Estimate the number of radio stations

It looks like a bit of both market sizing and brain teasing. Assuming you have no data to work on, the interviewer wants to see how you think through and structure the problem. For questions like this (and most case questions in general) it's important to remember that they care less about you calculating (1+.05)*16=24 than they do that you realized the problem needs to be structured as (1+g)*n=x.

For somethng like this I'd suggest first developing an initial structure you plan to apply (make sure it's one you can talk through). We will assume that all radio stations in this example are non-internet (e.g. no podcasts or online stations) and that their primary audiences access content through an actual radio rather than a computer, etc. We will also assume we are looking only at the US. 

• Let's assume there are 100,000 radio stations that fit our description in the US. Now we have to address the two criteria:
  • +1M listeners
    • +1 million listeners is a high number for an audience, so these stations have to be either 1) urban-based stations servicing a major city, 2) urban-based stations servicing a major region/the majority of the US, or 3) suburban/rural stations that have a regional/national listener base.
    • This level of success is quite rare for a radio station, so the stations must be either 1) well-established or 2) relatively new and growing in popularity.
    • Let's assume only 15% of stations fit this criteria (this number is purposely arbitrary; remember, we have no data to work with and the interviewer cares only about how you think through this problem).
    • Probability for first criteria * total stations = 0.15*100,000 = 15,000. Now we have to look at which of these 15,000 stations fix the next conditional.
  • Listen at least once per month
    • This rules out stations whose popularity is affected by seasonality, breaking news reports, and other external factors that prevent unifirm listener traffic.
    • Likely rush-hour stations have the best hold on their listener base in terms of loyalty (they also funny enough tend to have the most listeners).
    • Since most stations are not seasonal, we can assume 90% of these 15,000 +1M traffic stations have listeners tuned in at least once a month. 
    • Probability for second criteria * selected stations = 0.9*15,000 = 13,500 stations.

This is our answer. Based on our structured approach and assumptions to the problem, we can assume there are about 13,500 radio stations that fit both criteria.

Again, the answer is totally arbitrary. It's more about the steps you took to arrive at your conclusion, and if you can explain the logic behind each.

Hope this helps!