HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

square both sides, Is (x-z)^2=(y-z)^2?
st(1) (y-z)^2=(y-z)^2 Sufficient
st(2) |x|=|y| or x^2=y^2

x^2-2zx+z^2 ... y^2-2zy+z^2 <> y^2-2zx+z^2 ... y^2-2zy+z^z^2
since we don't know about 2zx and 2zy we cannot answer this question, Not Sufficient

a

HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

Question rephrased: Is the distance between x and z equal to the distance between y and z?

Statement 1: x=y
Since x and y are equal, each is the same distance from z.
SUFFICIENT.

Statement 2: |x| - z = |y| - z
Thus, |x| = |y|.
If x=y=1, then x and y are each the same distance from z.
If x=1, y=-1, and z=10, then x and y are not the same distance from z.
INSUFFICIENT.

The correct answer is A.

Note that, by treating this as a DISTANCE problem, we were able to evaluate the statements very efficiently.

HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

Squaring is a nice trick, but you can always just create three non-abs formulas (only one of which need be validated):

a.) x - z = y - z

OR

b.) x - z = z - y

OR

c.) z - x = y - z


(1) x = y

Applying to (a), we get y - z = y - z, which is always true. SUFFICIENT


(2) |x| - z = |y| - z

z's cancel to leave |x| = |y|

x = y, from before we know that this validate's

AND

-x = y

a.) x = y = 0, does NOT always evaluate to true
b.) -z = z, is NEVER true
c.) z = -z, is NEVER true

Given part (2), the main statement works when x = y but does NOT work when x = -y.

INSUFFICIENT

A is the answer

@pemdas, GmatGuruNY & krusta80:

Thank you for explaining this to me!