If \(x > y,\) then what is the value of \(\dfrac{3^x}{3^y}?\)

[Gmat_mission]

If \(x > y,\) then what is the value of \(\dfrac{3^x}{3^y}?\)

(1) \(2^{3x-3y}=64\)
(2) \(x\) and \(y\) are consecutive odd numbers.

Answer: D

Source: e-GMAT

[deloitte247]

$$\frac{3^x}{3^y}=3^{x-y},\ so\ what\ is\ \ 3^{\left(x-y\right)}$$

Statement 1
$$2^{\left(3x-3y\right)}=64$$ $$2^{\left(3x-3y\right)}=2^6$$ $$3x-3y=6$$ $$\frac{3\left(x-y\right)}{3}=\frac{6}{3}$$ $$Therefore,\ 3^{\left(x-y\right)}=3^2=\ 9\ \ $$
$$Statement\ 1\ \ is\ SUFFICIENT.$$

Statement 2
The difference of any two consecutive odd numbers is 2, so x-y will always be 2 and $$3^2=9$$
So, statement 2 is also SUFFICIENT

Since each statement alone is SUFFICIENT.
$$Answer\ Option\ D$$