Rather, the question is asking: is Y greater or equal to Z assuming there is an equality between x and y-z (or z-y).
Remember the definition of |x|. |x| is always greater or equal to 0.
If x > 0, then |x| = x.
If x = 0 then |x| = 0.
If x < 0, the |x| = -X. Since x < 0, we have to take -X to make it > 0.
So is |x| = y-z ?
We'll have a definite answer to the question if we have an equality between x and y-z (or z-y) And
if we know the sign of x or y-z.
1/ x + y = z
so x = z - y--- Not enough information because we need to know the sign of x or y-z.
2/ x < 0 --- Not enough information because we need a relationship between x and y-z
Together we have both an equality and the sign of x.
so |x| = |z-y| = y-z because x being < 0, so is z-y. z-y < 0
; therefore |x| = |z- y| = -(z-y) = y-z.C is the answer.
That's all, folks.
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Dakar Azu is The GMAT Doctor.
Dakar is an experienced GMAT teacher who can be reached at http://700gmatclub.com. He prepares aspiring business students thoroughly to get them well over the GMAT 700-score hurdle through his online GMAT courses.