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.
MediumTechnical
0 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.
EasyTechnical
0 practiced
As a product manager, explain what a Fermi estimation is and walk through a Fermi-style estimate for the classic prompt: 'How many piano tuners are there in New York City?' State your assumptions clearly, show arithmetic steps and orders of magnitude, and explain how you'd communicate confidence in the result to stakeholders.
MediumTechnical
0 practiced
Engineering estimates that reducing median page load from 800ms to 300ms will cost $150k/year in infrastructure and dev effort. Given current monthly revenue of $500k and an expected 2% retention improvement per 100ms reduction in load time, construct a simple analysis to determine whether the investment is justified. Show calculations and state assumptions.
MediumTechnical
0 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
0 practiced
You plan an A/B test to detect a 1 percentage point lift on a baseline conversion rate of 5% at 80% power and 5% significance. As a PM, estimate the required sample size per variant (order of magnitude), explain the intuition behind the formula, and suggest pragmatic strategies to reduce the required sample size.
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