I promise you: no one actually cares if you know how many pizzas are sold every year in Manhattan.
Even if you knew the “right” answer, it wouldn’t help you. In fact, it could distract you. This is one case where the correct answer isn’t necessarily the best one.
Estimation questions are entirely about the process you take to solve them. It’s the journey, not the destination, so to speak. Interviewers will use these questions to evaluate your problem-solving skills as well as your quantitative skills.
What’s the relevance to PMing, you might ask? Quite a bit, actually.
Other than the obvious (an ideal PM is good at problem solving and good at math), being able to estimate things is actually a valuable skill. After all, when you need to figure out what you might be able to expect for the revenue from a given feature, estimations will come in handy.
In life, as in the interview, you’ll be shooting for a number in the right ballpark. Precision is not expected.
Approach
Since estimation questions are fundamentally problem-solving questions, it should be no surprise that the key to these questions is the approach. You can ace these questions with a bit of structure (and some tips and tricks).
Step 1: Clarify the Question
You can’t answer a question that you don’t understand. That’s why it’s important to make sure you heard the question correctly and truly understand what’s being asked.
For example, if you’re asked how much money Gmail makes in ads every year, you’ll first want to repeat the question back to your interviewer. This is especially important if you’re a non-native English speaker or if you think you might have misheard the question.
Next, you’ll want to ask about anything that’s ambiguous. For example, in the above question, there’s actually a lot that’s ambiguous:
Does “money” mean profit or revenue?
If it’s profit, what are we including as costs? Do salaries count as a cost? How do we take into account the salary for a person who is only working on Gmail some of the time?
Does Gmail include just Gmail.com? What about when companies use hosted Gmail for their domain?
Do you mean the past year? Or averaging over all years since Gmail was launched?
Is this for the US only, or is it worldwide?
The answer to each of these questions would substantially affect your approach and result.
Step 2: Catalog What You Know (or Wish You Knew)
Once you understand what the question is, you’ll want to get a feel for what knowledge you have and what you need to compute. In some cases, you can ask your interviewer for key facts.
Because there are multiple approaches that can be effective, what you know can guide your approach.
For example, if you’re computing the revenue from Gmail annually in the US, you might know (or be able to ballpark) some of these facts:
The population of the US.
The percent of people in the US who own a computer.
The unemployment rate in the US.
Google’s annual revenue.
The cost-per-click of a typical advertisement.
The click-through rate of an advertisement.
How well a Gmail or other embedded ad does as compared with a search advertisement.
The number of ads shown on Gmail.
You might be able to ask your interviewer for some of these facts, but be prepared to compute some of these too. If it’s something that many candidates would know and you don’t (like the US population), then it’s probably fair game to ask.
When in doubt, leave your question open-ended: “Could you tell me the click-through rate of an advertisement, or would you prefer that I compute it?” If your interviewer pushes back by saying something like, “What do you think it is?” that’s a good sign that you might be relying on questions too much.
Steps 2 and 3 are done somewhat in parallel. You can come back to your Fact List as you’re developing your equation.
Step 3: Make an Equation
This is possibly the most important part of the whole process. Here is where things come together—
or fall apart.
You need to form an equation to solve the problem. Doing so will help you make progress and show your interviewer that you can tackle tough problems head on.
There are multiple approaches for any problem, but some are better than others. However, there’s often no “best” approach, as it depends on your knowledge and background.
If you are calculating the annual revenue for Gmail in the US, this approach might work well:
[# Gmail users in the US] x [annual clicks per user] x [average revenue per click]
If you think about the above values mathematically, the components will multiply together to give you the revenue.
This isn’t the only approach though. You could also try something like:
[Google US revenue] x [% revenue from ads] x [% ad revenue from embedded (non-search) ads] x [% embedded ad revenue from Gmail]
Before trodding down the path of one equation, it might be useful for you to brainstorm multiple equations and to have a plan of attack for each component. You don’t want to waste a bunch of time computing one part and then realize you aren’t able to compute the next one.
Step 4: Think About Edge Cases and Alternate Sources
Pause for a moment and think about the potential problems in your approach. This is a great opportunity to show your interviewer that you’re detail oriented and not afraid to challenge yourself.
No one wants to hire someone who will just brush problems under the rug.
For example, if you’re computing the number of pizza places in the US, have you considered college towns? Or, if you’re computing how much it would cost to wash all the windows in your city, have you taken into account broken windows (which you presumably won’t wash)? Or even car and bus windows?
Is there some source that you haven’t considered? For example, if you were computing the number of guns sold every year, have you included illegal sales? Sales to police as well as consumers? What about race tracks using blanks?
Think carefully about what situations might not fall into the framework you created in the previous step.
Some candidates worry about exposing faults to your interviewer. Don’t! Your interviewer has likely asked this question dozens of times. He’ll know where the flaws are whether or not you point them out.
Step 5: Break It Down
At this point, you have a strong framework solving the problem. You have an equation written which lead you to an answer. You’ve even analyzed potential edge cases and issues.
Now you want to find a way to solve each component of the equation. Let’s take a problem like computing the annual Gmail revenue in the US and assume we’re working off this equation:
[# Gmail users in the US] x [annual clicks per user] x [average revenue per click]
How can we compute the number of Gmail users in the US? If the interviewer won’t give us this information, we can compute it through an equation (yes, another one!) like this:
[# Gmail users in the US] =
# Hotmail users x Ratio of Gmail users to Hotmail users
Even an equation like this might work:
[# Gmail users in the US] =
# Smartphone users x [
% Android marketshare * % Android users w Gmail +
% iPhone marketshare * % iPhone users w Gmail +
% Blackberry marketshare * % Blackberry users w Gmail +
% Windows Phone marketshare * % Windows phone users w Gmail ]
The last equation might seem a bit crazy, but there’s some logic behind it: Gmail usage might be correlated with income, just as smartphone usage is.
For each part of the main equation, construct a sub-equation. Keep each part of the original equation separate; don’t try to merge them into one mammoth equation. You might even draw a line down the page (or whiteboard) to keep these computations entirely separate.
Step 6: Review & State Your Assumptions
We now have a series of equations and all that’s left to do is guess some numbers. You’ll need to rely
on your intuition and prior life experience. You might have an idea of how often you see Gmail addresses versus other addresses.
Be aware of your biases. Yes, everyone that you know has a smartphone, but is this really representative of the entire US? Probably not.
Pick nice, round numbers, and state your assumptions clearly to your interviewer. Keep the list of assumptions you made in Step 2 updated, or find some way to clearly identify where you’ve made an assumption.
Be sure to tell your interviewer why you’re making the assumptions you are. Your reasoning is more important than the precise number.
Step 7: Do the Math
All that is left is to actually multiply these values out. Remember that we’re shooting for the right ballpark, not absolute precision. Keep your numbers nice and round to make them easier to deal with.
Step 8: Sanity Check
Whew! You finally have an answer. Give that answer to your interviewer, but make sure you double check your work right after that. Make sure the value passes some quick sanity checks.
For example, suppose you compute that Gmail’s US revenue is 5 billion dollars. Does that sound right to you? This would indicate that Gmail is making $16 per person in the US. This would be shockingly high given that most of the US doesn’t use Gmail.
Go back through and check your work. If there’s an issue, it’s probably in one of the following areas:
Original equation.
Assumptions made.
Arithmetic.
It may help to do quick sanity checks on each part of the problem as well. If you found that Gmail had 150 million users in the US, this is a problem spot. It’s reasonable to believe that 50% of the US does not use Gmail.