There are many ways to solve this problem, I give one here but it really depends on where the interviewer is going with this case, one way is
1) Restate the case and ask a few pointed questions to give you more data and understand what's available, for example countries in which polar bears live (they do not just live on the pole) and when would they not want to live somewhere, what are factors that they need to live, (for example maybe they stay out of populated areas), what is the size of a territory, maybe they need a certain type of food to survive, are they an endangered species, what are growth rates of the population.
2) Structure your approach
One approach could be
- Countries polar bears live in
- Size of these countries
- times share of these areas that are favorable to polar bear living
- share of favorable area that is typically inhabited by polar bears
translate this to units, then multiply by
- number of polar bears per favorable area unit (for example look at territory size of a polar bear (e.g., do they live singly in a territory or together etc))
- interviewer may change structure or you may not get this information and instead you must factor in points such as life span, birth rates, etc.
3) What the case might involve into:
I once came across a similar case with wolves, the point there was to understand how much the population changed over time, you had to look at a) base population, b) added population (mating and then birth) c) subtracted population (disease, hunting, death) and had to look at how the living area affected this based on whether they could find mates or whether there as a risk of disease in a particular area.
I have listed a simple approach here, as said you may also find other ways to do this. If it is of help to you, I currently still offer free coachings, feel free to book one.