The number of apples that Sophia has is a multiple of $6$. When she sells one apple, the number of apples is a multiple of $n$. If $n$ is a positive integer less than $10$, how many possible values are there for $n$?
Let the number of apples = 6a
Let the multiple of n = bn
6a - 1 = bn
6a = bn + 1
6a will always be an even integer
Then n cannot be even because then bn + 1 would be odd
So.....n must be odd = 1,3,5,7,9