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I went top-down: California population, average household size, cars per household, how often people fill up, then backed into station count by capacity.
Break the problem down using a top-down estimation approach: start with California's population, estimate the number of vehicles, and then determine how many gas stations are needed to serve them. State your assumptions clearly and calculate step by step, focusing on logical reasoning rather than the exact number.
Pro tip: Acknowledge that this is a Fermi problem and that the process matters more than the precise answer; show your work and sanity-check your final number against known benchmarks (e.g., ~10,000 stations in California).
Confirm whether the question refers to all gas stations (including those at grocery stores) or only standalone stations, and whether it's for personal vehicles or all vehicles. This shows attention to detail.
Use a known figure: approximately 40 million people. Then estimate the number of vehicles: assume about 2 people per household and 1.5 vehicles per household, or simply 0.8 vehicles per capita, yielding ~32 million vehicles.
Calculate how many vehicles a typical gas station can serve. Assume each station has 8 pumps, each pump serves 2 cars per hour, and operates 12 hours a day, serving ~200 cars per day. Alternatively, use average fuel sold per station per day.
Divide total vehicles by the number of vehicles served per station per day, adjusting for frequency of refueling (e.g., once a week). For example, if each vehicle refuels weekly, total weekly refuels = 32M, and if each station serves 1,400 cars per week (200/day * 7), then stations = 32M / 1,400 ≈ 22,857. Sanity-check against known data.
Compare your estimate to known benchmarks (e.g., California has about 10,000 gas stations). If off, adjust assumptions (e.g., higher throughput per station) and explain discrepancies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.