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by Anju@Gurome » Fri Mar 15, 2013 8:37 am
paresh_patil wrote:Is x>y>z?
1) x-y = |x-z| + |z-y|
2) x>y
Statement 1: Note that, |x - z| ≥ 0 and |z - y| ≥ 0
Hence, (x - y) ≥ 0 ---> x ≥ y
Hence, (x - y) = |x - y|

Now, the equation can be interpreted as the sum of the distances of z from x and y on the number line is equal to the distance between x and y.

This is possible only if z is between x and y on the number line or x = y = z.
In either case, the answer to the question is NO.

Sufficient

Statement 2: No information about z.

Not sufficient

The correct answer is A.
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by GMATGuruNY » Fri Mar 15, 2013 8:57 am
paresh_patil wrote:Is x>y>z?
1) x-y = |x-z| + |z-y|
2) x>y
|a-b| = the DISTANCE between a and b.

Statement 1: x-y = |x-z| + |z-y|
In other words:
x-y = (the distance between x and z) + (the distance between z and y).

Draw a NUMBER LINE.
If x>y>z, we get:
Z <---------------> Y <-------(x-y)------> X

Here, x-y is LESS THAN the distance between x and z, violating the requirement that x-y = (the distance between x and z) + (the distance between z and y).
Thus, it is not possible that x>y>z.
SUFFICIENT.

Statement 2: x>y
No information about z.
INSUFFICIENT.

The correct answer is A.
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