Explanation

Since the ratio in this question has more than two elements, colon (or table) notation will be more useful than fraction notation:



The n conveys the fact that they are all multiples of some integer, but we don't know what integer; that's the definition of a ratio. The total of all the marbles is thus



Most likely, the number that can't be the total, the correct answer choice, is not divisible by 21. Since , we can confirm by checking whether each is divisible by 7 and by 3.

The 3's are really easy, because we simply have to sum the digits and see whether the sum is divisible by 3. So we can do that first. 6 + 3 = 9 divides by 3. 8 + 4 = 12 divides by 3. 1 + 2 + 6 = 9 divides by 3. 1 + 4 + 4 = 9 divides by 3. 1 + 6 + 8 = 15 divides by 3. All answer choices are still in.

On to 7. We have , , , 144 is not divisible by 7.

The correct answer is (D).