x and y are positive integers i.e both x and y are greater than zero (0).
$$x+y=3^x$$
$$y=3^x-x$$
Question: is y divisible by 6?
Statement 1: x is odd
If x=1
$$y=3^1-1=3-1=2$$
2 is not divisible by 6; it has a remainder
If x=3
$$y=3^3-3=27-3=24$$
24 is divisible by 6.
We cannot arrive at a definite answer for both scenarios, then statement 1 is NOT SUFFICIENT.
Statement 2: x is a multiple of 3
If x is an odd multiple of 3 e.g 3
$$y=3^3-3=27-3=24\ which\ is\ divisible\ by\ 6$$
If x is an even multiple of 3 e.g 6
$$y=3^6-6=729-6=723\ which\ is\ not\ divisible\ by\ 6$$
Since the information provided is not enough to arrive at a definite answer (i.e answer without remainder), then statement 2 also is NOT SUFFICIENT.
Combining both statements together
x is a multiple of 3 and x is an odd number.
Definitely, x is an odd multiple of 3.
If x=3,
$$y=3^3-3=27-3=24\ which\ is\ divisible\ by\ 6$$
If x=9
$$y=3^9-9=19683-9=19674\ which\ is\ divisible\ by\ 6$$.
Therefore, both statements together are SUFFICIENT.
Answer = OPTION C
