Where am I going wrong?

Let a=2, b=4, c=8; x=3, y=3/2, z=1.

Then 2z/(x+z) =2/4=1/2, and y/z = 3/2. NOT the same.

Let's build on Chakolate's solution....

If \(a^x=b^y=c^z\), \(\frac{b}{a}=\frac{c}{b}\), then it COULD be the case that a=2, b=4, c=8, x=3, y=3/2, z=1.
In this case, we get:
QUANTITY A: 2z/(x+z) = (2)(1)(3 + 1) = 2/4 = 1/2
QUANTITY B: y/x = (3/2)/3 = 1/2


It COULD be the case that a=2, b=4, c=8, x=0, y=0, z=0.
In this case, we get:
QUANTITY A: 2z/(x+z) = 0/0
QUANTITY B: y/x = 0/0
Can we say that 0/0 = 0/0?
No.
0/0 is undefined. In other words, it's not an actual number.
It's like asking "Which is greater, lemon or lime?"
Since we can only compare numbers in a Quantitative Comparison question, this is a faulty question.

If this were an official GRE question, there would be some proviso that says the denominator cannot be zero.

Cheers,
Brent