If x and y are positive integers and 3x+2y=13 what could be the value of y

If 'x' is a positive integer, then  ...

-- the smallest 'x' could be is ' 1 '
-- the smallest '3x' could be is ' 3 '.
-- the greatest '2y' could be is (13 - 3) = 10
-- the greatest 'y' could be is ' 5 '.

So, ALL of the possible values of (x,y) are:

==>  x=1, y=5

==>  x=3, y=2

And that's all.  There are no other possibilities.

It’s either a or c as the answer.