Management Consulting

Consulting Math interview questions

Consulting math interviews assess a candidate's ability to perform rapid, accurate calculations, structure complex problems, and communicate quantitative insights clearly under pressure. Interviewers look for logical problem-solving, estimation skills, and comfort with business metrics to evaluate analytical rigor.

15 questions (4 easy · 6 medium · 5 hard), each with what a strong answer covers and where people lose the point. Free to read, no account.

On this page (15 questions)
  1. 1.A company's sales increased from $250,000 last year to $300,000 this year. What is the percentage increase in sales?
  2. 2.If a product costs $1.75 and you sell 400 units, what is the total revenue?
  3. 3.A market has total annual sales of $500 million. Your company's sales in this market are $75 million. What is your market share?
  4. 4.A product sells for $20, and its cost of goods sold (COGS) is $12. What is the gross profit margin percentage?
  5. 5.Estimate the number of cars sold in the US last year.
  6. 6.Estimate the annual revenue of the coffee shop market in a major US city (e.g., Chicago).
  7. 7.A company sells 10,000 units at $50 each. Variable costs are $20 per unit, and total fixed costs are $150,000. What is the company's net profit? (Assume no taxes for simplicity).
  8. 8.A new product has fixed costs of $100,000. Its selling price is $25 per unit, and variable costs are $15 per unit. How many units must be sold to break even?
  9. 9.A marketing campaign costs $50,000 and is expected to generate an additional $150,000 in revenue. If the gross profit margin on this revenue is 40%, what is the ROI of the campaign?
  10. 10.A manufacturing company produces 50,000 units annually. Raw material costs are $5 per unit. If they can negotiate a 10% reduction in raw material costs, how much will their annual profit increase, assuming all other factors remain constant?
  11. 11.Estimate the annual market size (in USD) for electric scooter rentals in a major European capital (e.g., Paris).
  12. 12.A company is considering launching a new premium coffee blend. It expects to sell 20,000 units in the first year at $15 per unit. Variable costs are $7 per unit. Marketing costs are $50,000, and new equipment costs $30,000 (depreciated over 3 years). What is the net profit in the first year? (Assume no taxes).
  13. 13.A company is deciding between two investments. Investment A costs $200,000 and is expected to generate $75,000 in additional profit annually for 5 years. Investment B costs $150,000 and is expected to generate $60,000 in additional profit annually for 4 years. Which investment has a better ROI over its lifespan?
  14. 14.A software company currently sells its product for $100/month to 10,000 customers. They are considering increasing the price to $120/month, expecting a 15% churn rate due to the price hike. What is the impact on annual revenue?
  15. 15.A retail chain has 50 stores, each receiving 10 shipments per month. Each shipment costs $50 to transport. They are considering a new centralized distribution model that would reduce total shipments to 200 per month but increase the cost per shipment to $80 due to longer distances. What is the annual cost saving or increase?

1.A company's sales increased from $250,000 last year to $300,000 this year. What is the percentage increase in sales?

Warm-up

What a strong answer covers

  • Correctly identify the initial value ($250,000) and the final value ($300,000).
  • Apply the percentage increase formula: ((New Value - Old Value) / Old Value) * 100%.
  • Perform the subtraction, division, and multiplication accurately.
  • State the final percentage increase clearly.

Where people lose the point

  • Calculating the percentage change incorrectly by using the new value as the denominator.
  • Making arithmetic errors during the calculation steps.
  • Failing to express the final answer as a percentage.
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2.If a product costs $1.75 and you sell 400 units, what is the total revenue?

Warm-up

What a strong answer covers

  • Break down the multiplication into simpler, mental math-friendly steps (e.g., 1.75 * 100 * 4 or (2 - 0.25) * 400).
  • Perform the mental multiplication accurately and efficiently.
  • State the final total revenue clearly.

Where people lose the point

  • Making calculation errors, especially when dealing with decimals.
  • Not simplifying the multiplication, leading to more complex mental arithmetic.
  • Failing to articulate the steps taken to arrive at the answer.
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3.A market has total annual sales of $500 million. Your company's sales in this market are $75 million. What is your market share?

Warm-up

What a strong answer covers

  • Define market share as the company's sales divided by the total market sales.
  • Set up the calculation: $75 million / $500 million.
  • Perform the division accurately.
  • Express the result as a percentage.

Where people lose the point

  • Inverting the fraction (e.g., dividing total market sales by company sales).
  • Making arithmetic errors during the division.
  • Failing to convert the decimal result into a percentage.
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4.A product sells for $20, and its cost of goods sold (COGS) is $12. What is the gross profit margin percentage?

Warm-up

What a strong answer covers

  • Calculate the gross profit per unit (Selling Price - COGS).
  • Calculate the gross profit margin percentage using the formula: (Gross Profit / Selling Price) * 100%.
  • Perform the calculations accurately.
  • State the final gross profit margin percentage.

Where people lose the point

  • Using COGS as the denominator instead of the selling price when calculating the margin.
  • Making arithmetic errors in the subtraction or division.
  • Forgetting to multiply by 100 to express the result as a percentage.
Link to this question

5.Estimate the number of cars sold in the US last year.

Core

What a strong answer covers

  • Start with a reasonable estimate for the US population (e.g., 330 million).
  • Segment the population into households and estimate average household size.
  • Estimate the average number of cars per household and the average lifespan of a car.
  • Combine these assumptions to derive an annual car sales figure, clearly stating each assumption and the logic behind it.

Where people lose the point

  • Using an unrealistic or unstated US population figure.
  • Failing to break down the problem into logical, sequential steps.
  • Making assumptions without providing any justification or rationale.
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6.Estimate the annual revenue of the coffee shop market in a major US city (e.g., Chicago).

Core

What a strong answer covers

  • Start with Chicago's population (e.g., 2.7 million) and consider relevant demographics.
  • Estimate the percentage of the population that regularly consumes coffee from coffee shops.
  • Estimate the average frequency of coffee shop visits per person per week/month and the average price per coffee.
  • Multiply these factors to arrive at an estimated total annual revenue, clearly articulating all assumptions.

Where people lose the point

  • Overlooking key segments (e.g., tourists, students) or double-counting.
  • Making unrealistic assumptions for coffee consumption frequency or average price without justification.
  • Failing to clearly structure the market sizing approach (e.g., top-down) and state assumptions.
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7.A company sells 10,000 units at $50 each. Variable costs are $20 per unit, and total fixed costs are $150,000. What is the company's net profit? (Assume no taxes for simplicity).

Core

What a strong answer covers

  • Calculate total revenue by multiplying units sold by the selling price per unit.
  • Calculate total variable costs by multiplying units sold by the variable cost per unit.
  • Determine total costs by summing total variable costs and total fixed costs.
  • Calculate net profit by subtracting total costs from total revenue.

Where people lose the point

  • Confusing fixed and variable costs or misapplying them in calculations.
  • Making arithmetic errors in any of the multi-step calculations.
  • Failing to clearly articulate each step of the profitability calculation.
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8.A new product has fixed costs of $100,000. Its selling price is $25 per unit, and variable costs are $15 per unit. How many units must be sold to break even?

Core

What a strong answer covers

  • Calculate the contribution margin per unit (Selling Price per Unit - Variable Cost per Unit).
  • Apply the breakeven formula: Total Fixed Costs / Contribution Margin per Unit.
  • Perform the calculations accurately.
  • State the number of units required to break even.

Where people lose the point

  • Using the selling price per unit instead of the contribution margin per unit in the breakeven formula.
  • Making arithmetic errors during the calculation.
  • Failing to clearly define the contribution margin before using it.
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9.A marketing campaign costs $50,000 and is expected to generate an additional $150,000 in revenue. If the gross profit margin on this revenue is 40%, what is the ROI of the campaign?

Core

What a strong answer covers

  • Calculate the net profit generated by the campaign by applying the gross profit margin to the additional revenue.
  • Apply the ROI formula: ((Net Profit from Campaign - Cost of Campaign) / Cost of Campaign) * 100%.
  • Perform all calculations accurately.
  • Express the final ROI as a percentage.

Where people lose the point

  • Forgetting to apply the profit margin to the additional revenue, thus overstating profit.
  • Making arithmetic errors in the multi-step calculation.
  • Incorrectly setting up the ROI formula (e.g., dividing by profit instead of cost).
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10.A manufacturing company produces 50,000 units annually. Raw material costs are $5 per unit. If they can negotiate a 10% reduction in raw material costs, how much will their annual profit increase, assuming all other factors remain constant?

Core

What a strong answer covers

  • Calculate the current total annual raw material cost.
  • Calculate the new raw material cost per unit after the 10% reduction.
  • Determine the total annual savings from this reduction.
  • State that this saving directly translates to an increase in annual profit, assuming no other changes.

Where people lose the point

  • Applying the percentage reduction incorrectly (e.g., reducing total cost by 10% instead of per-unit cost).
  • Failing to calculate the total annual impact of the cost reduction.
  • Arithmetic errors in calculating the new cost or total savings.
Link to this question

11.Estimate the annual market size (in USD) for electric scooter rentals in a major European capital (e.g., Paris).

Hard

What a strong answer covers

  • Start with Paris's population and estimate the number of tourists annually.
  • Segment the population/tourists by likelihood to use scooters (e.g., age, lifestyle, purpose of travel).
  • Estimate average usage frequency (rides per user per year) and average ride duration/distance.
  • Estimate the average price per ride, considering pricing models (unlock fee + per minute).
  • Multiply these factors to arrive at an annual market size, clearly stating and justifying all assumptions, including potential seasonality or regulatory impacts.

Where people lose the point

  • Missing key user segments (e.g., residents vs. tourists) or failing to account for their different usage patterns.
  • Overlooking external factors like weather, public transport availability, or local regulations that impact usage.
  • Making unsubstantiated assumptions for usage frequency or pricing, leading to unrealistic estimates.
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12.A company is considering launching a new premium coffee blend. It expects to sell 20,000 units in the first year at $15 per unit. Variable costs are $7 per unit. Marketing costs are $50,000, and new equipment costs $30,000 (depreciated over 3 years). What is the net profit in the first year? (Assume no taxes).

Hard

What a strong answer covers

  • Calculate total revenue for the first year (Units * Selling Price).
  • Calculate total variable costs for the first year (Units * Variable Cost per Unit).
  • Identify and calculate total fixed costs for the first year, including marketing costs and the first year's depreciation of equipment (Equipment Cost / Depreciation Period).
  • Calculate total costs (Total Variable Costs + Total Fixed Costs).
  • Determine net profit by subtracting total costs from total revenue.

Where people lose the point

  • Incorrectly handling depreciation by expensing the full equipment cost in year one instead of depreciating it.
  • Misclassifying costs (e.g., treating equipment purchase as a one-time expense instead of a depreciable asset).
  • Making arithmetic errors in the multi-step calculation, especially with depreciation.
Link to this question

13.A company is deciding between two investments. Investment A costs $200,000 and is expected to generate $75,000 in additional profit annually for 5 years. Investment B costs $150,000 and is expected to generate $60,000 in additional profit annually for 4 years. Which investment has a better ROI over its lifespan?

Hard

What a strong answer covers

  • For Investment A, calculate the total profit generated over its 5-year lifespan.
  • For Investment B, calculate the total profit generated over its 4-year lifespan.
  • Calculate the ROI for Investment A using the formula: ((Total Profit - Cost) / Cost) * 100%.
  • Calculate the ROI for Investment B using the same formula.
  • Compare the two calculated ROIs and clearly state which investment offers a better return over its lifespan.

Where people lose the point

  • Failing to consider the full lifespan of each investment when calculating total profit.
  • Making arithmetic errors in calculating total profits or the ROI percentages.
  • Not clearly articulating the comparison and the rationale for choosing one investment over the other.
Link to this question

14.A software company currently sells its product for $100/month to 10,000 customers. They are considering increasing the price to $120/month, expecting a 15% churn rate due to the price hike. What is the impact on annual revenue?

Hard

What a strong answer covers

  • Calculate the current annual revenue (Current Price * Number of Customers * 12 months).
  • Calculate the number of customers remaining after the 15% churn rate.
  • Calculate the new annual revenue with the increased price and the reduced customer base.
  • Determine the net impact on annual revenue by comparing the new annual revenue to the current annual revenue.

Where people lose the point

  • Incorrectly calculating the number of customers after churn (e.g., applying churn to the new price instead of the customer count).
  • Making arithmetic errors in any of the multi-step calculations.
  • Failing to clearly state the net impact (increase or decrease) on annual revenue.
Link to this question

15.A retail chain has 50 stores, each receiving 10 shipments per month. Each shipment costs $50 to transport. They are considering a new centralized distribution model that would reduce total shipments to 200 per month but increase the cost per shipment to $80 due to longer distances. What is the annual cost saving or increase?

Hard

What a strong answer covers

  • Calculate the current total monthly shipments (Number of Stores * Shipments per Store).
  • Calculate the current total monthly transport cost (Current Total Shipments * Cost per Shipment).
  • Calculate the new total monthly transport cost under the centralized model (New Total Shipments * New Cost per Shipment).
  • Determine the monthly cost difference (Current Monthly Cost - New Monthly Cost).
  • Multiply the monthly difference by 12 to find the annual cost saving or increase.

Where people lose the point

  • Making arithmetic errors in any of the multi-step calculations.
  • Failing to convert the monthly cost impact to an annual figure.
  • Incorrectly identifying whether the change results in a saving or an increase.
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A company's sales increased from $250,000 last year to $300,000 this year. What is the percentage increase in sales?

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How Consulting Math answers get judged

The weights a Consulting Math interviewer is holding, whether or not they say so out loud. Round Zero scores your practice answers against exactly these, and quotes your own words back as the evidence for each.

Accuracy of Calculations

40%

The extent to which all numerical calculations are precise and free of arithmetic errors.

Logical Approach & Structure

30%

The clarity and logical flow of the problem-solving methodology, including breaking down complex problems into manageable steps.

Reasonable Assumptions & Justification

15%

The ability to make reasonable, defensible assumptions when exact data is unavailable, and to clearly articulate the rationale behind them.

Clarity of Communication

15%

The ability to clearly articulate the thought process, assumptions, and final results in a structured and understandable manner.

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Practising Consulting Math: common questions

What Consulting Math interview questions should I practice?
Start with the core areas Consulting Math interviewers probe: A company's sales increased from $250,000 last year to $300,000 this year. What is the percentage increase in sales; If a product costs $1.75 and you sell 400 units, what is the total revenue; A market has total annual sales of $500 million. Your company's sales in this market are $75 million. What is your market share. This page outlines strong answers and common mistakes, and the scored path drills each one with follow-ups.
Is the Consulting Math practice free?
Yes. The Consulting Math path runs free inside Round Zero: lessons, practice questions and flashcards. Drills are unlimited on every plan, free included. So is the full scorecard. Free also covers 3 complete scored interviews, no card.
How is this different from a Consulting Math question list?
A static list gives you questions with no feedback. Round Zero runs a live scored practice that probes your actual answers, rotates difficulty, and tells you exactly what to fix, grounded in a Consulting Math rubric.
How should I prepare for a Consulting Math interview?
Learn the concepts, drill the questions until answers come fast, then prove it in a scored mock. Round Zero sequences all three so you know you are ready, not just that you read about Consulting Math.
How is a Consulting Math answer scored?
Consulting Math answers are scored on accuracy of calculations, logical approach & structure, reasonable assumptions & justification, clarity of communication, with evidence quoted from what you actually said, so feedback is specific instead of generic praise.