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Well, why bother with ratios? The question says the diagram has 2 black dots and 1 green dot for every 2 red dots.
This means something of this sequence: R,R,B,B,G
The diagram is incomplete if you do not have these 5 dots as the mix is no longer the same. So the total number of dots has to be a multiple of 5. From the answer choices, you have 3, 18, 36, 45, 52. Out of these 5 choices, only 45 is a multiple of 5 and therefore is a complete diagram.
I agree with the answer it has to be 45. The dots should be in the following sequence. R R B B G and since no other dots make a pair, and their are 5 dots in total, the answer should be a multiple of 5, and hence 45.