Sorry, I did a poor job explaining what I did wrong.
Is |x-z| = |y-z|?
1) x=y|x-z| = |y-z|
So, I did this one of two ways:
The first way: squaring both sides:
|x-z| = |y-z|
(x-z)*(x-z) = (y-z)*(y-z)
x^2-2xz+z^2 = y^2-2yz+z^2
x^2-2xz=y^2-2yz
x(x-2z)=y(y-2z)
x=y
y(y-2z)=y(y-2z)
Sufficient
The second way was to take the positive and negative cases of |x-z| = |y-z| i.e.
x-z = y-z
x=y
y-z=y-z
OR
x-z=z-y
x=y
y-z=z-y
See my problem?
Zarrolou wrote:
WholeLottaLove wrote:
Here is my problem. I solved this two ways and got two different answers. The first method was to square both sides and simplify and in doing so I got the right answer. The other way was to take the positive and negative cases of the stem in which case I got two separate solutions and the incorrect answer, i.e.
(x-z) = (y-z) OR
(x-z) = (z-y)
Can someone tell me why the second method wouldn't be used in this case?
Source: Total GMAT Math
Is |x-z| = |y-z|?1) x=ySo \(|y-z| = |y-z|\), sufficient.
2) |x|-z = |y|-zSo \(|x|=|y|\) this could mean \(y=x\) (as above) or \(y=-x\). In the case y=x the answer is YES, in the other case (x=-y) you get \(|-y-z| = |y-z|\) and the answer could be NO, consider z=1 and y=2 for example; or YES (all zeros).
Not sufficient
I am sorry but I did not get what you did for the second statement... and there is no need t square the terms here. This could be solved more easily