Business Problem Solving and Recommendations Questions

Frameworks and skills for taking ambiguous business questions through analysis to clear, actionable recommendations. Includes decomposing complex problems into analyzable components, identifying key drivers, selecting focused analyses, synthesizing data backed findings, and articulating specific next steps and implementation considerations. Emphasizes communicating recommendations in business terms, estimating potential impact when possible, acknowledging trade offs and limitations, prioritizing among multiple actions, and tailoring communication to different stakeholders. Covers translating research or analytic results into feasible product or operational changes and defending choices with evidence.

EasyTechnical

61 practiced

You need to estimate the minimum sample size for an A/B test where baseline conversion is 5%, desired minimum detectable effect is +0.8 percentage points, alpha=0.05, and power=0.8. Describe how you would compute this and which assumptions you must validate before launching the experiment. You can express formulas or describe tools you'd use.

EasyBehavioral

73 practiced

Tell me about a time you translated ambiguous analytic results into a clear recommendation for a business stakeholder. Briefly describe the situation, the analysis you ran, the recommendation you made, and how you handled uncertainty when presenting the outcome.

EasyTechnical

56 practiced

Write a PostgreSQL query to compute 7-day retention for users who signed up in a given week. Table: events(user_id, event_name, event_timestamp, signup_date). Define retention as share of users with any event between signup_date+1 and signup_date+7. Provide a query that returns cohort_week and retention_rate.

Sample Answer

Approach: build cohorts by week using each user’s signup_date, then check whether that user has any event between signup_date + 1 day and signup_date + 7 days (inclusive). Compute share of users retained per cohort.

sql

WITH users AS (
  -- one row per user with their signup_date
  SELECT DISTINCT user_id, signup_date::date AS signup_date
  FROM events
),
cohorts AS (
  SELECT
    user_id,
    signup_date,
    date_trunc('week', signup_date)::date AS cohort_week
  FROM users
),
retained AS (
  -- mark users who had any event in days 1..7 after signup
  SELECT
    c.cohort_week,
    c.user_id,
    CASE WHEN EXISTS (
      SELECT 1
      FROM events e
      WHERE e.user_id = c.user_id
        AND e.event_timestamp::date BETWEEN c.signup_date + INTERVAL '1 day' AND c.signup_date + INTERVAL '7 day'
    ) THEN 1 ELSE 0 END AS retained_flag
  FROM cohorts c
)
SELECT
  cohort_week,
  ROUND(100.0 * SUM(retained_flag)::numeric / NULLIF(COUNT(user_id), 0), 2) AS retention_rate_percent
FROM retained
GROUP BY cohort_week
ORDER BY cohort_week;

Key points:- cohort_week uses date_trunc('week') to group signups.- retained_flag uses EXISTS to avoid double-counting multiple events.- NULLIF prevents division-by-zero for empty cohorts.Edge cases: users with no events after signup, timezone issues in event_timestamp (cast to date), and ensuring signup_date is the true signup (use users table if available).

EasyTechnical

67 practiced

Your product manager reports an 8% month-over-month revenue drop and asks you to investigate and recommend next steps. Describe how you would decompose the problem into analyzable components (e.g., user segments, product funnels, pricing), which first 5 metrics you would compute, which data sources you would query, and an initial hypothesis you would validate.

HardTechnical

69 practiced

You must estimate annual revenue upside from converting 10% of dormant users to active. Available: total users, active users, average revenue per active user (ARPA), reactivation cost per user. Describe your back-of-the-envelope calculation, assumptions, sensitivity to key inputs, and how you'd present risk-adjusted ROI to stakeholders.

Sample Answer

Approach (one-line): estimate incremental annual revenue = #reactivated_users × ARPA − reactivation_costs; convert to ROI and show sensitivity & risk-adjusted figures.

Back-of-envelope calculation (formula + example):- Inputs: total_users (T), active_users (A), ARPA (R), reactivation_cost_per_user (C), target conversion of dormant = 10%.- Dormant = T − A. Reactivated = 0.10 × Dormant.- Incremental_revenue = Reactivated × R- Total_reactivation_cost = Reactivated × C- Net_uplift = Incremental_revenue − Total_reactivation_cost- ROI = Net_uplift / Total_reactivation_cost

Example numbers: T=1,000,000; A=200,000 → Dormant=800,000 → Reactivated=80,000.If R=$30/yr, C=$5 → Revenue = 80,000×30=$2.4M; Cost=80,000×5=$400k; Net=$2.0M; ROI=500%.

Key assumptions (call out & justify):- ARPA applies equally to reactivated users (assume no immediate churn or lower spend).- Reactivated users become “active” for a full year.- Reactivation cost is fully allocated per user (marketing + incentives).- No cannibalization of current active users’ spend.

Sensitivity analysis (what to vary):- Conversion rate (run scenarios at 5%, 10%, 20%)- ARPA (±20% to reflect lower engagement)- Reactivation cost (±50% for different channels)Present as a small table or tornado chart showing Net_uplift under each scenario; highlight break-even cost given assumed ARPA.

Risk-adjusted ROI & presentation to stakeholders:- Show three cases: conservative (5% conv, ARPA−20%), base (10%, ARPA), aggressive (20%, ARPA+10%). Report Net_uplift, payback period, and ROI.- Adjust for probability: assign likelihoods (e.g., 25%/50%/25%) to compute expected net uplift.- Include qualitative risks: data quality, attribution, reactivation short-lived, regulatory limits.- Recommend pilot: run a segmented A/B test (n≈10–50k) to measure conversion and short-term ARPA; present projected scaling with confidence intervals and suggested go/no-go thresholds.

Deliverable format: one-page dashboard with inputs, scenario table, sensitivity chart, break-even analysis, expected ROI and recommended pilot plan with metrics to validate assumptions.

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