y-a < distance z-a < distance z-b < distance y-b (note that these are color-coded to the statements above)
so, distance y-a < distance y-b
"yes"
SUFFICIENT

statement (2):
same thing as statement (1), except for the second term of the inequality above isn't there anymore.
i.e., distance y-a < distance z-b < distance y-b.
SUFFICIENT

ans = (d)
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