CARD #1: Use the number 0 to represent the yellow marbles and 1 through 9 to represent the other marbles.
Since we are only allotting one out of the 10 numbers for the yellow marbles, then we should also find a set of marbles wherein the ratio of the yellow marbles to the total marbles is 1/10. Out of the options, the situation with 30 red marbles, 40 blue marbles, 20 green marbles, and 10 yellow marbles match the ratio.
CARD #2: Use the numbers 0 through 4 to represent the yellow marbles and 5 through 9 to represent the other marbles.
We will follow the same logic as the previous pair. Since we used 5 numbers out of the 10 for yellow marbles, then we should find a situation wherein the ratio of the yellow marbles to the total marbles is 1/2. From the options, the situation with 16 red marbles, 32 blue marbles, 32 green marbles, and 80 yellow marbles satisfy the ratio.
CARD #3: Use the numbers 0 through 2 to represent the yellow marbles and 3 through 9 to represent the other marbles.
For this card, 3 out of the 10 numbers are allotted for the yellow marbles. Thus, the ratio of the yellow marbles to the total marbles should be 3/10. We can see that the only situation that satisfies this is the one with 60 red marbles, 120 blue marbles, 30 green marbles, and 90 yellow marbles.
CARD #4: Use the numbers 0 through 3 to represent the yellow marbles and 4 through 9 to represent the other marbles.
Lastly, we will apply the same logic for this card. The 4 numbers allotted for yellow marbles will tell us that the ratio of the yellow marbles to the total marbles should be 2/5. The only situation that satisfies this would be the one with 20 red marbles, 30 blue marbles, 10 green marbles, and 40 yellow marbles.
