­In a study conducted over several years, seabird and domesticated cat

I would easily classify this question as Hard. A fair bit of struggle involved because of the long statements and complicated relations and comparisons. 

Bird and cat pops changed from year to year (so they were not constant. We assume that they changed every year)

Given R: If cat pop increased, probability of bird pop decreasing became 3 times. 

So even if cat pop decreases, there is a pobability that bird pop will also decrease (albeit smaller). 

Predictions:
- R will hold
- Cat pop will decrease during more years of the second study than it did in their first study
(IMPORTANT POINT - COMPARISON between first study and second study, not between the number of years of increase/decrease in either one study alone)

Now we choose for "Can be inferred to be true" and "Can be inferred to be false"

If the researchers' projections are accurate, the island's seabird population is likely to increase during more years of the second study than it did in the first.

Predictions are accurate. We know that in second study, cat pop will decrease in more years than in first study.
So the cat pop will increase or stay the same in fewer years in the second study than in the first study. The probability of bird pop decreasing becomes much greater (3 times) in these years, and there will be fewer of these years. So, we are likely to see fewer years of bird pop decreasing in second study than in first study. So we are likely to see more years of bird pop increasing in second study than in first study. 
The word "likely" gives me a lot of confidence in this option. ANSWER

During the first study, most years had an increase in the island's domesticated cat population.

As we said before, we do not know how the split was between "no of years of cat pop increases" and "no of years of cat pop decreases" in the first study. There is no such comparison given. 

If the researchers' projections are accurate, the island's seabird population is likely to increase during most of the years of the second study.

As we said before, we do not know how the split was between "no of years of bird pop increases" and "no of years of bird pop decreases" in the first study and hence nothing can be said about second study either. There is no such comparison given. 

During the first study, the island's seabird population decreased only when the island's domesticated cat population increased.

We know that there is a probability of bird pop decreasing even when cat pop decreases. That probability is not 0. It becomes 3 times when cat pop increases. Hence we know that "cat pop increase" is not necessary for "bird pop decrease". ANSWER
Hence this statement can be inferred to be false.

During the first study, most years during which the island's seabird population decreased were years during which the island's domesticated cat population increased.­

Cannot say whether it is true or false. It is natural that it could be true but it could be false also. e.g. what if out of 20 years of first study, in 18 years cat pop decreased and in 2 years cat pop increased. Out of those 18 years, bird pop decreased in 6 years but in both years of cat pop increase, bird pop decreased. This is possible. 
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