Exercise 2

Question 1) How many dentists are there in New York?

Question 2) How would you improve the Uber app?

You can submit your answers in the comments section of this blog post to receive feedback. You can also see other people’s answers, the feedback they received, and give your own feedback in the same section.

The article how to answer an estimation question in a product manager job interview helps you prepare for estimation interview questions. And the article how to answer a product improvement question in a product manager job interview helps you prepare for product improvement questions.

Here is a list of estimation questions for product manager job interviews and here is a list of product improvement questions for product manager job interviews.


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Mark Madison

1) How many dentists are there in New York?

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.

The answer is about 12,000 dentists work in NY.

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.

Product Management Exercises

You’ve done a great job of answering the first question. It’s very detailed, logical, and easy to follow. I would give a 6 out of 10 on the second one mainly because it’s not as detailed as the first answer. Feel free to provide a more detailed answer and I’ll be happy to share my feedback.

Nabarupa Banerjee

What about this simple approach (or is it too simple):

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.


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.


How would you improve the Uber app?

Let me give a high level overview of my understanding of Uber (this might be optional)

What is the purpose of Uber?

– Ride app- Its a location based mobile app that lets customers (riders) get rides with a private driver.

Who is the user of Uber?

It has two types of users – people who need rides and people who drive Uber cars.

High level features for riders
-Guaranteed ride – A rider is guaranteed a ride within a predictable time to their desired destination.
-Tracking – The rider can even track the driver as he/she is en-route to pick the rider.
-Cashless – The rider does not need to pay with cash/credit card. The payment is known up-front and is the rider’s Uber account is charged after the ride is completed.
-Feedback – Uber lets the rider leave feedback for the driver for driving, cleanliness, behavior etc so that the experience can be improved over time
Safe – Uber does background checks of drivers and guarantees the safety of the Uber rider (this has been in question lately with customers complaining about crimes/assaults during Uber rides)

High level features for driver

– Crowd-sourced drivers- Anyone can sign up as a driver as long as they have a safe driving record and no criminal record
– Flexible work hours – A driver can have flexible working hours
-Flexible earning – A driver can make as much money as they want based on hours they drive and rides they take

What can be done to improve Uber
AT this point – we may ask the interviewer what the purpose of the improvement should be? If they ask you to make an assumption, you can say – Given all the exposure that Uber has come under with customers complaining about safety issues with Uber, I would recommend focusing on the user segment – rider and trying to solve for their compromised safety perception of Uber

1. Enforce use of go-pro cameras in all Uber vehicles

2. Create a camera vision model which uses supervised and unsupervised learning (over time) to learn about suspicious behavior, unsafe- situations. Use existing police surveillance tapes, home surveillance tapes (shared by customers) as data input to the model.

3. Have real life alerts to cops and Uber customer service when the model detects potential crime happening. Rider’s cell phone would be called and the driver’s cell phone would be called immediately to confirm if something is happening (by Uber’s customer service). The ML algo would learn and get better with false positives over time.

4. Also add a “safety” feedback section in the feedback section of the app for drivers and riders so that self reported data can be collected. This data can be prejudiced about if a pattern emerges with negative feedback about a certain driver/passenger – they can be blacklisted.

Metrics to measure improvement:
Measure feedback from customers about perception of safety (similar to NPS) with the installation of the camera and the addition of feedback section about safety
This would not have direct monetary impact on Uber’s revenue stream but the need of the hour is the perception of the company and this gesture will go a long way in improving that


Great answer!


Would improve the Uber App by to create the feature of book a ride for a friend. The app should allow to do the following things:
1. Book a ride for the friend as a separate feature and enable you to track the ride
2. Provide you with notification when the ride has ended or started, rather than you having to confirm manually with the person
3. Book multiple cabs even when a single ride is on so that both my friend and I can travel

Product Management Exercises

I think the idea of being able to book a ride for a friend is a great idea. I would expand on the answer further. Please have a look at my feedback for thoughtstrokes below. You’ll need to show a more structure thinking that goes beyond a feature description to impress the tough interviewers:)


Book a ride for friend apps
1. Ability to track
2. Ability to book multiple rides
3. Notification for ride completion

Product Management Exercises

Thanks for submitting your answer. You will need a lot more detail to impress the interviewer at a tech firm. Maybe I should have explained this in more detail earlier but it’s important to highlight
– What problem you are solving
– What is the persona of the user who has this problem
– Explain how your solution solves that problem
– Provide metrics on how you would measure the adoption / success of the feature
– Risks associated with it
There might be many more questions asked by them. It’s very important to provide more detail to show your thinking process. Remember, it’s not about the feature. It’s about the problem you are trying to solve, how you’re solving, and how you’re measuring its success.