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

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Re: ­In a study conducted over several years, seabird and domesticated cat [#permalink]
The answer given is surely wrong as same option cannot be both false and true.

You could get to the answer more easily by eliminating the options rather than homing on directly to the answer. The two ways could be as shown below.

(I) Understand Para:
Decrease in Seabird's population(S) is three times more likely if Cat's population(C) increases. Thus, we can compare decrease in S in relation to increase/decrease in C.
Thus (Decrease in S and increase in C)/(Decrease in S and decrease in C) = A/B = 3
For sure, both A and B cannot be 0.
During the first study, the island's seabird population decreased only when the island's domesticated cat population increased.

The above option however makes B zero, a situation NOT possible.
Hence surely false.

Next, as the C is expected to decrease more often in second study compared to the first period, D should increase in more years comparatively. Hence first option can be inferred to be true.

(II) Using options
Even if one has not understood the para, one can get to the answer by elimination options.
The Para does not give anything concrete, so the extreme option should be a strong contender for false and opposite for true.
Only when >> Most >> More would be sequence for looking for extremes. Hence option D (using only when) should be false and A( using More) should be true.

Let us now answer by scanning each choice..

Option A and C talk of same thing...
Quote:
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.
C. If the researchers' projections are accurate, the island's seabird population is likely to increase during most of the years of the second study.

A compares the increase between two periods while option C makes a sweeping statement on the second study period. The para talks of relative decrease in C in the two periods, so we can make a statement based on comparison of decrease in two periods.
Quote:
B. During the first study, most years had an increase in the island's domesticated cat population.

Again, nothing can be said about a particular period. It is very well possible that increase in C was just for 2-3 years out of 30 years.
Quote:
D. During the first study, the island's seabird population decreased only when the island's domesticated cat population increased.
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.­

D and E talk about increase in S. D talks of extreme scenario and is likely to be false.­

Editing the answers accordingly. Please let me know incase the OA is different in OG.
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­In a study conducted over several years, seabird and domesticated cat [#permalink]
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

Originally posted by jaky_nguyen on 11 Mar 2024, 05:04.
Last edited by jaky_nguyen on 12 Mar 2024, 02:21, edited 2 times in total.
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­In a study conducted over several years, seabird and domesticated cat [#permalink]
­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.­
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­In a study conducted over several years, seabird and domesticated cat [#permalink]
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.

PReciSioN wrote:
­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.­

Posted from my mobile device
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­In a study conducted over several years, seabird and domesticated cat [#permalink]

jaky_nguyen wrote:
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.

PReciSioN wrote:
­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.­

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.­
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­In a study conducted over several years, seabird and domesticated cat [#permalink]
PReciSioN wrote:
jaky_nguyen wrote:
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.

PReciSioN wrote:
­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.­

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
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Re: ­In a study conducted over several years, seabird and domesticated cat [#permalink]
1
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Quote:
Quote:
­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. ­
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­In a study conducted over several years, seabird and domesticated cat [#permalink]
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

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Re: ­In a study conducted over several years, seabird and domesticated cat [#permalink]
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savalt wrote:
­
All Data Insight question: TPA [ Official Guide DI Review 2023-24]

­In a study conducted over several years, seabird and domesticated cat populations on a geographically isolated island changed from year to year. Researchers found that over the course of the study, the relationship (R) between seabirds and domesticated cats was such that 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. The researchers are about to begin a second, follow-up study with the same duration as the first study. Based on recent trends, the researchers made the following projections: R will hold and the island's domesticated cat population will decrease during more years of the second study than it did in their first study.

Assuming that the information above is true, select for Can be inferred as true the statement that can be most reasonably inferred as true from the information provided, and select for Can be inferred as false the statement that can be most reasonably inferred as false from the information provided. Make only two selections, one in each column.­

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 increase in more years than in first study. Since the probability of bird pop decreasing becomes 3 times then in each of these years, we are likely to see more years of bird pop decreasing 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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Re: ­In a study conducted over several years, seabird and domesticated cat [#permalink]
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?
Re: ­In a study conducted over several years, seabird and domesticated cat [#permalink]
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