+1 vote
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Bijan, how do you sanity check the results you arrive at for # of dentists in NYC? Thanks!

I would first confirm if the interviewer is referring to New York City or the state of New York. Assuming, they are referring to New York City, I know the population of NY is about 10M.

Now, I want to find out how many patients can a dentist serve. This will help me calculate the total number of dentists needed to serve 10M.

To estimate the number of patients a dentist can support, I need to estimate the number of hours a dentist spends on a patient. I typically visit my dentist twice a year and each visit takes 30 mins. However, once every 4 years, I make a longer visit (say an oral surgery, root canal, etc) that lasts for about 2 hours. In other words, I spend about 2x30min+(1/4)x2hour = 60min + 30min = 1.5hour per year with a dentist. Now, it’s important to remember that the average time per year per patient varies depending on the age group and insurance status. You can ask the interviewer if they want a more accurate estimate on the average time per patient or not. If they do, you can use a table that helps you show break down of the time spent per patient based on age and insurance status. Something like below (assume people are evenly distributed between 0 to 80, meaning each age group population is 10million / 80 = 125K

0-20 year olds – no insurance – 20% of population in this group = 20% x 20 years x 125K per year = 500K visit 30 min per year
0-20 year olds – with insurance – 80% of population in this group = 80% x 20 years x 125K per year = 2 million visit 120 min per year
20-50 year olds – no insurance – 20% of population in this group = 20% x 30 years x 125K per year = 750K visit 30 min per year
20-50 year olds- with insurance – 80% of population in this group = 80% x 30 years x 125K per year = 3 million visit 150 min per year
50-80 year olds – no insurance – 20% of population in this group = 20% x 30 years x 125K per year = 750K visit 60 min per year
50-80 year olds – with insurance – 80% of population in this group = 80% x 30 years x 125K per year = 3 million visit 180 min per year
(Note that we are making bunch of assumptions on the breakdown of no-insurnace vs. insurance population, time visit per age group, etc). Now, to calculate the average time one spends, just take the average from above time.
(500K x 30 min + 2,000K x 120 min + 750K x 30 min + 3,000K x 150min + 750K x 60min + 3,000K x 180min) / 10,000K = 131 min almost equal 2 hour

For the sake of this report, I will go with 2 hour. Now, we can assume that a dentist works 40 hours x 52 weeks x 75% utilization = 1,560 hours per year. Divid 1,560 by 2 hours and you get 1560/2 = 780 patients. Now, we just need to divide NY population (total number of patients) by 780 (number of patients per dentists) to estimate the total number of dentist in NY:
10Million / 780 = about 12,000.

2) How would you improve the Uber app?

I would launch a new functionality that lets uber pick up and drop off things for the people who like to deliver things in short distances within same day (e.g. envelops). The beauty of this service is that this doesn’t take the uber driver any passenger room. Also, the driver does not have to immediately start driving in the destination’s direction (unless requested by the sender of the merchandise).
I can measure its adaption based on number of requests coming in per month, additional revenue generated, and the increase in revenue per 8 hour of drive per driver.
+1
Thanks for the great answer. You’ve done a great job of answering the first question. It’s very detailed, logical, and easy to follow.

Make Equation:

Number of Dentist in New York = eligible population who visit dentist/ number of patient dentist treats every year

Assumption and Facts:

1. Population of New York = 8 million (fact)
2. Dentist spend on average 2 hrs per patient (assumptions)
3. Dentist works 8 hours per day for 5 days ; 40 working hours per week (assumptions)
4. 85% of 8 million are in the age bracket 5 to 85 who visit dentist for consultation, routine checkup, surgery etc. = 6.8 million (assumptions)
5. People visit dentist twice per year (assumptions)
Do the Math

Number of patient dentist treats every week = 40 hours per week working time / 2 hours per patient

= 40 / 2

= 20 patient per week

Number of patient dentist treats in a year = 20 * 52 weeks per year

= 1040 patients per dentist

Eligible population who visit dentist        = 85% of 8 million * 2 times/ per year
= 6.8 million * 2
= 13.6 million
Number of Dentist in New York = eligible population who visit dentist/ number of patient dentist treats every week
= 13.6 million / 1040 patients
= 13,000 dentists
+1 vote

How many dentists are there in NY:

Population of NY is approximately 8.2M

Based on my visits to several dentists – they see approximately 10 patients each day and patients normally see dentists at least twice a year.

In 1 month, a dentist approximately works 20 days a month (working flexible hours) seeing 10 patients each day.
Therefore in 6 months – they see 6 * 20 * 10 = 1200 patients
After 6 months, lets assume that the same patients start repeating.

If 1 dentist can serve 1200 patients in 6 months
Then for 8.2 M patients in 6 months, we need = 8200000/1200 = 6833 dentists = approximately 7000 dentists

Since there are patients that probably need more visits (children, adults with serious dental issues)- this number can be increased by 30% to be 9100 dentists.
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It’s an acceptable solution as a quick back of the napkin calculation. Your number is still good enough of an estimate but you might be asked for more accurate information, in which case you could break down frequency of visits based on age and insurance status.