If $\frac {a}{3^{x-1}}=\frac{b}{3^{y+2}}=\frac{c}{3^{z-1}}=\frac 15\;$ then which of the following equals $a×b×c$? The problem is:

If $\frac {a}{3^{x-1}}=\frac{b}{3^{y+2}}=\frac{c}{3^{z-1}}=\frac 15,\;$ then  which of the following equals $a×b×c$ ?
A) $\frac {1}{375}$
B)  $\frac{1}{125}$
C)  $\frac{27}{125}$
D)  $\frac{3}{125}$
E)  $\frac{27}{5}$

I think the question is wrong.
My counterexample:

Let $x=m,\; y=m-3,\; z=m.$
Then $a=b=c=\frac{3^{m-1}}{5}.$
So,  $a×b×c=\frac{3^{3m-3}}{125},\; m\in\mathbb{R}.$

Am I right?

Yes some information is missing, indeed we have that
$$\frac {a}{3^{x-1}}=\frac{b}{3^{y+2}}=\frac{c}{3^{z-1}}=\frac 15$$
then 
$$abc=\frac{3^{(x+y+z)}}{125}$$
then we need a condition for $t=x+y+z\in \mathbb R$, since $3^{t}$ can assume any value  $\in(0,\infty)$.
