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// QUANT INTERVIEW PREP

Fermi Estimation Quant Interview Prep & Practice

Estimation questions test whether you can get within a factor of a few with nothing but reasoning. Interviewers care more about the decomposition than the number.

Sample Fermi Estimation Questions

  1. Question 1 · Fermi Estimation drill

    How many piano tuners are there in Chicago?

    See the solution ↓

  2. Question 2 · Fermi Estimation drill

    How many golf balls fit inside a school bus?

    See the solution ↓

  3. Question 3 · Fermi Estimation drill

    How many gas stations are there in the United States?

    See the solution ↓

  4. Question 4 · Fermi Estimation drill

    How many passenger elevators are in service in New York City?

    See the solution ↓

  5. Question 5 · Fermi Estimation drill

    How many packages does Amazon ship per day in the United States?

    See the solution ↓

Step-by-Step Solutions

  1. Solution 1

    How many piano tuners are there in Chicago?

    Answer: About 225 tuners

    ~2.7M people -> ~1M households -> ~100k pianos (10%). Each tuned ~1x/yr. Tuner does ~4/day * 250 days = 1,000/yr -> ~100-250 tuners.

  2. Solution 2

    How many golf balls fit inside a school bus?

    Answer: About 500,000 golf balls

    Bus interior ≈ 50 m³. Golf ball volume ≈ 4.2e-5 m³. Packing efficiency ~64%. (50 * 0.64) / 4.2e-5 ≈ 500,000.

  3. Solution 3

    How many gas stations are there in the United States?

    Answer: About 150,000 stations

    ~280M vehicles, each filling up about every 10 days -> ~200M fills/wk. Station has ~8 pumps, ~24 fills/pump/day -> ~1,340 fills/wk. 200M / 1,340 ≈ 150,000.

  4. Solution 4

    How many passenger elevators are in service in New York City?

    Answer: About 70,000 elevators

    NYC has ~1M buildings. ~70,000 buildings with 4+ floors with an average of 1-2 elevators -> ~70k.

  5. Solution 5

    How many packages does Amazon ship per day in the United States?

    Answer: About 16,000,000 packages

    Amazon ships ~6 billion packages/year in the US. 6B / 365 ≈ 16.4M daily.

How to Pass the Fermi Estimation Screen

Break the quantity into factors you can each estimate, and say every assumption out loud.

Round to one significant figure as you go. The goal is the right order of magnitude, not three decimal places.

Cross-check with a second route. If two independent decompositions land within a factor of two, you can defend the answer.

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