What is the remainder when positive integer n is divided by 12?

Giving it a shot.

What is the remainder when positive integer n is divided by 12?

I can set up an equation to look for what I am solving for (r):

\(\frac{n}{12} = Q1 + \frac{r}{12}\)

1) When n is divided by 6 then remainder is zero

\(\frac{n}{6} = Q2 + \frac{0}{6}\)

This tells us that n is a multiple of 6, so can be [6, 12, 18, 24, 30, ...]
This will yield various values for r when divided by 12. insufficient

2) n is not a multiple of 12

This tells us that r cannot equal 0, but may be any integer from 1 to 11.
There are still many values for n. insufficient

(1) & (2)

We know that n is divisible by 6, and can have a remainder from 1 to 11.
6, 18, 30, ... all qualify for n, but will always have a remainder of 6. sufficient