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Vlad

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6

Math for case interviews

I was just curious to know what kinds of math and algebra one should know for case interviews? The online web practice sites that randomize numbers are useful for helping you improve multiplication, addition, division, and so forth, but I am wondering what you might need to know beyond those basic. Everyone says that all you need for interviews is "back of the envelope" math, but I find that a bit misleading, as I've done fairly complicated practice problems on McK PST practice tests.

In other words, what kinds of math, besides the back of the envelope stuff, should one know and practice when preparing for case interviews?

Thanks.

I was just curious to know what kinds of math and algebra one should know for case interviews? The online web practice sites that randomize numbers are useful for helping you improve multiplication, addition, division, and so forth, but I am wondering what you might need to know beyond those basic. Everyone says that all you need for interviews is "back of the envelope" math, but I find that a bit misleading, as I've done fairly complicated practice problems on McK PST practice tests.

In other words, what kinds of math, besides the back of the envelope stuff, should one know and practice when preparing for case interviews?

Thanks.

(edited)

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Hi,

I recommend downloading all casebooks available online and check the math problems. You'll have a good list. Here are some of them to keep in mind:

  • Interest rates calculations
  • Compound margin
  • NPV using the Rule of 72, Perpetuity
  • CAGR using the Rule of 72
  • Currencies exchange calculations
  • Speed, time, distance calculations
  • Equations, systems of equations
  • Ratio & Proportions
  • Solving the problems by calculating the area (Integrals)
  • Profit / breakeven formula
  • Correlations, outliers (being able to spot on the graphs, tables)

Best

Hi,

I recommend downloading all casebooks available online and check the math problems. You'll have a good list. Here are some of them to keep in mind:

  • Interest rates calculations
  • Compound margin
  • NPV using the Rule of 72, Perpetuity
  • CAGR using the Rule of 72
  • Currencies exchange calculations
  • Speed, time, distance calculations
  • Equations, systems of equations
  • Ratio & Proportions
  • Solving the problems by calculating the area (Integrals)
  • Profit / breakeven formula
  • Correlations, outliers (being able to spot on the graphs, tables)

Best

(edited)

Hi Vlad, when would you need to calculate the integral? — Anonymous B on Feb 26, 2020

Hi Paul,

I’m a former McKinsey consultant, and the answer to your question is longer and more in-depth than can be covered in a simple message board post. I actually created an online course to teach the quantitative and mental calculation skills you need to succeed in Case Interviews called FastMath Ace the Case, and I have written some articles with more detail on this topic which are in in the PrepLounge Bootcamp section and on the FastMath site. You can learn more about the FastMath Ace the Case (and receive a 25% discount) at: http://www.fastmath.net/ace-the-case/?pc=preplounge_bc_001

Fast Math for Case Interviews

At a high level, the question of “what quant skills do you need for Case Interviews” is somewhat like asking what words should you know to become a successful writer. For a writer, it’s not so much the specific words you know, but how you put them together to create a story. With Case Interviews, it’s not so much the individual mathematical operations, but how you sequence them to perform relevant analysis and develop recommendations from the numerical results. It’s important to understand that Quantitative Analysis is an integral part of being a management consultant and therefore integral to the interview process. You can’t really be a management consultant without doing quantitative analysis.

You are correct in your intuition that “back of the envelope” math is not sufficient for Case Interviews. In most cases, you need to be very precise with your math (Market Sizing and compound growth calculations are exceptions). Luckily the numbers used in Case Interviews (what I will call Case Numbers) have certain properties that make them easier to calculate with. Case Numbers usually only have a few significant digits (like 20 Million), or are what I call Clean Numbers, which means they are a clean fraction times a power of 10. For example, a Case Number might be 25,000 which is equal to ¼ × 100,000. A Clean Numbers like 25,000 is a lot easier to calculate with — if you know the proper methods — than a generic five-digit number like 23,617. If you see resources with example numbers like 23,617, I don't believe it’s an effective resource to use to prepare for Case Interviews because you’ll be practicing brute force calculation skills you won’t need in actual interviews.

Quant Topics in Case Interviews

Case Interviews can cover a wide variety of quantitative topics, and it’s not practical or feasible to memorize detailed equations for all the scenarios you might encounter. Luckily the actual math concepts and formulas required in Case Interviews are relatively straight-forward.

Math Operations
You’ll need to do the following types of mathematical operations:

  • Addition and subtraction
  • Multiplication and division
  • Calculations with percentages and fractions (multiplication and division)

Quantitative Concepts
You’ll also need to understand the following concepts:

  • Solving linear equations (no quadratics or higher order functions)
  • Compound growth – and how to approximate it
  • Simple NPV calculations (e.g. perpetuities) and rule of 72
  • Weighted averages and expected value

These topics will cover 95% of Case interview quant problems. Now there are lots of business metrics that use the above operations, like gross margin, EBITDA margin, response rates, etc, but operations involved will be multiplication, division, addition and subtraction. The quant problems themselves might be complex, but if you can interpret the question properly, and understand it properly, you should be able to identify how to solve it (i.e. a proper sequence of mathematical operations), or develop an algebraic solution based on the parameters given. You won’t need to do complex DCF or arbitrary NVP calculations for the large management consulting firms, but you might need these advanced skills for certain Finance or PE interviews. I don’t think it’s worth practicing things like systems of equations, or calculating the area of a triangle, or precise currency exchange calculations for Case Interviews.

Many people make the mistake of studying more advanced concepts without mastering the above basic skills. So the next question is how can you better prepare for the quantitive component of Case Interviews. The first step I would recommend is learning how to calculate efficiently with Case Numbers. This is the first section of the FastMath Ace the Case online course. As mentioned, Case Numbers have specific properties that make them easier to calculate with if you know the proper methods. Next, learn how to use these methods to quickly solve Marketing Sizing and Estimation problems, and Breakeven and Profitability Analysis questions. Then, review the more advanced quant concepts like compound growth and NPV. Then study lots of Case Interview quant problems and the solution methods. This is basically the outline for the FastMath Ace the Case online course (http://www.fastmath.net/ace-the-case/?pc=preplounge_bc_001).

If you want to use other resources, I recommend only using consulting interview specific resources, like the cases on PrepLounge, or MBA case books. I have found other quant resources like GMAT or GRE prep resources to not be useful they’re not representative of actual Case Interview quant problems. Furthermore, other mental math resources usually, have generic numbers (like 89 + 117), but not numbers representative of Case Numbers, also aren’t useful. Even some Case Interview specific quant and mental math resources have example problems that I don’t believe are representation of Case Numbers e.g. multiplying by 237, or adding random numbers. In summary, you should be resources designed specifically for Case Interviews, and have problems that are representative of actual Case Interview problems.

For some information on myself, I’m a former McKinsey consultant and I have a Bachelor’s degree from Harvard with Highest Honors in Electrical and Computer Engineering, and an MBA from MIT Sloan. I have hosted workshops on quantitative interview skills at Harvard Business School, Wharton, MIT, London Business School, Georgetown, and other leading universities. Thousands of candidates from around the world have used FastMath Ace the Case to prepare for Case Interviews, and my students have joined elite firms such as McKinsey, Bain, BCG, PwC, Accenture, and Deloitte.

Fast Math for Case Interviews

Hi Paul,

I’m a former McKinsey consultant, and the answer to your question is longer and more in-depth than can be covered in a simple message board post. I actually created an online course to teach the quantitative and mental calculation skills you need to succeed in Case Interviews called FastMath Ace the Case, and I have written some articles with more detail on this topic which are in in the PrepLounge Bootcamp section and on the FastMath site. You can learn more about the FastMath Ace the Case (and receive a 25% discount) at: http://www.fastmath.net/ace-the-case/?pc=preplounge_bc_001

Fast Math for Case Interviews

At a high level, the question of “what quant skills do you need for Case Interviews” is somewhat like asking what words should you know to become a successful writer. For a writer, it’s not so much the specific words you know, but how you put them together to create a story. With Case Interviews, it’s not so much the individual mathematical operations, but how you sequence them to perform relevant analysis and develop recommendations from the numerical results. It’s important to understand that Quantitative Analysis is an integral part of being a management consultant and therefore integral to the interview process. You can’t really be a management consultant without doing quantitative analysis.

You are correct in your intuition that “back of the envelope” math is not sufficient for Case Interviews. In most cases, you need to be very precise with your math (Market Sizing and compound growth calculations are exceptions). Luckily the numbers used in Case Interviews (what I will call Case Numbers) have certain properties that make them easier to calculate with. Case Numbers usually only have a few significant digits (like 20 Million), or are what I call Clean Numbers, which means they are a clean fraction times a power of 10. For example, a Case Number might be 25,000 which is equal to ¼ × 100,000. A Clean Numbers like 25,000 is a lot easier to calculate with — if you know the proper methods — than a generic five-digit number like 23,617. If you see resources with example numbers like 23,617, I don't believe it’s an effective resource to use to prepare for Case Interviews because you’ll be practicing brute force calculation skills you won’t need in actual interviews.

Quant Topics in Case Interviews

Case Interviews can cover a wide variety of quantitative topics, and it’s not practical or feasible to memorize detailed equations for all the scenarios you might encounter. Luckily the actual math concepts and formulas required in Case Interviews are relatively straight-forward.

Math Operations
You’ll need to do the following types of mathematical operations:

  • Addition and subtraction
  • Multiplication and division
  • Calculations with percentages and fractions (multiplication and division)

Quantitative Concepts
You’ll also need to understand the following concepts:

  • Solving linear equations (no quadratics or higher order functions)
  • Compound growth – and how to approximate it
  • Simple NPV calculations (e.g. perpetuities) and rule of 72
  • Weighted averages and expected value

These topics will cover 95% of Case interview quant problems. Now there are lots of business metrics that use the above operations, like gross margin, EBITDA margin, response rates, etc, but operations involved will be multiplication, division, addition and subtraction. The quant problems themselves might be complex, but if you can interpret the question properly, and understand it properly, you should be able to identify how to solve it (i.e. a proper sequence of mathematical operations), or develop an algebraic solution based on the parameters given. You won’t need to do complex DCF or arbitrary NVP calculations for the large management consulting firms, but you might need these advanced skills for certain Finance or PE interviews. I don’t think it’s worth practicing things like systems of equations, or calculating the area of a triangle, or precise currency exchange calculations for Case Interviews.

Many people make the mistake of studying more advanced concepts without mastering the above basic skills. So the next question is how can you better prepare for the quantitive component of Case Interviews. The first step I would recommend is learning how to calculate efficiently with Case Numbers. This is the first section of the FastMath Ace the Case online course. As mentioned, Case Numbers have specific properties that make them easier to calculate with if you know the proper methods. Next, learn how to use these methods to quickly solve Marketing Sizing and Estimation problems, and Breakeven and Profitability Analysis questions. Then, review the more advanced quant concepts like compound growth and NPV. Then study lots of Case Interview quant problems and the solution methods. This is basically the outline for the FastMath Ace the Case online course (http://www.fastmath.net/ace-the-case/?pc=preplounge_bc_001).

If you want to use other resources, I recommend only using consulting interview specific resources, like the cases on PrepLounge, or MBA case books. I have found other quant resources like GMAT or GRE prep resources to not be useful they’re not representative of actual Case Interview quant problems. Furthermore, other mental math resources usually, have generic numbers (like 89 + 117), but not numbers representative of Case Numbers, also aren’t useful. Even some Case Interview specific quant and mental math resources have example problems that I don’t believe are representation of Case Numbers e.g. multiplying by 237, or adding random numbers. In summary, you should be resources designed specifically for Case Interviews, and have problems that are representative of actual Case Interview problems.

For some information on myself, I’m a former McKinsey consultant and I have a Bachelor’s degree from Harvard with Highest Honors in Electrical and Computer Engineering, and an MBA from MIT Sloan. I have hosted workshops on quantitative interview skills at Harvard Business School, Wharton, MIT, London Business School, Georgetown, and other leading universities. Thousands of candidates from around the world have used FastMath Ace the Case to prepare for Case Interviews, and my students have joined elite firms such as McKinsey, Bain, BCG, PwC, Accenture, and Deloitte.

Fast Math for Case Interviews

(edited)

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Hi Paul,

I agree that in consulting interviews you will have to deal with basic math only (the most complicated thing could probably be a discounted cash flow computation).

The most important thing in preparation would be not to prepare on simple math only, but on math with time pressure (eg doing exercises with a timer with a strict time constraint for each question). Many candidates do mistakes in areas they would not have any problem to deal with without pressure due to the fact they trained on math only, and not on math under pressure.

Best,

Francesco

Hi Paul,

I agree that in consulting interviews you will have to deal with basic math only (the most complicated thing could probably be a discounted cash flow computation).

The most important thing in preparation would be not to prepare on simple math only, but on math with time pressure (eg doing exercises with a timer with a strict time constraint for each question). Many candidates do mistakes in areas they would not have any problem to deal with without pressure due to the fact they trained on math only, and not on math under pressure.

Best,

Francesco

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Dear Paul,

Basically, it's mostly basic math calculation with some financial formulas. Just keep them in mind:

• Break-even Calculation = Fixed Cost / Contribution Margin; Fixed Cost / (Price – Variable Cost)

• Debt Ratio = Total Debt / Total Assets

• Debt-to-Equity Ratio = Total Debt / Total Equity

• Four Cs (marketing from a customer’s point of view): Convenience, Cost to the user, Communication, Customer needs and wants

• Four Ps (starting or expanding a business): Product, Price, Place, PromotionGross Profit = Sales – Cost of Goods Sold
Gross Profit Margin = Gross Profit / Total Revenue

• Profit = Total Revenue – Total Costs
• Return on Assets = Net Income / Total Assets
• Return on Equity = Net Income / Shareholder’s Equity
• Return on Investment = Net Income / Initial Investment
• SWOT Analysis: Strengths, Weaknesses, Opportunities, ThreatsTotals Costs = Fixed Costs + Variable Costs
• Total Revenue = Price x Volume

Hope it helps,

Best,

André

Dear Paul,

Basically, it's mostly basic math calculation with some financial formulas. Just keep them in mind:

• Break-even Calculation = Fixed Cost / Contribution Margin; Fixed Cost / (Price – Variable Cost)

• Debt Ratio = Total Debt / Total Assets

• Debt-to-Equity Ratio = Total Debt / Total Equity

• Four Cs (marketing from a customer’s point of view): Convenience, Cost to the user, Communication, Customer needs and wants

• Four Ps (starting or expanding a business): Product, Price, Place, PromotionGross Profit = Sales – Cost of Goods Sold
Gross Profit Margin = Gross Profit / Total Revenue

• Profit = Total Revenue – Total Costs
• Return on Assets = Net Income / Total Assets
• Return on Equity = Net Income / Shareholder’s Equity
• Return on Investment = Net Income / Initial Investment
• SWOT Analysis: Strengths, Weaknesses, Opportunities, ThreatsTotals Costs = Fixed Costs + Variable Costs
• Total Revenue = Price x Volume

Hope it helps,

Best,

André

Hi everyone,

Thanks for the replies. I guess I am talking about the kind of math beyond the basics and I think some good things have been mentioned. The reason I ask is that I was recently viewing a case on YouTube and the interviewee had a bunch of information and he just threw it out hastily in an algebraic formula, which I didn't understand. Cheng's site is great for improving your skills and I've seen a dramatic improvement in my skills since I've started using it. However, I can't help but feel that there is a good deal of math beyond this level that should also be known and I am not exactly sure how to go about preparing for these (algebra, percentages, fractions, probability, etc.). The concepts like NPV, ROI, and so on are fairly straightforward, but these more fundamental math problems are what has been causing me concern.

Thanks all

Hi everyone,

Thanks for the replies. I guess I am talking about the kind of math beyond the basics and I think some good things have been mentioned. The reason I ask is that I was recently viewing a case on YouTube and the interviewee had a bunch of information and he just threw it out hastily in an algebraic formula, which I didn't understand. Cheng's site is great for improving your skills and I've seen a dramatic improvement in my skills since I've started using it. However, I can't help but feel that there is a good deal of math beyond this level that should also be known and I am not exactly sure how to go about preparing for these (algebra, percentages, fractions, probability, etc.). The concepts like NPV, ROI, and so on are fairly straightforward, but these more fundamental math problems are what has been causing me concern.

Thanks all

Hi,

For interviews, basics maths is required. Let's break it into two different cateogry. Precise and Estimation with 20% accuracy. The math in both the categories remains same- addition, subtraction, divisiono and multiplication. However, it depends on the context what sort of answer is required, either precise or 20% close.

You can practice it on this platform or headover to Vcitor Cheng's website for free tool. That should suffice it.

Cheers!

Hi,

For interviews, basics maths is required. Let's break it into two different cateogry. Precise and Estimation with 20% accuracy. The math in both the categories remains same- addition, subtraction, divisiono and multiplication. However, it depends on the context what sort of answer is required, either precise or 20% close.

You can practice it on this platform or headover to Vcitor Cheng's website for free tool. That should suffice it.

Cheers!

Related BootCamp article(s)

Fast Math: How to Master Mental Math

Apply these tips and tricks for outstanding mental math shortcuts to impress your interviewer in your next case interview.

Quiz

Getting Up to Speed

In order to repeatedly demonstrate prerequisite skills under the pressure of a real case interview, you need to learn the basics and practice cases.

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