usually a good way to sanity check your answer is using a differnt driver than the one you have used for estimating the market.
For example if you use the population to estimate a certain market, you can use a different driver (as average revenue by shop / vet clinic... Average revenue per employee... number of shops per population served...)
Regarding the Vet clinic case:
- on the Vet clinics I would probably start with the population, then making some assumptions on the average size of a family/ number of families in the country... then some assumption on the share of families with a pet... depending on the geography/ local culture... then number of pet by family... When you have a reasonable number of pets (market), you can make some assumption on the number of times a pet need to see a vet
- when you have the total visits (lets assume a normal visit takes 30/40 mins - you can derive the maximum number of visits a clinc can make in one day/ and then one year
- you can easilly determine the maximum number of visits a clinic can make per day, by assuming an average number of employees per clinic (maybe 5-10)...
A case sizing should take 10 to 15 mins max... Difficult to tell you the number of steps... it really depends on the case... but usually the more filters you can immagine, the more deep thinking you can demonstrate to the interviewer... off course not boiling the ocean... just keep in mind to not go longer than 15 mins