10 steps to solving any sizing question – How many baseballs fit inside a Boeing 747?

Sizing questions are tough. They can be ambiguous, complex, and you’re expected to present a sound solution with minimal data. The following are examples of sizing questions:

  • “How many rounds of golf are played in the U.S. annually?”
  • “How many baseballs would fit into a Boeing 747?”

To master sizing questions, three skills are needed:

  1. Concise, clear note taking
  2. Facility with numbers, units, and back-of-the-envelope calculations
  3. Constant, live communication

What follows are the top 10 steps you must take to master those pesky sizing questions and impress any interviewer.

At the beginning…

1) If necessary, ask for some time (30 seconds to 1 minute) upfront to gather your thoughts. Take this time to sketch out an early course of action and generate interviewer questions to clarify what’s being asked. But there’s nuance here: if this market sizing question seems to be the entire framing of your case interview, then you can take a pause to structure your thoughts just like for any other case prompt. Though if this market sizing question is just given to you as the math component of the case, know that top candidates won’t take a pause and will instead talk through the entire answer from start to finish.

On numbers and calculations…

2) Round your answers at each step. If a calculation results in 101 golf balls, use 100 golf balls for the next step. If your answer is $8200, use $8000. This will minimize future mistakes and communicate to the interviewer that you know what you’re doing. If rounding doesn’t change the answer by more than 10%, proceed. Be clear to say that you’re rounding, and if the interviewer wants you to use the exact calculated number for the next step, they’ll stop you and say so

3) When you need to make numerical assumptions, pick friendly numbers (e.g., 5, 10, 25, 50, 100, etc.). For instance, if you need to estimate the percentage of people in the U.S. that play basketball, it’s better to assume 5% than 7%.

4) Clearly label units when taking notes. Don’t get units confused – it’s one of the most common mistakes in sizing questions. Don’t end up with an answer for the average calls/hour/user when the interviewer is asking for the average minutes/user/month. Yikes.

5) Avoid numerical ranges. If the question is “How many baseballs would fit into a Boeing 747?”, don’t start your thinking process by saying “First, I’d estimate the volume of a 747 to be between 10,000 and 20,000 cubic feet.” Stick with one number. Ranges provide unnecessary complication and will double the number of calculations.

6) Use a “sniff test” for each calculation. If the answer doesn’t feel right, communicate that doubt with the interviewer (e.g., “The answer seems high to me”). Double-check assumptions and steps taken. If it still doesn’t feel right, it’s OK to move on, but make a note of this potential problem area.

On structuring and communicating…

7) It’s OK to communicate doubts and mistakes. If you mess up, here’s what to say:

“Hmm…something here’s not adding up right. Is it okay if I take a few steps back and rework my calculations?”

OR

“Hmm…this answer doesn’t look right. Do you think XYZ is too aggressive an assumption?”

You can insert any question in lieu of “too aggressive an assumption.” The key is that you’re not just asking what you’re doing wrong, you’re hypothesizing on the source of the error.

8) Read interviewer body language. As you’re communicating the steps taken, it can be easy to focus solely on your notepad and calculations. Periodically look-up to see how the interviewer is responding. If they have a quizzical look, it’s ok to continue, but again, make a note that this may be a problem area. If they’re nodding consistently, you’re in good shape.

9) Communicate each step clearly and concisely. Case studies and sizing questions are as much about communication skills as they are about problem-solving skills. What value is a great solution if you can’t persuade the client to implement your recommendations? You must clearly talk them through your thought process.

10) Don’t over-complicate the solution. To try to impress the interviewer, applicants will often add unnecessary steps that lead to mistakes. Only complicate your solution when it leads to a qualitatively better response. Here’s an example:

If the question is, “How many bottles of wine are consumed annually in the U.S.?” – separating wine consumers into an active consumers group (drink a glass everyday) vs a casual consumers group (drink a glass every week) is correct and makes a qualitative difference. Further segmenting into male vs female active consumers and male vs female casual consumers is an example of over-complication. For market sizing questions, segment in the way you feel best designates trends in purchasing behavior.

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