What is the ratio x : y: z ?

Hi all,

I read here:

https://www.manhattangmat.com/errata-fdp-5ed.cfm

about some mistakes in the guide of Manhattan GMAT FDPs, 5th edition.
I focused my attention on the third one: "The answer to the question as written is (E). The question should stipulate that xyz > 0".
This was the DS exercise:

Solution:
(1) INSUFFICIENT, because if you try to isolate x/y you get a variable expression.
(2) the same
(1)+(2) SUFFICIENT:
x + y = 2z &
2x+ 3y = z so
x+ y = 2(2*+ 3y)
x + y = 4x + 6y and finally you get
x/y = 5/(-3)
You can do the same to get y/z = -3
So you have x : y = -5/3 & y / z =-3/1 -> x : y : z = 5 : -3 : 1

Now, saying x:y = 1:2 or 2:4 is the same.
In the same way, I can say x:y=1:2 or -1:-2.
So, given x : y : z = 5 : -3 : 1 we may have two variables positive and one negative, or two negative and one positive, but that doesn't matter, because we are interested in the ratio (that, if wholly multiplied by -1, doesn't change its meaning).
In the Errata from the link I've posted, Manhattan GMAT team says that we must specify xyz > 0 , that means we must specify that we want the two-variables-positive-and-one-negative case. But I believe is not necessary; in fact we do not care about the single variables, but about their ratio.

In conclusion I think that the answer to this DS is C even without the condition xyz > 0.

Someone can confirm me this?

Thank you.

Ric