Master Quantitative Interview Questions with Interview Math: Over 50 Problems and Solutions

Interview Math: Over 50 Problems and Solutions for Quant Case Interview Questions

If you are preparing for a case interview at a top consulting firm, you know that you need to master quantitative skills. Case interviews are not only about solving business problems, but also about demonstrating your ability to think logically, analytically, and creatively under pressure.

InterviewMathOver50ProblemsandSolutionsforQuantCaseInterviewQuestionsdownloadpdf

But how do you practice these skills effectively? How do you tackle different types of quantitative questions that may come up in case interviews? How do you avoid common mistakes and pitfalls that may cost you your dream job?

That's where Interview Math: Over 50 Problems and Solutions for Quant Case Interview Questions by Lewis C. Lin comes in. This book is a comprehensive guide that provides you with 50+ practice problems and detailed answers to help you master quantitative interview questions.

In this article, we will give you a summary of the main topics covered in the book, the benefits of reading it, and some tips on how to use it effectively. We will also provide you with some examples of quantitative questions and solutions from the book, as well as some frequently asked questions about the book and the author.

Market Sizing

Market sizing is one of the most common types of quantitative questions that you may encounter in case interviews. Market sizing involves estimating the size or potential of a market, such as the number of customers, revenue, or units sold.

Market sizing is important because it helps you assess the attractiveness and feasibility of a business opportunity, as well as identify key drivers and assumptions behind your analysis. Market sizing also tests your ability to break down complex problems into simpler components, use logical reasoning, and make reasonable estimates based on available data or common sense.

There are two main types of market sizing questions: top-down and bottom-up. Top-down questions start with a large population or market and apply filters or segments to narrow it down to a specific target market. Bottom-up questions start with a small unit or customer and multiply it by the number of units or customers in the market.

Here are some examples of market sizing questions and solutions from the book:

• How many golf balls are sold in the US each year?

This is a top-down question. We can start with the total population of the US, which is about 330 million. Then we can estimate the percentage of people who play golf, which is about 10%. That gives us 33 million golfers. Next, we can estimate the average number of golf balls that each golfer buys per year, which is about 20. That gives us 660 million golf balls. Finally, we can adjust for any factors that may affect the demand, such as seasonality, price, quality, etc. For simplicity, we can assume that these factors cancel out each other and keep our estimate at 660 million golf balls.

• How much revenue does Starbucks make from selling coffee in New York City in a day?

This is a bottom-up question. We can start with the average revenue per cup of coffee, which is about $3. Then we can estimate the number of cups of coffee that each Starbucks store sells per day, which is about 500. That gives us $1,500 per store per day. Next, we can estimate the number of Starbucks stores in New York City, which is about 300. That gives us $450,000 per day for all stores. Finally, we can adjust for any factors that may affect the revenue, such as location, competition, promotions, etc. For simplicity, we can assume that these factors cancel out each other and keep our estimate at $450,000 per day.

Revenue Estimates

Revenue estimates are another common type of quantitative questions that you may encounter in case interviews. Revenue estimates involve estimating the revenue or sales of a company, product, or service.

Revenue estimates are important because they help you evaluate the performance and growth potential of a business, as well as identify key drivers and assumptions behind your analysis. Revenue estimates also test your ability to use data sources, apply formulas, and make projections based on trends and scenarios.

There are two main types of revenue estimates questions: historical and future. Historical questions ask you to estimate the revenue or sales of a company, product, or service in the past based on available data or information. Future questions ask you to estimate the revenue or sales of a company, product, or service in the future based on assumptions or scenarios.

Here are some examples of revenue estimates questions and solutions from the book:

• How much revenue did Netflix make from streaming in 2019?

This is a historical question. We can use data sources such as Netflix's annual report or website to find the relevant information. According to Netflix's annual report for 2019, Netflix had 167 million paid streaming memberships worldwide at the end of 2019. The average monthly revenue per membership was $10.40. Therefore, the annual revenue from streaming was 167 million x $10.40 x 12 = $20.8 billion.

• How much revenue will Uber make from ridesharing in 2025?

This is a future question. We need to make some assumptions or scenarios to project the revenue. One possible scenario is based on the growth rate and market share of Uber. We can assume that Uber's current revenue from ridesharing is $10 billion and its current market share is 20%. We can also assume that the total ridesharing market will grow at 10% annually and Uber will maintain its market share at 20%. Therefore, the total ridesharing market in 2025 will be $10 billion x (1 + 0.1)^6 = $17.9 billion and Uber's revenue from ridesharing in 2025 will be $17.9 billion x 0.2 = $3.6 billion.

Profitability

Profitability is another common type of quantitative questions that you may encounter in case interviews. Profitability involves estimating the profit or margin of a company, product, or service.

Breakeven

Breakeven is another common type of quantitative questions that you may encounter in case interviews. Breakeven involves finding the point where the revenue and cost of a company, product, or service are equal.

Breakeven is important because it helps you determine the feasibility and viability of a business opportunity, as well as identify key drivers and assumptions behind your analysis. Breakeven also tests your ability to use formulas, solve equations, and manipulate variables.

There are two main types of breakeven questions: unit and dollar. Unit breakeven questions ask you to find the number of units that need to be sold to break even. Dollar breakeven questions ask you to find the amount of revenue that needs to be generated to break even.

Here are some examples of breakeven questions and solutions from the book:

• How many iPhones does Apple need to sell to break even on its R&D costs?

This is a unit breakeven question. We need to use the formula: Breakeven units = Fixed costs / Contribution margin per unit. Fixed costs are the costs that do not vary with the number of units sold, such as R&D costs. Contribution margin per unit is the difference between the selling price and the variable cost per unit. Variable costs are the costs that vary with the number of units sold, such as materials and labor. We can assume that Apple's R&D costs are $10 billion and its selling price per iPhone is $1,000. We can also assume that its variable cost per iPhone is $500. Therefore, the contribution margin per iPhone is $1,000 - $500 = $500. Using the formula, we get: Breakeven units = $10 billion / $500 = 20 million iPhones.

• How much revenue does Netflix need to generate to break even on its content costs?

This is a dollar breakeven question. We need to use the formula: Breakeven revenue = Fixed costs / Contribution margin ratio. Fixed costs are the costs that do not vary with the amount of revenue generated, such as content costs. Contribution margin ratio is the percentage of revenue that remains after deducting variable costs. Variable costs are the costs that vary with the amount of revenue generated, such as marketing and distribution. We can assume that Netflix's content costs are $15 billion and its contribution margin ratio is 40%. Using the formula, we get: Breakeven revenue = $15 billion / 0.4 = $37.5 billion.

Pricing

Pricing is another common type of quantitative questions that you may encounter in case interviews. Pricing involves finding the optimal price or strategy for a company, product, or service.

Pricing is important because it helps you maximize the profit or value of a business opportunity, as well as understand the customer behavior and market dynamics behind your analysis. Pricing also tests your ability to use frameworks, models, and scenarios to evaluate different pricing options.

There are two main types of pricing questions: cost-based and value-based. Cost-based pricing questions ask you to find the price based on the cost structure and a target margin or markup. Value-based pricing questions ask you to find the price based on the customer's willingness to pay and the competitive landscape.

Here are some examples of pricing questions and solutions from the book:

• How would you price a new smartphone app?

This is a value-based pricing question. We need to use a framework or model to estimate the customer's willingness to pay and the competitive landscape. One possible framework is the Van Westendorp Price Sensitivity Meter, which uses four questions to elicit customer feedback on pricing: 1) At what price would you consider the app to be so expensive that you would not consider buying it? 2) At what price would you consider the app to be priced so low that you would feel the quality is too low? 3) At what price would you consider the app to be starting to get expensive, but you still might consider buying it? 4) At what price would you consider the app to be a bargaina great buy for the money? Based on the answers to these questions, we can plot a graph and find the optimal price range where most customers are willing to pay and perceive value. We can also compare this price range with the prices of similar or substitute apps in the market and adjust accordingly.

• How would you price a new electric car?

This is a cost-based pricing question. We need to use the formula: Price = Cost + Margin. Cost is the total cost of producing and delivering the car, including fixed and variable costs. Margin is the percentage of profit that we want to make on each car. We can assume that the cost of producing and delivering a new electric car is $30,000 and we want to make a 20% margin on each car. Using the formula, we get: Price = $30,000 + 0.2 x $30,000 = $36,000.

Customer Lifetime Value

Customer lifetime value is another common type of quantitative questions that you may encounter in case interviews. Customer lifetime value involves estimating the present value of the future cash flows generated by a customer over their lifetime.

Customer lifetime value is important because it helps you measure the long-term profitability and loyalty of a customer, as well as prioritize and allocate resources for customer acquisition and retention. Customer lifetime value also tests your ability to use formulas, discount rates, and retention rates to calculate the value of a customer.

There are two main types of customer lifetime value questions: simple and complex. Simple questions ask you to find the customer lifetime value based on a single purchase or subscription. Complex questions ask you to find the customer lifetime value based on multiple purchases or subscriptions over time.

Here are some examples of customer lifetime value questions and solutions from the book:

• How much is a Netflix customer worth?

This is a simple question. We need to use the formula: Customer lifetime value = Average revenue per customer x Customer lifetime. Average revenue per customer is the amount of money that a customer pays to Netflix per month or year. Customer lifetime is the number of months or years that a customer stays with Netflix. We can assume that the average revenue per customer is $10 per month and the customer lifetime is 3 years. Using the formula, we get: Customer lifetime value = $10 x 12 x 3 = $360.

• How much is a Starbucks customer worth?

This is a complex question. We need to use the formula: Customer lifetime value = (Average revenue per customer x Gross margin) / (1 + Discount rate - Retention rate). Average revenue per customer is the amount of money that a customer spends at Starbucks per visit or per year. Gross margin is the percentage of revenue that remains after deducting the cost of goods sold. Discount rate is the interest rate used to discount future cash flows to present value. Retention rate is the percentage of customers who return to Starbucks in a given period. We can assume that the average revenue per customer is $5 per visit, the gross margin is 70%, the discount rate is 10%, and the retention rate is 80%. Using the formula, we get: Customer lifetime value = ($5 x 0.7) / (1 + 0.1 - 0.8) = $17.5.

Other Quantitative Topics

Besides the topics mentioned above, there are some other quantitative topics that may come up in case interviews, such as growth rate, market share, elasticity, break-even analysis, net present value, internal rate of return, payback period, etc.

These topics are important because they help you analyze different aspects and scenarios of a business problem, such as how fast or slow a market or company is growing, how much or little a market or company is capturing, how sensitive or responsive customers are to price changes, how long or short it takes for an investment to recover its initial cost, etc.

To prepare for these topics, you need to familiarize yourself with the definitions, formulas, and applications of these concepts and principles. You also need to practice using different data sources, tools, and methods to calculate and interpret these metrics and indicators.

Here are some examples of other quantitative topics questions and solutions from the book:

• What is the growth rate of Netflix's streaming revenue from 2018 to 2019?

According to Netflix's annual report for 2019, Netflix's streaming revenue in 2019 was $20.2 billion and in 2018 was $15.8 billion. Using the formula, we get: Growth rate = ($20.2 billion - $15.8 billion) / $15.8 billion = 0.28 or 28%.

• What is the market share of Uber in the US ridesharing market?

This is a market share question. We need to use the formula: Market share = Company's revenue / Total market revenue. Company's revenue is the amount of money that a company makes from its product or service in a given market. Total market revenue is the amount of money that all companies make from their products or services in a given market. We can use data sources such as industry reports or websites to find these values. We can assume that Uber's revenue from ridesharing in the US in 2019 was $10 billion and the total ridesharing market revenue in the US in 2019 was $25 billion. Using the formula, we get: Market share = $10 billion / $25 billion = 0.4 or 40%.

• What is the price elasticity of demand for Netflix's streaming service?

This is an elasticity question. We need to use the formula: Price elasticity of demand = Percentage change in quantity demanded / Percentage change in price. Percentage change in quantity demanded is the relative change in the number of units that customers buy when the price changes. Percentage change in price is the relative change in the price of the product or service. We can use data sources such as surveys or experiments to find these values. We can assume that when Netflix increased its monthly subscription price from $10 to $12, its number of paid streaming memberships decreased from 167 million to 160 million. Using the formula, we get: Price elasticity of demand = (160 million - 167 million) / 167 million / ($12 - $10) / $10 = -0.28 / 0.2 = -1.4.

Conclusion

In this article, we have given you a summary of Interview Math: Over 50 Problems and Solutions for Quant Case Interview Questions by Lewis C. Lin, a comprehensive guide that provides you with 50+ practice problems and detailed answers to help you master quantitative interview questions.

We have covered the main topics that are covered in the book, such as market sizing, revenue estimates, profitability, breakeven, pricing, customer lifetime value, and other quantitative topics. We have also provided you with some examples of quantitative questions and solutions from the book, as well as some frequently asked questions about the book and the author.

If you are preparing for a case interview at a top consulting firm, you should definitely read this book and practice interview math questions regularly. This will help you improve your quantitative skills, confidence, and performance in case interviews.

To get a copy of the book or download a PDF version, you can visit Amazon.com or Lewis C. Lin's website at www.lewis-lin.com.

FAQs

• Q1: Who is the author of the book and what is his background?

A1: The author of the book is Lewis C. Lin, a former McKinsey consultant and Google product manager who has coached thousands of candidates for case interviews at top consulting firms and tech companies. He is also the founder and CEO of Impact Interview, an interview coaching firm that helps job seekers land their dream jobs.

• Q2: How can I get a copy of the book or download a PDF version?

A2: You can get a copy of the book or download a PDF version from Amazon.com or Lewis C. Lin's website at www.lewis-lin.com.

• Q3: How can I contact the author or get more information about his services?

A3: You can contact the author or get more information about his services by visiting his website at www.lewis-lin.com or emailing him at lewis@lewis-lin.com.

• Q4: How can I improve my mental math skills for case interviews?

A4: You can improve your mental math skills for case interviews by practicing regularly, using shortcuts and tricks, and checking your calculations. You can also use online tools or apps such as Mental Math, Math Workout, or Math Tricks to sharpen your mental math skills.

• Q5: How can I ace case interviews and land a job at a top consulting firm?

A5: You can ace case interviews and land a job at a top consulting firm by preparing well, practicing a lot, and performing well. You should prepare well by researching the firm, the industry, and the role that you are applying for. You should practice a lot by doing mock interviews with peers, mentors, or coaches, and getting feedback on your strengths and weaknesses. You should perform well by demonstrating your problem-solving, communication, and interpersonal skills, as well as your fit and motivation for the firm and the role. 71b