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How many ping pong balls fit into a helicopter? How much laundry detergent is used in the US per year? What’s the weight of the empire state building?

Google and many other tech companies are infamous for asking seemingly ridiculous “estimation questions,” also known as Fermi Problems. These questions are common in case interviews, software engineering interviews, and especially, **product management interviews**.

So, how is a PM interviewee supposed to answer this question? Are you expected to come up with a reasonable final number? Is there a particular strategy the interviewer is seeking?

After coaching hundreds of clients as a PM Coach with PMLesson, I’ve learned strategies that do and that clearly **do not** work. Here’s my advice.

Before you even go to the interview, take time to memorize a few basic numbers. It’s helpful to have these numbers in mind to bound your answer with reasonable estimates, and most of the time, these basic facts will help in your solution. Here are some facts to start with:

**US population:**300M**World population:**7.5B**US households:**100M**Area of Continental US:**3M square miles**Life expectancy:**80**Median household income:**$50,000**Revenue by company:**Netflix ($12B), Apple ($215B), Google ($109B), AirBnB ($3B), Dropbox ($1B)

Don’t over-memorize. You’ll just need to know a few basics to ground your answer. It’s not impressive for you to memorize the answers to all possible interview questions. This interview question tests **how you think**, not the final answer.

Ask questions to clarify the scope of the problem in question.

Let’s say the interviewer asks you to estimate the weight of a schoolbus.

- Does the weight estimate include a full tank of gas?
- Does the weight estimate include humans inside the schoolbus?
- How many people is the schoolbus expected to seat in total?

Your interviewer may respond by telling you to make assumptions as needed. That’s okay — asking these questions will ensure you and your interviewer are on the same page.

For estimation questions, it’s critical to explain your structure prior to answering. Specifically, how will you go about **breaking down the problem** into component pieces so that the problem becomes more tractable?

Let’s take a few examples to clarify:

*For this question, we isolate each component of a schoolbus and estimate its contribution to the overall weight.*

- Metal Exterior
- Engine
- Gas Tank (especially if full)
- Tires
- Interior (seats, driving wheel, etc.)
- External accessories (mirrors, lights, etc.)

Now that we’ve broken down the problem (and the schoolbus), we can estimate the individual weight of each piece.

*For this question, we can break down the problem by first breaking down the places we find laundry detergent used. We’ll then estimate the amount of laundry detergent used in each case.*

- Individual at-home hand washing
- Individual at-home laundry machines
- Laundromats
- High-grade commercial laundry machines for enterprise use

We already memorized that there are 3M square miles of land in the continental US. Our approach here will be to estimate the road density for a square mile of the US. Specifically, given a square mile of the US, how much road is in it? We can break down this problem into rural and urban square miles, as we’d expect the road density to be substantially different.

Generally, with these estimation questions, there are a variety of great approaches. Think about the problem critically and explain to the interviewer beforehand how you’re planning to go about answering the question.

This is the fun (and scary) part. You’ve broken down the problem, considered exceptions, and explained your approach. Now, you actually have to come up with some numbers!

Before freaking out, just remember: the interviewer **does not care** what your actual numbers are. Be confident and make assumptions as best as you can. Explain why you’ve decided to choose a particular number!

Let’s take a couple examples to demonstrate:

How would you go about estimating the weight of elements like tires, if you have absolutely no idea?

Let’s think logically based on what we know. Most humans can pick up a tire, so it can’t be more than 50lbs. It’s also definitely not an item that can be easily tossed around, so let’s lower bound it by 15lbs. The average in-between estimate is 30lbs, so we can assume a tire might weigh about 30lbs.

We can then apply this logic to other elements of the car, by breaking down the problem and estimating smaller quantities. Explain your methodology and try to reason through the problem with logic.

We need to calculate the road density of a square mile. Let’s imagine a square mile of the US, and, on average, across cities and rural environments, we can guess that it might be around 2 miles of road per square mile. Why is this?

We can imagine a square mile of the US, and it’s reasonable to imagine that there’s a road crossing across both the length and height of the square mile. Of course, in rural environments there may be no roads at all, but in cities and even small towns, there will be much more road. On average, this could be a fair estimate.

After you’ve estimated the various components, you’ll need to provide a final number. Usually, this requires plugging all your mini-estimates into your larger equation and summing the total. For instance, in the schoolbus weight question, sum each component’s weight for the final number.

Remember, there’s no right answer. Be confident. Summarize your approach.

There’s one last crucial piece to mention before finishing your answer.

Unless you’re the next Stephen Hawking, your answer is wrong. Tell your interviewer if, based on a quick gut check, you think your answer is an overestimate or an underestimate.

Explain to your interviewer what factors you would consider if you had more time. What elements did you ignore because you didn’t foresee them to factor significantly in the calculation? This helps anticipate your interviewer’s qualms with your answer.

If you found this article helpful, please clap 👏 to show your appreciation. You can read through an entire estimation question & answer on PMLesson’s website. Here are some other helpful articles by me:

L O A D I N G

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