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

Is there an OE? How could the same answer be inferred as both true and false?

Hi @chetan2u, 
I have a concern and hope to get your help 
R refers to the likelihood of decrease in S but not increase in S, how could we infer if C decreases, S would increase? It could be that C decreases, S unchanged 

In that case how could we infer option A as true? ­

And as you mention '(Decrease in S and increase in C)/(Decrease in S and decrease in C) = A/B = 3', E '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' should be true

If
A = 3, B =1, out of 4 years of decrease in S, 3 years C increase
A = 6, B = 2, out of 8 years of decrease in S, 6 years C increase­

­Given 1) Relation R - During the first study, SB was 3x as likely to decrease if Cat increased. This means if there were x years when the Cat population decreased AND the SB population decreased, then there were 3x years when the cat population increased AND SB decreased. 
2) year to year changes, so only increase or decrease possible.
3) Second study has same no of years and R will hold.
4) More no of years with cat population decreasing. 

Now, while I agree that option D MUST BE FALSE, I initially thought it is not correct that A must be true.

One example I came up with to show this -> 



On thinking a little deeper, I now don't agree with the red highlighted part in my statement 1 at the top. Rather I feel that the likelihood of SB decrease if Cat increase is linked to no of years with Cat increase & SB decrease divided by no of years with cat increase or in study 1 (3/4) and not simply 3 as I was initially assuming. 

Just posting this for someone who might have been thinking along the same lines as I was initially.­

Hi PReciSioN,
There is one thing I concern:
As you mention '2) year to year changes, so only increase or decrease possible.' This only applies to the 1st study, while the projection doesn't mention anything about this in 2nd study. So it could be that there would be years in which S or C will be unchanged in 2nd study.




Posted from my mobile device

 

­Yes jaky_nguyen , it is not mentioned that the second study has only increase/ decrease in the populations on a year to year basis. It might have populations which are same accross years. But this strenthens our answer of A even more. Given that the number of years with decreasing cat populations are given to be less than original study, and now if we consider that some years the population might be same, this means the number of years where cat population increases is even less. Since during years of increasing cat population, SB population is 3 times more likely to decrease, this implies that in the new study SB population will NOT decrease for more years than in original study. Now this NOT DECREASE can be via an increase or via population remaining same but I feel that it would be unreasonable to assume that the increase in the number of NOT DECREASE SB years is purely due to the SB population remaining the same. It is likely (again in the words of the option-A) that SB population increased for more number of years.­

­Thank you for clarifying my concern but I can't find any in Paragraph supporting this 'I feel that it would be unreasonable to assume that the increase in the number of NOT DECREASE SB years is purely due to the SB population remaining the same.' 

Also consider my example below, option A can't be infered as true 


And looking at both my example and yours, option E can be infered as true: '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.' ­
3 years with increase in C out of 4 years decrease in SB

­Hi jaky_nguyen , 

Like I mentioned in my original post, we should not associate the likelihood of SB decrease if cat increases with the absolute number of years in which SB decreases AND cat increases. Rather the likelihood should be the ratio. 
In your example, in study -1 , the likelihood (probability) of SB decrease if cat increases (this is conditional probability) is 3/7 (3 years of SB decrease & cat increase divided by 7 years in which cat increased.) This probaility of 3/7 should be 3 times the probability of SB decrease if cat decrease which is not the case in your example (and it wasnt the case in my original example as well.). 
Furthermore, in your second example likelihood of SB decrease if cat increase is 6/6 = 1. In your example, the relation R given by does not hold. 

As for why E is incorrect. take this example. Suppose in study 1, cat increased for 10 years and for 3 of those 10 years, SB decreased. So this probability is 3/10. As per relation R, the probability of SB decrease if Cat decrease is 1/10 (3 times less). This can be the case if cat decreased for 100 years, and for 10 of those 100 years SB decreased. As you can see in this case the majority of years in which SB decreases is when cat decreases, but still the likelihood of SB decreasing is more when cat increases simply due to the fact that the number of years in which cat decreases is much more. ­

Hi PReciSioN,

Thank you for explaining the both points about the likelihood and option E.
 ­
According to your explanation of the likelihood, I have another example: 

+ Study 1:
Cat: 6 yrs with increase; SB: 3 yrs increase + 3 yrs decrease
Cat: 6 years with decrease; SB: 5 yrs increase + 1 yrs decrease
+ Study 2:
Cat: 3 yrs with increase; SB: 2 yrs increase + 1 yrs decrease
Cat: 9 years with decrease; SB: 5 yrs increase + 3 yrs unchanged + 1 yrs decrease

In this case, SB is likely to increase during less years in the second study
 

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. 
­

Hi KarishmaB,

I have a question regarding to option 1: "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."

The predictions in study 2 don't mention Bird and cat pops changed from year to year as in study 1. Therefore, Bird and cat pops could be unchanged in study 2.

Considering my below example:

+ Study 1:
Cat: 6 yrs with increase; SB: 3 yrs increase + 3 yrs decrease
Cat: 6 years with decrease; SB: 5 yrs increase + 1 yrs decrease
+ Study 2:
Cat: 3 yrs with increase; SB: 2 yrs increase + 1 yrs decrease
Cat: 9 years with decrease; SB: 5 yrs increase + 3 yrs unchanged + 1 yrs decrease

=> while bird in study 1 increased in 8 years, bird in study 2 increased in 7 years, fewer than in study 1.

Does this mean this option could be true or false?

Still having problems with getting the answer here. All the solutions above are either too confusing or flawed.

KarishmaB can you please explain a bit more in detail. The solution that you have given above seems to have mixed a few things and doesn’t seem correct. (For ex: while evaluating the options you have assumed that the cat pop will increase where as in the question stem it mentions that the cat pop will decrease)­

One important point to note in the problem is stated in the 2nd line that the population from year to year changed. Thus a case where the population stayed the same is not possible.

Option D is Must be false because if during the first study, the island's seabird population decreased only when the island's domesticated cat population increased then it MUST BE TRUE that when cat pop decreased, bird pop increased.

Now actually the above statement contradicts the premise of the argument - that bird pop is 3x more likely to decrease when cat pop increases. This is because the probability that bird pop decreases when cat pop decreases will be ZERO; hence, the prob of bird pop decreasing when cat pop increases will ALSO be ZERO (because 3x more likely of ZERO is, well, ZERO), but we just saw from choice D that its probability is NOT ZERO.

So yeah, choice D is a criminal.­

­Ah, Edited! The question was tricky to solve and trickier to put into words to explain! Let me know if it helps now.

 

Hi jaky_nguyen

Happy to chip in. I believe your example goes slightly against the data given. Allow me to explain:

R(relationship) = The island's seabird population was three times as likely to decrease from the previous year if the island's domesticated cat population increased (even if slightly) during the same year.

So, as per your example of Study 1:
Cat: 6 years with increase; SB: 6 years decrease (3 times as likely as when Cat population does not increase even slightly)
Cat: 6 years without increase (means Cat population decreases because population changes year to year); SB: Uncertain. Might still increase or decrease depending on how much Cat pop decreases. (Remember even a slight increase in Cat population makes a decrease in Seabird population 3 times as likely. So, a decrease in Cat population could still lead to a decrease in SB population, albeit at a lower likelihood.)

Now, for Study 2:
The passage says that R holds. This means we still find the same relationship as above. So...
Cat: 3 years with increase; SB: All three years with decrease (SB increase during these years is out of the question)
Cat: 9 years with decrease; SB: Again uncertain, as above. Might still increase or decrease depending on how much Cat population decreases. 

So, how is Statement A true?

Let's start with R:
The island's seabird population was three times as likely to decrease from the previous year if the island's domesticated cat population increased (even if slightly) during the same year.

Now, the predictions are:

1. R will hold
2. The island's domesticated cat population will decrease during more years of the second study than it did in the first study.

Now, if we flip prediction 2, we get:
The island's domesticated cat population will increase during fewer years of the second study than it did in the first study.

Now, if we apply "R", we get:
The islands seabird population will decrease during fewer years of the second study than it did in the first study. 

Now, if we flip the above sentence, we get:
The islands seabird population will increase during more years of the second study than it did in the first study. 
This is the same as choice A: 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.

Hope this clarifies.
Happy learning! 

-Abhishek ­

As per the question, SB decreases in all those years when cat population increases but when CP decreases SB may still decrease. So how can we say that SB population is likely to increase more during the second study as nothing is mentioned about the SB population increasing when CP decreases? How is option A justified in this case?

 

Firstly,
The premise states that

This means that the population either increases or decreases. It never remains the same. So in this problem, if the population is not increasing, then it is said to be decreasing. The case of "No Change" does not exist as per the problem statement.

R states:
If Cat population increases, Probability of Sea Bird Population decrease = 3x = 1 (Let's take the max value for the worst case scenario. You can take any other value)
If Cat population decreases, Probability of Sea Bird Population decrease = x = 0.33

It follows that, If Cat population decreases, Probability of Sea Bird Population INCREASE = 1-0.33 = 0.67

So you can clearly see that incase the cat population decreases,

Probability of Sea Bird Population Increase > Probability of Sea Bird Population decrease.

So, Given that cat population decreases for more no. of years in the 2nd study, it is atleast 2 times more likely that the Sea Bird Population would increase (0.67) in those years than it is likely to decrease (0.33).