Estimation & Analytical Thinking Questions

Estimation techniques (e.g., Fermi problems, back-of-the-envelope calculations) and analytical problem-solving approaches used in technical interviews and software engineering. Covers problem decomposition, quantitative reasoning, data interpretation, and constructing defensible assumptions to reach plausible conclusions.

HardTechnical

77 practiced

You have a prior belief that feature X has a 70% chance of increasing conversion by more than 1%. After a pilot of 1,000 users you observe a 0.8% uplift with p=0.2. Using Bayesian reasoning (qualitatively), explain how you would update your belief and decide whether to run a larger experiment. Include criteria for sample size and threshold for decision-making.

MediumTechnical

80 practiced

A partner integration will make 150,000 API calls per day to your service. Cloud billing is $0.40 per million requests and $0.12 per GB of outbound data. Average response size is 2KB. Estimate the incremental monthly cost (request + bandwidth) and propose ways to reduce recurring costs if needed.

MediumTechnical

74 practiced

Your SaaS product has $100k MRR, a monthly churn rate of 3%, and monthly new MRR additions of $5k. Estimate MRR after 6 months if churn remains constant and prices don't change. Show the month-by-month calculation or a closed-form approach, and state assumptions.

MediumTechnical

79 practiced

Describe how you'd use Monte Carlo simulation to estimate the distribution of expected revenue for a new product when conversion rates and ARPU are uncertain. Specify likely input distributions, number of simulation runs, outputs you'd report (percentiles, mean), and how you'd communicate results to stakeholders.

EasyTechnical

103 practiced

You're asked to estimate monthly ad impressions for a new social feature. As a PM, explain how you would decompose this estimation problem into subcomponents (users, sessions, impressions per session, etc.), what data sources you'd seek, and the order in which you'd resolve uncertainties to produce a defensible estimate.

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