Consulting & Case Interview Math Practice Guide

The truth is you do not need to be an expert mathematician to work as a consultant, still, you will need to do a lot of calculations when working in this field. 

The math concepts utilized in consulting are not more challenging than those studied from academic math. More exactly, it is different and attempting to solve problems the same way as in school will not be effective. 

This article will explain to you what makes math so important for aspiring consultants and provide you with some crucial math areas in which you need to be proficient in as well as how to best practice consulting math.

Do you need math in consulting or case interviews?

Math is omnipresent in case interviews…

This industry is known for its complex business problems and challenging strategic decisions, which require a strong foundation in mathematics. Thus, mathematics is a fundamental skill that is essential for success in consulting case interviews. 

Consulting companies usually use case interviews to test candidates' quantitative skills and problem-solving abilities, which means that proficiency in math is a must-have skill for any aspiring consultant.

Candidates who are proficient in math have a significant advantage in the case interview process. They are better equipped to analyze data, create models, and make informed decisions based on quantitative analysis. This is because math skills enable candidates to think logically and analytically, which is crucial in the consulting industry.

In addition to helping candidates solve complex business problems, good math skills can also help them to solve the case more efficiently. By quickly identifying the key data points and using mathematical formulas to analyze them, interviewees can save time and leave more time for insightful ideas and recommendations.

… because it’s always there in real consulting work

Additionally to case interviews, the consulting industry as a whole also places a high value on mathematical ability. Without a strong foundation in math, consultants may struggle to work effectively in their daily duty.

Math skills are essential for performing data analysis and modeling, which are crucial aspects of the consulting job. Consulting firms rely heavily on data-driven insights to deliver value to clients, and math skills are necessary to analyze data, identify patterns, and draw meaningful conclusions that can help clients make informed decisions.

Secondly, to develop engaging talks and reports that successfully illustrate information and suggestions, solid arithmetic skills are also required. 

These abilities are essential since clients rely on consultants to provide them with actionable insights that can drive their business forward. By using mathematical formulas and models, consultants can present complex data in a clear and concise manner, making it easier for clients to understand and act upon.

Furthermore, math skills are crucial for financial analysis, which is another critical aspect of the consulting job. Consultants must be able to analyze financial data, create financial models, and make informed decisions based on quantitative analysis. This requires a strong foundation in math, including knowledge of statistics, probability, and financial mathematics.

7 Types of math you need in consulting

Basic operations (add, subtract, multiply, divide)

Definition: Basic math refers to the fundamental arithmetic operations used in mathematics. It includes addition (+), subtraction (-), multiplication (x), and division (/), which are used to perform simple calculations and solve basic math problems.

These fundamental arithmetic operations are used in various calculations and are necessary for understanding more advanced math concepts. Basic math is used to calculate various metrics, ratios, and other complex work in consulting as well as case interviews. Without a strong foundation in basic math, it would be challenging to perform such calculations accurately and efficiently.

Example:

Suppose a consulting project requires calculating the total cost of producing 10,000 units of a product. The cost per unit is $50 for direct materials, $30 for direct labor, and $20 for overhead expenses. To calculate the total cost, we need to use addition and multiplication:

Total cost = (Direct materials cost per unit + Direct labor cost per unit + Overhead cost per unit) x Number of units

Total cost = ($50 + $30 + $20) x 10,000 = $1,000,000

Ratios and percentages

Definition: Ratio is a comparison of two or more quantities, while percentage is a ratio expressed as a fraction of 100. Ratios and percentages are used to express relationships between different variables and are commonly used in finance, statistics, and other fields.

Consultants frequently use ratios and percentages to analyze financial statements, assess market share, and evaluate operational performance. Additionally, they evaluate various scenarios and spot shifts over time using this kind of calculation.

Example:

Suppose a consulting project requires analyzing the profitability of a company. We need to calculate the gross profit margin, which is the ratio of gross profit to revenue expressed as a percentage. If the gross profit is $500,000 and the revenue is $1,000,000, we can calculate the gross profit margin as follows:

Gross profit margin = (Gross profit / Revenue) x 100%

Gross profit margin = ($500,000 / $1,000,000) x 100% = 50%

Management accounting formulas and principles

Definition: Accounting math is a set of mathematical principles and methods used in accounting to record, classify, and analyze financial data. It includes the calculation of various financial ratios, such as profit margin, return on investment, and debt-to-equity ratio, which are used to evaluate a company's financial health.

Accounting math involves the use of specific formulas and calculations to prepare financial statements, such as balance sheets, income statements, and cash flow statements. Consultants regularly have to use accounting math to interpret financial data, identify areas for improvement, and develop financial models.

Common accounting math formulas:

Balance Sheet Equation: Assets = Liabilities + Equity

Income Statement Equation: Revenue - Expenses = Net Income

Gross Margin Ratio = (Revenue - Cost of Goods Sold) / Revenue

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

Current Ratio = Current Assets / Current Liabilities

Example:

Suppose a consulting project requires analyzing the financial statements of a company. We need to calculate the current ratio, which is a measure of the company's liquidity. If the current assets are $1,000,000 and the current liabilities are $500,000, we can calculate the current ratio as follows:

Current ratio = Current assets / Current liabilities

Current ratio = $1,000,000 / $500,000 = 2

Basic finance formulas and principles

Definition: Finance math refers to the mathematical principles and methods used in finance to analyze and manage financial data. It includes the calculation of financial ratios, such as return on investment, net present value, and internal rate of return, which are used to evaluate investment opportunities and make financial decisions.

Finance math includes advanced financial modeling and analysis techniques, such as discounted cash flow analysis, net present value calculations, and internal rate of return analysis. Consultants will need to use finance math with purposes like evaluate investment opportunities, assess risk, and make strategic recommendations.

Common accounting math formulas:

Present Value (PV) = Future Value / (1+interest rate)^number of period

Future Value (FV) = Present Value x (1+interest rate)^number of period

Net Present Value (NPV) = sum of all present values of cash inflows - sum of all present values of cash outflows

Internal Rate of Return (IRR) = the interest rate at which the NPV of an investment is zero

Return on Investment (ROI) = (Gain from Investment - Cost of Investment) / Cost of Investment

Example:

Suppose a consulting project requires evaluating investment opportunities. We need to calculate the net present value (NPV) of an investment, which is the difference between the present value of cash inflows and the present value of cash outflows. If the cash inflows for the first year are $50,000 and the cash inflows for the second year are $100,000, and the discount rate is 10%, we can calculate the NPV as follows:

NPV = Cash inflow year 1 / (1 + Discount rate)^1 + Cash inflow year 2 / (1 + Discount rate)^2

NPV = $50,000 / (1 + 10%)^1 + $100,000 / (1 + 10%)^2 = $126,456.83

Basic statistics and probabilities

Definition: Probability is the branch of mathematics that deals with the study of random events and their likelihood of occurring. It involves calculating the probability of different outcomes based on the available information and using this information to make predictions.

Probability is used in consulting to assess the likelihood of different outcomes and events, and to develop risk management strategies. Consultants use probability to analyze market trends, identify potential risks, make forecasts, and develop contingency plans.

Example:

Suppose a consulting project requires analyzing customer data to identify patterns. We need to calculate the probability of a customer making a purchase given that they have visited the company's website. If the number of website visitors is 10,000 and the number of customers who made a purchase is 500, we can calculate the probability as follows:

Probability of purchase given website visit = Number of customers who made a purchase / Number of website visitors

Probability of purchase given website visit = 500 / 10,000 = 5%

“Weighted” calculations

Definition: This is a method of calculating a value based on the weights assigned to different variables. It is commonly used in finance and economics to determine the overall performance of a portfolio, and in other fields to calculate averages of different sets of data.

A weighted average is used to calculate the average of a set of numbers, with each number being multiplied by a corresponding weight. This type of math is very useful for consultants since it helps them to analyze financial data, such as revenue growth or customer satisfaction, and to develop performance metrics.

Example:

Suppose a consulting project requires analyzing survey data. We need to calculate the overall satisfaction score for a product, which is based on ratings for different features. If the ratings for feature A, B, and C are 3, 4, and 5 respectively, and the weights for these features are 30%, 40%, and 30% respectively, we can calculate the overall satisfaction score as follows:

Overall satisfaction score = Rating for feature A x Weight for feature A + Rating for feature B x Weight for feature B + Rating for feature C x Weight for feature C

Overall satisfaction score = 3 x 0.3 + 4 x 0.4 + 5 x 0.3 = 3.0

Exhibits (chart, tables, diagrams)

Definition: An exhibit is a graphical representation (chart) of data that is used to present information in a clear and easily understandable format. It can be used to display trends, patterns, and relationships between different variables, making it a useful tool for visualizing complex data sets.

Consultants need to use charts and graphs to present complex data and analysis in a clear and concise manner. They use various types of charts, such as pie charts, bar charts, and line graphs, to convey important information to clients and stakeholders. They also help consultants to identify trends and patterns in data, making it easier to draw meaningful conclusions and make informed suggestions.

This part of mathematics is quite diversified since there are numerous types of charts, tables, and diagrams, thus I cannot provide examples for every situation. Learn more at: Six types of chart in case interview

 

Consulting mental math

Why is mental math in consulting important?

This may also be categorized as a type of mathematics, but I've decided to address it separately to emphasize the significance it is. In the consulting industry, quick math is essential. Although the resulting numbers don't have to be 100% accurate (usually the error margin will be around 5%) , you will have to give a quick result.

In many circumstances, there is not a sufficient amount of time to get out a calculator, indeed, they are not even permitted in tests and case interviews. Hence, Mental math is a crucial component of an interview that frequently gets noticed by interviewers when it helps candidates to solve the questions and show their mental agility. 

When you have become a consultant, mental calculation is even more important since it not only helps us save a ton of time but also builds credibility with people around. You wouldn't want to look sluggish and perplexed in front of your managers, clients or interviewers, would you?

How to do mental math for consulting?

For our Comprehensive Math Drills, we have developed a methodical approach to mental calculations with large numbers, consisting of two main steps: ESTIMATION and ADJUSTMENT. This method is used for multiplication, division, and percentage.

Step 1 - Estimation

• Simplify the large numbers by taking out the zeroes (e.g. 6,700,000 becomes 6.7 and 000000)
• Round the resulting 1-to-2-digit numbers for easier calculations (e.g.: 6.7 becomes 7)

Step 2 - Adjustment

• Perform simple calculations with the multiplicands
• Adjust in the opposite direction of the previous rounding and put the zeroes back in

Step 3 - Percentages

• To do percentages, multiply the original number with the numerator then divide by 100.

Detail example:

• Multiplication: 1,234 x 5,678

Take out zeroes: 12.34 x 56.78 | 00 00

Round: 12 x 60 | 00 00

Calculate: 720 | 0 000

Adjust and add zeros: 7,200,000 (equal down-rounding and up-rounding roughly cancels each other out)

Accurate result: 7,006,652 | Error margin: 2.7%

• Division 8,509 / 45

Take out zeroes: 85 / 4.5 | 00 / 0

Round: 90 / 4.5 | 00 / 0

Calculate: 20 | 0

Adjust and add zeros: 190 (up-rounding means downward adjustment)

Accurate result: 189.09 | Error margin: 0.48%

• Percentage 70% of 15,940

Convert %: 0.7 x 15,940

Take out zeroes: 7 x 15.9 | One 0 in, three 0 out

Rounding: 7 x 16 | One 0 in, three 0 out

Calculate: 112 | One 0 in, three 0 out

Add zeros: 11,200

Adjust : 11,150 (up-rounding means downward adjustment)

Accurate result: 11,158 | Error margin: 0.07%

For percentage calculations, it is even easier with the “Zeroes management”. We know that the final answer will have roughly the same number of digits as the original 15,940, something like 1x,xxx or x,xxx. So when having 112 after step “Calculate”, we know the final answer would be close to 11,200.

Mental Math Tips:

• Write down numbers: it’s always a good idea to have a visual of the numbers themselves on paper. This makes it 100 times easier,  especially with “zeroes management” work.
• Sanity check: always take a very brief moment to ask yourself “is this result logical?”; if 70% of 15,940 equals 111,500, perhaps something is wrong with your “zeroes management”. Sometimes you can compare the outcome with another obvious data
• Shortcut percentages: convert percentages into easy, common calculations (e.g.: 33%, 25%, 20% into /3, /4, /5…) if possible. In fact, know as many of these shortcuts as you can.
• It is better to be long than to be wrong: If your mental math is not good and cannot calculate quickly, do not hesitate to ask for a little more time to get the most accurate answer.

Consulting math practice

Step 1: Learn about yourself

The first step to acing consulting math is to understand yourself, your strengths, your weaknesses and your needs. Assess your current skill level and identify areas where you need to improve. This can be done by reviewing your previous academic performance, past work experiences, and feedback from others.

One of the best ways to learn more about the consulting industry and the type of math skills required is to network with those who have experience in this field. They can provide valuable advice and insights on what to expect during tests/interviews and which math skills are most important. 

This is an extremely important step, but it might be challenging to carry out since many people do not know/have contact with any consultants, former consultants and interviewers. If there are a few people in your network, that's fantastic; if not, you can use our Coaching services to get the most reliable information from current consultants.

Step 2: Developing an actionable plan 

Once you have a clear understanding of yourself, you now need to establish a clear, actionable strategy to improve your consulting math skills. This plan should include a list of resources and activities that will help you promote self-study and focus on the areas that need the most improvement.

There are many resources available for consulting math practice, including online courses, textbooks, and practice mental exercise. You may also want to consider hiring a tutor or attending a community to receive personalized guidance and feedback.

When developing your plan, it is important to set realistic goals and establish a timeline for achieving them. This will help you stay motivated and track your progress along the way.

Step 3: Implement the plan

Now that you have a plan in place, it's time to implement it. Set aside dedicated time each day or week to practice your consulting math skills. Consistency is key, so make sure you stick to your schedule and do not skip any practice sessions.

When practicing, it is important to focus on understanding the underlying concepts rather than simply memorizing formulas and equations. Work through practice problems step-by-step and identify where you might be making mistakes. 

Moreover, reviewing your work and seeking feedback from others can help you improve your approach and increase your accuracy.

Step 4: Adjust the plan to best suit your capacity

Finally, It is crucial to modify your strategy as necessary to accommodate your capabilities. If you find that you are struggling with a particular concept or area, don't be afraid to pivot and adjust your plan accordingly. Consider seeking additional resources or seeking guidance from others who have experience.

At the same time, do NOT get too caught up in perfecting every aspect of consulting math is also matter. Recognize your strengths and weaknesses and focus on improving in areas where you can make the most progress. 

Remember that the goal is not to be perfect but to demonstrate your ability to approach and solve complex problems in a logical and efficient manner.

Common math mistakes in consulting 

Messing up formulas

The inability to apply the formula errors or mess up with numbers/signs is a common mistake made by candidates. Anyone may make this error because of both internal factors like mathematical confusion and external factors like time pressure.

To avoid this issue, you must first be cautious throughout the procedure, go step-by-step, and carefully examine the data and signs. If you need extra time, kindly request it, keep in mind that the important thing is getting the proper outcome. 

Secondly, practice using different formulas to solve various problems before the interview. Ensure that you have a clear understanding of when and how to apply each formula.

Excess or missing zeroes

Another common math mistake is losing units in calculations. When performing calculations, you must keep track of units to ensure that your answer is meaningful and relevant to the context of the problem. Losing units can make your answer meaningless and confusing, which could lead to wrong conclusions.

In order to avoid making this error, it's essential to label each step of your calculation and remember to carry the units as you work with them. Keeping your calculations well-organized will prevent you from losing track of the units. 

Another tip is try to reduce the unit of each metric as much as possible by assigning it to a term. For example, you can write “42,000,000” to “42M”. This will both ease your calculations and avoid confusion, but remember to add the units back to the final result 

Missing the bigger picture

The math done during a consulting case interview serves as a tool, not an end in and of itself. It is crucial to remember that calculations are part of a more significant business problem that you have to solve. 

Many candidates get wrapped up in calculations, arrive at the correct final number, but forget why they were doing the math and the real purpose of the number they have just found out.

To prevent this mistake, remember the significance of the figures you are calculating in the context of your particular business case. One tactic to use is to write the question asked at the top of your sheet before deep diving into your math. 

As you go through your calculation and as you prepare to present your solution, keep reminding yourself the question you were originally asked and ask yourself if the result you got from your calculation is actually answering it. Then when you explain your answer, do so in a way that clearly shows you understand what your final number means.