Are you having your product manager interview soon? It takes a lot of preparation to rock the typical interview questions. Start with this simple guide to answering quantitative questions by Jackie Bavaro, co-author of Cracking the PM Interview, with an example solution by the Product School.
The Quantitative Question – How many dishes get broken per month in San Francisco?
With this question, the interviewer will assess your analytical skills. Don’t worry too much about getting a right answer because you’ll likely not even be in the ballpark. What matters the most is the process through which you solve difficult problems.
- Start by thinking out loud and asking questions, but choose which ones you’ll ask and which ones you are expected to figure out. Maybe a good starting point is the number of people in San Francisco, do you know the population of the city? What is an approximate ratio of people to dishes? What kind of dishes are used in a household? Which situations cause a dish to get broken? Do men break more dishes than women?
- Take a step back and catalog what you know or wish you knew. The interviewer told you that San Francisco has a population of around 800,000. You can figure out the number of dishes per person by taking yourself as a benchmark. You are not sure about whether there’s a difference in terms of gender for this problem so you will not consider this variable.
- Use the information you’ve gathered and come up with an equation.
Broken dishes = Average monthly dishes used in SF * Probability of accident
Broken dishes = Monthly dish-washing accidents per person * Population of SF
Broken dishes = Unit sales of dishes in SF * % sales due to broken dishes
- Estimate, or find ways to estimate the variables in your equation. You think that the dishes to individuals ratio is 5:1. You assume that the main cause of broken dishes is accidents during the washing of the dishes which occur once every 2 months.
- Think about corner cases and adjustments. Maybe there is an important Greek population in San Francisco; will Greek weddings impact the final result? Is the incidence of broken dishes higher in households with children?
- Break out your math skills and calculate!
- Double check. Think about the number that you’ve gotten as a result. Do 600,000 broken dishes per month make sense? Did you under or overestimate something?
It might seem challenging to attempt to solve this kind of questions on the spot under a stressful situation. We recommend that you challenge yourself with similar questions and follow these 7 steps. Practice will allow you to tackle these problems with fluency. There’s another critical product manager interview question you need to master, so don’t forget to check out 5 Steps to Tackle the Product Question (With a Sample)
If you are interested in learning more about Product Management, we offer an 8-week part-time product management course in San Francisco.