greenwich wrote:Is |x-z|=|z-y|?
(1) x=y
(2)|x|-z=|y|-z
|a-b| = |b-a| = the DISTANCE between a and b.
Question rephrased:
Is the distance between z and x equal to the distance between z and y?
Put more succinctly:
Is z equidistant from x and y?
Statement 1: x=y
Since x and y are the same value, z must be equidistant from x and y.
SUFFICIENT.
Statement 2: |x|-z = |y|-z
Adding z to each side, we get:
|x| = |y|.
If x=-1, z=0, and y=1, then z is equidistant from x and y:
.....x=-1.....z=0.....y=1.....
If x=-1, y=1, and z=2, then z is closer to y than to x and thus is NOT equidistant from x and y:
.....x=-1................y=1.....z=2.....
INSUFFICIENT.
The correct answer is
A.
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