Capital One·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

May 2026

Summary

Capital One data scientist case question, the math-heavy kind where they give you a full P&L setup and want you to derive unit volumes from a target margin. One question, pretty involved.

Questions Asked (1)

Given a two-product burger business with fixed prices, unit costs, a 2:3 vegan-to-classic sales mix, and $375M in fixed costs, how many total burgers need to be sold in Year 2 to hit a 34.43% profit margin? Set up and solve the equation from first principles.

Pricing & MonetizationProduct Analytics & Metrics

Author's notes

This took me longer to set up than I expected.

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Suggested Approach

Start by defining the profit margin equation from first principles: Profit = Revenue - Total Costs, and Profit Margin = Profit / Revenue. Express total revenue and total variable costs in terms of total burgers sold (N) using the given sales mix, then set up the equation with fixed costs and solve for N.

Pro tip: Double-check that your sales mix is applied correctly: if the ratio is vegan:classic = 2:3, then vegan burgers are 2/5 of total sales and classic are 3/5. Also, ensure you convert the profit margin percentage to a decimal before solving.

1. Define variables and given values

Let N be the total number of burgers sold. Let P_v and P_c be the prices of vegan and classic burgers, and C_v and C_c be their unit costs. The fixed costs are $375M. The sales mix is vegan:classic = 2:3, so vegan burgers = (2/5)N and classic burgers = (3/5)N.

2. Express total revenue and total variable costs

Total Revenue = P_v*(2/5)N + P_c*(3/5)N = N*(2P_v + 3P_c)/5. Total Variable Costs = C_v*(2/5)N + C_c*(3/5)N = N*(2C_v + 3C_c)/5. Total Costs = Total Variable Costs + Fixed Costs.

3. Set up the profit margin equation

Profit Margin = (Total Revenue - Total Costs) / Total Revenue = 0.3443. Substitute the expressions from step 2: [N*(2P_v+3P_c)/5 - (N*(2C_v+3C_c)/5 + 375,000,000)] / [N*(2P_v+3P_c)/5] = 0.3443.

4. Solve for N

Simplify the equation: Let R = (2P_v+3P_c)/5 and V = (2C_v+3C_c)/5. Then (N*R - N*V - 375M) / (N*R) = 0.3443. Rearrange: 1 - V/R - 375M/(N*R) = 0.3443. So, 375M/(N*R) = 1 - V/R - 0.3443. Thus, N = 375M / [R*(1 - V/R - 0.3443)] = 375M / [R - V - 0.3443R] = 375M / [0.6557R - V]. Plug in the actual price and cost values to compute N.

5. Verify and interpret

Check that the computed N makes sense (positive, integer). Ensure the profit margin calculation with N yields 34.43%. Discuss any assumptions, such as linearity and constant mix.

Key Points to Mention

Profit margin formula: (Revenue - Costs) / Revenue
Sales mix application: vegan = 2/5 of total, classic = 3/5
Fixed costs are independent of volume and must be covered
Variable costs scale with number of burgers sold
Solving for N requires isolating N in the equation
Assumption of constant sales mix and linear cost behavior

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