Self-study
Ditrama is a federation made up of three autonomous regions: Korva, Mitro, and Guadar. █████ ███ ███████ ███████████████ █████ ████ ██████ ████████ █ █████ ██ ███████ ████████ █████ ██ ███ █████ ██ ███ █████ ██████████ ██ ███████ ████████ ██ ████ ███████ ██ █████ ██ █ ██████ ██████████ ███████ ████ █████ ███ ██████████ ██ ███████ ████████ █████ ████████ ███ ███ █████ █████████ ████████ ████ ██████ ███ ██████████ ██████ ██ █████ ███ ███████████████ ███ █████ ██████ ████ █████████ ██████████ ███ ██████████
Objective: Make an Inference
The stimulus tells us about a federation called Ditrama, which is made up of the regions Korva, Mitro, and Guadar. The federation's revenue is divided between the regions every year based on their share of the federation's population. So if in a given year Korva had 50 residents, Mitro had 20 residents, and Guadar had 30 residents, then Korva would get 50% of revenue, Mitro would get 20%, and Guadar would get 30%.
Now we learn something a bit surprising: last year, Korva got a decreased share of revenue even though the population increased. But this is only surprising until we consider the difference between numbers and proportions: revenue-sharing is based on the proportion of population in each region, not the raw number of residents. Considering the above example, the revenue division would be the exact same if Korva had 100 residents, Mitro had 40 residents, and Guadar had 60 residents, because the proportions would still be the same.
If Korva received less revenue, that tells us its proportion of the population decreased. And for the proportion of population to decrease even though the number of residents increased, that means the total population of the other two regions must have increased proportionally more than Korva's population. Take the example above, where Korva started with 50 residents, and Mitro plus Guadar together started with 50 residents. If Korva now has 60 residents (a one-fifth increase) but Mitro plus Guadar together have 70 residents (a two-fifths increase), then Korva now has a smaller share of the population despite having an increase in residents.
So that's our inference: the other two provinces, taken together, must have had a proportionally larger increase in population than did Korva. Keep in mind, though, we don't know how this increase is split between Mitro and Guadar. Maybe both of their populations increased, but maybe only one did, by a large enough amount that it still outweighed Korva's increase.
24.
If the statements above are █████ █████ ███ ██ ███ █████████ ████ ████ ████ ████ █████ ██ ███ ██████████ ██████ ██ █████ ████ ████████ ███████████████ ██ ███████ ███ ██████
a
Of the three ████████ █████ ███ ███ ████████ ██████ ██ ██████████
We can't infer this because we only know about the change in population and revenue, not how those numbers compare between regions. It could be true that Korva's revenue share decreased but it still gets more than Mitro or Guadar—we don't know.
b
The population of █████ ████ ██ █ ███████ ██████████ ████ ██ ███ ██ ████████ ██████
This doesn't have to be true because the revenue split depends on Korva's population growth compared to the other regions, not compared to itself. It could be true that Korva had record population growth but Mitro or Guadar still grew proportionally more.
c
The populations of █████ ███ ██████ ████ █████████ ██ █ ██████████ ████ ████████ ███ ██████████ ██ █████ ███ ██████████ ██ █████ ██████████
(C) comes close, but it doesn't have to be true that both other regions have a proportionally greater increase. It could be true, but it could also be true that only one other region beat Korva's increase.
Let's say Korva starts with 50 residents, Mitro with 20, and Guadar with 30. Korva's population grows to 60, Mitro's population grows to 60, and Guadar's population stays at 30. Korva's share of the population has still decreased from 50% to 40%, even though only one other region's population grew.
d
Of the three ████████ █████████ █████████ ████████ ██ ██████████ ███ ███ █████████
This doesn't have to be true because we don't know the regions' starting populations. If Korva starts with a relatively large population, it could have a larger numeric growth that still amounts to a smaller proportional growth, compared to another region.
Consider if Korva starts with 80 residents, and Mitro and Guadar each have 10. If Korva's population increases to 100 (+20 residents), and Mitro and Guadar each increase to 25 (+15 residents), Korva's share of the population has still decreased even though it had the largest number of new residents.
e
Korva’s population grew ██ █ ███████ ██████████ ████ ███ ███ ██████████ ██ ██ █████ ███ ██ ███ █████ ███ ██████████ ████████
The stimulus tells us that Korva's share of the overall population declined even though its population grew. That means at least one other region must have had proportionally more growth than Korva—there's no other way Korva's share of the population would decline.
Because we only know about Korva's share, we don't know if only one or both of the other regions grew more than Korva did. (E) is correct because it specifies "at least one" of the other regions, and doesn't try to infer beyond the knowledge we have.