what is case study questions in maths

Case interview maths (formulas, practice problems, and tips)

Today we’re going to give you everything you need in order to breeze through maths calculations during your case interviews. 

Becoming confident with maths skills is THE first step that we recommend to candidates like Karthik , who got an offer from McKinsey. 

And one of the first things you’ll need to know are the 6 core maths formulas that are used extensively in case interviews. 

Let’s dive in!

• Case interview maths formulas
• Must-know formulas
• Optional formulas
• Cheat sheet
• Practice questions
• Case maths apps and tools
• Tips and tricks
• Practice with experts

Click here to practise 1-on-1 with MBB ex-interviewers

1. case interview maths formulas, 1.1. must-know maths formulas.

Here’s a summarised list of the most important maths formulas that you should really master for your case interviews:

If you want to take a moment to learn more about these topics, you can read our in-depth article about  finance concepts for case interviews .

1.2. Optional maths formulas

In addition to the above, you may also want to learn the formulas below. 

Having an in-depth understanding of the business terms below and their corresponding formulas is NOT required to get offers at McKinsey, BCG, Bain and other firms. But having a rough idea of what they are can be handy.

EBITDA = Earnings Before Interest Tax Depreciation and Amortisation

EBIDTA is essentially profits with interest, taxes, depreciation and amortisation added back to it.

It's useful for comparing companies across industries as it takes out the accounting effects of debt and taxes which vary widely between, say, Meta (little to no debt) and ExxonMobil (tons of debt to finance infrastructure projects). More  here .

NPV = Net Present Value

NPV tells you the current value of one or more future cashflows. 

For example, if you have the option to receive one of the two following options, then you could use NPV to choose the more profitable option:

• Option 1 : receive $100 in 1 year and $100 in 2 years
• Option 2 : receive $175 in 1 year

If we assume that the interest rate is 5% then option 1 turns out to be slightly better. You can learn more about the formula and how it works  here .

Return on equity = Profits / Shareholder equity

Return on equity (ROE) is a measure of financial performance similar to ROI. ROI is usually used for standalone projects while ROE is used for companies. More  here .

Return on assets = Profits / Total assets

Return on assets (ROA) is an alternative measure to ROE and a good indicator of how profitable a company is compared to its total assets. More  here .

1.3 Case interview maths cheat sheet

If you’d like to get a free PDF cheat sheet that summarises the most important formulas and tips from this case interview maths guide, just click on the link below.

Download free pdf case interview maths cheat sheet

2. Case interview maths practice questions

If you’d like some examples of case interview maths questions, then this is the section for you!

Doing maths calculations is typically just one step in a broader case, and so the most realistic practice is to solve problems within the context of a full case.

So, below we’ve compiled a set of maths questions that come directly from  case interview examples  published by McKinsey and Bain. 

We recommend that you try solving each problem yourself before looking at the solution. 

Now here’s the first question!

2.1 Payback period - McKinsey case example

This is a paraphrased version of question 3 on  McKinsey’s Beautify practice case :

How long will it take for your client to make back its original investment, given the following data?

• After the investment, you’ll get 10% incremental revenue
• You’ll have to invest €50m in IT, €25m in training, €50m in remodeling, and €25m in inventory
• Annual costs after the initial investment will be €10m 
• The client’s annual revenues are €1.3b

Note: take a moment to try solving this problem yourself, then you can get the answer under  question 3 on McKinsey’s website . 

2.2 Cost reduction - McKinsey case example

This is a paraphrased version of question 2 on  McKinsey’s Diconsa practice case :

How much money in total would families in rural Mexico save per year if they could pick up benefits payments from Diconsa stores?

• Pick up currently costs 50 pesos per month for each family
• If pick up were available at Diconsa stores, the cost would be reduced by 30%
• Assume that the population of Mexico is 100m 
• 20% of Mexico’s population is in rural areas, and half of these people receive benefits
• Assume that all families in Mexico have 4 members

Note: take a moment to try solving this problem yourself, then you can get the answer under  question 2 on McKinsey’s website . 

2.3 Product launch - McKinsey case maths example

This is a paraphrased version of question 2 on  McKinsey’s Electro-Light practice case :

What share of the total electrolyte drink market would the client need in order to break even on their new Electro-Light drink product?

• The target price for Electro-Light is $2 for each 16 oz (1/8th gallon) bottle
• Electro-Light would require $40m in fixed costs
• Each bottle of Electro-Light costs $1.90 to produce and deliver
• The electrolyte drink market makes up 5% of the US sports-drink market
• The US sports-drink market sells 8b gallons of beverages per year

2.4 Pricing strategy - McKinsey case maths example

This is a paraphrased version of question 3 on  McKinsey’s Talbot Trucks practice case :

What is the highest price Talbot Trucks can charge for their new electric truck, such that the total cost of ownership is equal to diesel trucks? 

• Assume the total cost of ownership for all trucks consists of these 5 components: driver, depreciation, fuel, maintenance, other. 
• A driver costs €3k/month for diesel and electric trucks
• Diesel trucks and electric trucks have a lifetime of 4 years, and a €0 residual value
• Diesel trucks use 30 liters of diesel per 100km, and diesel fuel costs €1/liter
• Electric trucks use 100kWh of energy per 100km, and energy costs €0.15/kWh
• Annual maintenance is €5k for diesel trucks and €3k for electric trucks
• Other costs (e.g. insurance, taxes, and tolls) is €10k for diesel trucks and €5k for electric trucks
• Diesel trucks cost €100k

2.5 Inclusive hiring - McKinsey case maths example

This is a paraphrased version of question 3 on  McKinsey’s  Shops Corporation practice case :

How many female managers should be hired next year to reach the goal of 40% women executives in 10 years? 

• There are 300 executives now, and that number will be the same in 10 years
• 25% of the executives are currently women
• The career levels at the company (from junior to senior) are as follows: professional, manager, director, executive
• In the next 5 years, ⅔ of the managers that are hired will become directors. And in years 6-10, ⅓ of those directors will become executives. 
• Assume 50% of the hired managers will leave the company
• Assume that everything else in the company’s pipeline stays the same after hiring the new managers

2.6 Breakeven point - Bain case maths example

This is a paraphrased version of the calculation portion of  Bain’s Coffee Shop Co. practice case : 

How many cups of coffee does a newly opened coffee shop need to sell in the first year in order to break even?

• The price of coffee will be £3/cup
• Each cup of coffee costs £1/cup to produce 
• It will cost £245,610 to open the coffee shop
• It will cost £163,740/year to run the coffee shop

Note: take a moment to try solving this problem yourself, then you can get the answer  on Bain’s website .

2.7 Driving revenue - Bain case maths example

This is a paraphrased version of the calculation part of  Bain’s FashionCo practice case : 

Which option (A or B) will drive the most revenue this year?

Option A: Rewards program

• There are 10m total customers
• The avg. annual spend per person is $100 before any sale (assume sales are evenly distributed throughout the year)
• Customers will pay a $50 one-time activation fee to join the program
• 25% of customers will join the rewards program this year
• Customers who join the rewards program always get 20% off

Option B: Intermittent sales

• For 3 months of the year, all products are discounted by 20%
• During the 3 months of discounts, purchases will increase by 100%

3. Case maths apps and tools

In the case maths problems in the previous section, there were essentially 2 broad steps: 

• Set up the equation
• Perform the calculations

After learning the formulas earlier in this guide, you should be able to manage the first step. But performing the mental maths calculations will probably take some more practice. 

Mental maths is a muscle. But for most of us, it’s a muscle you haven’t exercised since high school. As a result, your  case interview preparation  should include some maths training.

If you don't remember how to calculate basic additions, substractions, divisions and multiplications without a calculator, that's what you should focus on first.

In addition, Khan Academy has also put together some helpful resources. Here are the ones we recommend if you need an in-depth arithmetic refresher:

• Additions and subtractions
• Multiplications and divisions
• Percentages

Scientific notation

Once you're feeling comfortable with the basics you'll need to regularly exercise your mental maths muscle in order to become as fast and accurate as possible.

• Preplounge's maths tool . This web tool is very helpful to practice additions, subtractions, multiplications, divisions and percentages. You can both sharpen your precise and estimation maths with it.
• Victor Cheng's maths tool . This tool is similar to the Preplounge one, but the user experience is less smooth in our opinion.
• Mental math cards challenge app  (iOS). This mobile app lets you work on your mental maths easily on your phone. Don't let the old school graphics deter you from using it. The app itself is actually very good.
• Mental math games  (Android). If you're an Android user this one is a good substitute to the mental math cards challenge one on iOS.

4. Case interview maths tips and tricks

4.1. calculators are not allowed in case interviews.

If you weren’t aware of this rule already, then you’ll need to know this: 

Calculators are not allowed in case interviews. This applies to both in-person and virtual case interviews. And that’s why it’s crucial for candidates to practice doing mental maths quickly and accurately before attending a case interview. 

And unfortunately, doing calculations without a calculator can be really slow if you use standard long divisions and multiplications. 

But there are some tricks and techniques that you can use to simplify calculations and make them easier and faster to solve in your head. That’s what we’re going to cover in the rest of this section. 

Let’s begin with rounding numbers.

4.2. Round numbers for speed and accuracy

The next 5 subsections all cover tips that will help you do mental calculations faster. Here’s an overview of each of these tips: 

And the first one that we’ll cover here is rounding numbers. 

The tricky thing about rounding numbers is that if you round them too much you risk:

• Distorting the final result
• Or your interviewer telling you to round the numbers less

Rounding numbers is more of an art than a science, but in our experience, the following two tips tend to work well:

• We usually recommend that you avoid rounding numbers by more than +/- 10%. This is a rough rule of thumb but gives good results based on conversations with past candidates.
• You also need to alternate between rounding up and rounding down so the effects cancel out. For instance, if you're calculating A x B, we would recommend rounding A UP, and rounding B DOWN so the rounding balances out.

Note that you won't always be able to round numbers. In addition, even after you round numbers the calculations could still be difficult. So let's go through a few other tips that can help in these situations.

4.3. Abbreviate large numbers

Large numbers are difficult to deal with because of all the 0s. To be faster you need to use notations that enable you to get rid of these annoying 0s. We recommend you use labels and the scientific notation if you aren't already doing so.

Labels (k, m, b)

Use labels for thousand (k), million (m), and billion (b). You'll write numbers faster and it will force you to simplify calculations. Let's use 20,000 x 6,000,000 as an example.

• No labels: 20,000 x 6,000,000 = ... ???
• Labels: 20k x 6m = 120k x m = 120b

This approach also works for divisions. Let's try 480,000,000,000 divided by 240,000,000.

• No labels: 480,000,000,000 / 240,000,000 = ... ???
• Labels: 480b / 240m = 480k / 240 = 2k

When you can't use labels, the scientific notation is a good alternative. If you're not sure what this is, you're really missing out. But fortunately, Khan Academy has put together a good primer on that topic  here .

• Multiplication example: 600 x 500 = 6 x 5 x 102 X 102 = 30 x 104 = 300,000 = 300k
• Division example: (720,000 / 1,200) / 30 = (72 / (12 x 3)) x (104 / (102 x 10)) = (72 / 36) x (10) = 20

When you're comfortable with labels and the scientific notation you can even start mixing them:

• Mixed notation example: 200k x 600k = 2 x 6 x 104 x m = 2 x 6 x 10 x b = 120b

4.4. Use factoring to make calculations simpler

To be fast at maths, you need to avoid writing down long divisions and multiplications because they take a LOT of time. In our experience, doing multiple easy calculations is faster and leads to less errors than doing one big long calculation.

A great way to achieve this is to factor and expand expressions to create simpler calculations. If you're not sure what the basics of factoring and expanding are, you can use Khan Academy again  here  and  here . Let's start with factoring.

Simple numbers: 5, 15, 25, 50, 75, etc.

In case interviews some numbers come up very frequently, and it's useful to know shortcuts to handle them. Here are some of these numbers: 5, 15, 25, 50, 75, etc. 

These numbers are common, but not particularly easy to handle.

For instance, consider 36 x 25. It's not obvious what the result is. And a lot of people would need to write down the multiplication on paper to find the answer. However there's a MUCH faster way based on the fact that 25 = 100 / 4. Here's the fast way to get to the answer:

• 36 x 25 = (36 / 4) x 100 = 9 x 100 = 900

Here's another example: 68 x 25. Again, the answer is not immediately obvious. Unless you use the shortcut we just talked about; divide by 4 first and then multiply by 100:

• 68 x 25 = (68 / 4) x 100 = 17 x 100 = 1,700

Factoring works both for multiplications and divisions. When dividing by 25, you just need to divide by 100 first, and then multiply by 4. In many situations this will save you wasting time on a long division. Here are a couple of examples:

• 2,600 / 25 = (2,600 / 100) x 4 = 26 x 4 = 104
• 1,625 / 25 = (1,625 / 100) x 4 = 16.25 x 4 = 65

The great thing about this factoring approach is that you can actually use it for other numbers than 25. Here is a list to get you started:

• 2.5 = 10 / 4
• 7.5 = 10 x 3 / 4
• 15 = 10 x 3 / 2
• 25 = 100 / 4
• 50 = 100 / 2
• 75 = 100 x 3 / 4

Once you're comfortable using this approach you can also mix it with the scientific notation on numbers such as 0.75, 0.5, 0.25, etc.

Factoring the numerator / denominator

For divisions, if there are no simple numbers (e.g. 5, 25, 50, etc.), the next best thing you can do is to try to factor the numerator and / or denominator to simplify the calculations. Here are a few examples:

• Factoring the numerator: 300 / 4 = 3 x 100 / 4 = 3 x 25 = 75
• Factoring the denominator: 432 / 12 = (432 / 4) / 3 = 108 / 3 = 36
• Looking for common factors: 90 / 42 = 6 x 15 / 6 x 7 = 15 / 7

4.5. Expand numbers to make calculations easier

Another easy way to avoid writing down long divisions and multiplications is to expand calculations into simple expressions.

Expanding with additions

Expanding with additions is intuitive to most people. The idea is to break down one of the terms into two simpler numbers (e.g. 5; 10; 25; etc.) so the calculations become easier. Here are a couple of examples:

• Multiplication: 68 x 35 = 68 x (10 + 25) = 680 + 68 x 100 / 4 = 680 + 1,700 = 2,380
• Division: 705 / 15 = (600 + 105) / 15 = (15 x 40) / 15 + 105 / 15 = 40 + 7 = 47

Notice that when expanding 35 we've carefully chosen to expand to 25 so that we could use the helpful tip we learned in the factoring section. You should keep that in mind when expanding expressions.

Expanding with subtractions

Expanding with subtractions is less intuitive to most people. But it's actually extremely effective, especially if one of the terms you are dealing with ends with a high digit like 7, 8 or 9. Here are a couple of examples:

• Multiplication: 68 x 35 = (70 - 2) x 35 = 70 x 35 - 70 = 70 x 100 / 4 + 700 - 70 = 1,750 + 630 = 2,380
• Division: 570 / 30 = (600 - 30) / 30 = 20 - 1= 19

4.6. Simplify growth rate calculations

You will also often have to deal with growth rates in case interviews. These can lead to extremely time-consuming calculations, so it's important that you learn how to deal with them efficiently.

Multiply growth rates together

Let's imagine your client's revenue is $100m. You estimate it will grow by 20% next year and 10% the year after that. In that situation, the revenues in two years will be equal to:

• Revenue in two years = $100m x (1 + 20%) x (1 + 10%) = $100m x 1.2 x 1.1 = $100m x (1.2 + 0.12) = $100m x 1.32 = $132m

Growing at 20% for one year followed by 10% for another year therefore corresponds to growing by 32% overall.

To find the compound growth you simply need to multiply them together and subtract one: (1.1 x 1.2) - 1= 1.32 - 1 = 0.32 = 32%. This is the quickest way to calculate compound growth rates precisely.

Note that this approach also works perfectly with negative growth rates. Let's imagine for instance that sales grow by 20% next year, and then decrease by 20% the following year. Here's the corresponding compound growth rate:

• Compound growth rate = (1.2 x 0.8) - 1 = 0.96 - 1 = -0.04 = -4%

See how growing by 20% and then shrinking by 20% is not equal to flat growth (0%). This is an important result to keep in mind.

Estimate compound growth rates

Multiplying growth rates is a really efficient approach when calculating compound growth over a short period of time (e.g. 2 or 3 years).

But let's imagine you want to calculate the effect of 7% growth over five years. The precise calculation you would need to do is:

• Precise growth rate: 1.07 x 1.07 x 1.07 x 1.07 x 1.07 - 1 = ... ???

Doing this calculation would take a lot of time. Fortunately, there's a useful estimation method you can use. You can approximate the compound growth using the following formula:

• Estimate growth rate = Growth rate x Number of years

In our example:

• Estimate growth rate: 7% x 5 years = 35%

In reality if you do the precise calculation (1.075 - 1) you will find that the actual growth rate is 40%. The estimation method therefore gives a result that's actually quite close. In case interviews your interviewer will always be happy with you taking that shortcut as doing the precise calculation takes too much time.

4.7. Memorise key statistics

In addition to the tricks and shortcuts we’ve just covered, it can also help to memorise some common statistics. 

For example, it would be good to know the population of the city and country where your target office is located. 

In general, this type of data is useful to know, but it's particularly important when you face  market sizing questions . 

So, to help you learn (or refresh on) some important numbers, here is a short summary:

Of course this is not a comprehensive set of numbers, so you may need to tailor it to your own location or situation.   

5. Practice with experts

Sitting down and working through the maths formulas we've gone through in this article is a key part of your case interview preparation. But it isn’t enough.

At some point you’ll want to practise making calculations under interview conditions.

You can try to do this with friends or family. However, if you really want the best possible preparation for your case interview, you'll also want to work with ex-consultants who have experience running interviews at McKinsey, Bain, BCG, etc.

If you know anyone who fits that description, fantastic! But for most of us, it's tough to find the right connections to make this happen. And it might also be difficult to practice multiple hours with that person unless you know them really well.

Here's the good news. We've already made the connections for you. We’ve created a coaching service where you can do mock interviews 1-on-1 with ex-interviewers from MBB firms. Learn more and start scheduling sessions today.

Related articles:

CBSE Expert

CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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Case interview math: the free CaseCoach guide

When you relay your desire to break into management consulting, a typical quip that can often follow is: “How many golf balls fit in an airplane?”. While most management consulting firms have moved away from these types of questions, they still expect you to confidently and reliably navigate mathematical problems on the fly in case interviews.

Regardless of your degree or past experience, you’ll need to be able to perform calculations quickly and accurately, while demonstrating that you understand the overall structure of the problem and the implications of your solution.

The good news is that in case interviews, candidates are only required to demonstrate a high-school level of math skills. However, with no calculators allowed and an interviewer looking over their shoulder, many people find this aspect of the interview challenging.

This article will walk you through everything you need to know in order to ace case math, including the style of questions you can expect, the skills you’ll need to hone, and how you should prepare.

Key takeaways

• Consultants need to have strong mental arithmetic skills in order to perform key analyses and build credibility with clients.
• In case interviews, math problems can take the form of straight calculations, exhibits that require calculations, word problems, and estimation questions.
• To succeed in case math, we recommend following a four-step process of: ‘Verbalize, Calculate, Sense-check, Interpret’.
• It’s important to keep your work tidy and simple, and to communicate with your interviewer as you work through the problem.
• While you don’t need advanced knowledge to do well in case interview math, you do need to know the basic operations, key math concepts, and business math.
• To stand out to your interviewer, you need to work through math problems confidently and efficiently. Keeping track of zeros, simplifying your calculations, and memorizing frequently-used fractions will help you do this.
• It’s vital to prepare for case math. The Case Math Course – provided as part of our Interview Prep Course – includes 21 video lectures that cover everything you need to know in detail.
• Once you’re comfortable with the theory, you can build your skills and confidence quickly with the calculation and case math drills in our Interview Prep Course. You can then practice live cases with other candidates in our Practice Room .

Why is math an important component of case interviews?

You might be wondering why, in an age where you can access a calculator or Microsoft Excel on your phone or laptop in seconds, interviewers still judge applicants on the strength of their mental arithmetic.

The rise of Excel and other mathematical modeling software has certainly saved consultants a lot of time and effort in recent years. However, when it comes to interacting with senior executives – where the perception of competence is paramount – mental math is unlikely to ever go out of style.

Consultants are often required to calculate values at a moment’s notice. Typical scenarios include being asked to:

• assess the impact of a proposed cost-saving measure
• estimate the revenue that a potential new product will generate
• using orders of magnitude to determine what a set of numbers could mean for the client and the problem at hand

How is consulting math tested in a case interview?

In this section, we’re going to address the types of math problems you’re likely to encounter in a case interview.

Straight calculations

It’s possible that an interviewer will give you a (relatively) straightforward math problem to solve as a standalone question.

Usually, however, these calculations take the form of follow-up questions in a larger case study.

In a product launch case, the interviewer might ask you to calculate the average price of a product for a company that sells:

• 10,000 units at $15 per unit through one channel, and
• 20,000 units at $12 per unit through another channel.

You’d need to quickly compute that the average price is (10,000 x $15 + 20,000 x $12) / (10,000 + 20,000) = $13.

Consulting charts and exhibits that require calculations

There are several types of calculations that your interviewer might propose or ask you to perform based on data in a chart or exhibit.

Here’s an example of an exhibit that you might be given in a market entry case:

In this example, your interviewer might ask you to identify which city offers the greatest potential market for customers aged 20 to 40.

You might then be asked to calculate the percentage difference between the largest and second-largest markets.

You could eliminate Hillwood and Bedrock immediately, simply by eyeballing the surface areas of the ‘20 to 30 years’ and ‘30 to 40 years’ segments and noticing that they are the smallest.

Then it would be worth computing the values for the remaining three cities, which are more difficult to differentiate visually.

You would do this by multiplying the share of their population in the 20-40 age range by their total population, as follows:

• King’s Landing: (26% + 18%) x 11.4 mn ≈ 5.0 mn
• Citadel: (60% + 11%) x 5.5 mn ≈ 3.9 mn
• Metropolis: (20% + 20%) x 13.5 mn ≈ 5.4 mn

Metropolis has the largest potential market, with 5.4 million customers aged 20 to 40. This is 8% larger than the potential market of King’s Landing (5.4 / 5.0 = 1.08).

Word problems

Word problems are another staple of case interviews. They’re likely to be fairly familiar, as you’ll almost certainly have encountered them at some point in your schooling.

In the context of a case interview, word problems usually require algebraic calculations. Candidates are expected to extract the most important facts and figures from the word problem, present them in the form of an equation, and then perform the calculations.

One common type of word problem that often crops up in case interviews is the ‘breakeven analysis’. This requires candidates to calculate the amount of sales that a company needs to make to recover its costs (i.e. to make neither a profit nor a loss).

Let’s say your client is a mid-sized Peruvian copper-mining firm that’s invested $50 million in land purchases, development costs, and equipment. They’ve approached your firm to find out how much copper they need to sell to recoup that investment.

In the current market, CopperCollect expects to gross about $10,000 per tonne of copper sold. It costs the firm about $3,000 per tonne to extract, ship, and store the copper.

In this scenario, you’d need to divide the firm’s total investment ($50 million) by the gross profit per tonne ($7,000) to find that the mining firm has to sell ~7,200 tonnes of copper to break even.

Estimation questions

The last type of quantitative question you’re likely to encounter in a case interview is the estimation question (also known as the ‘market sizing’ question).

In estimation questions, candidates are required to arrive at a value based on very little upfront data – or sometimes none at all. Here are some examples:

• How many petrol pumps are there in the UK?
• What is the annual revenue of a global sandwich chain?
• What is the size of the market for lattes in the US?
• How many newspapers are sold in Spain?

Estimation questions provide candidates with a good opportunity to demonstrate their ability to make common-sense assumptions and extrapolate a small amount of data using a structured approach. You can learn more about how to do this in our article on nailing market sizing case questions .

Our tips for succeeding case interview math

Follow a four-step process.

As with many other aspects of case interviews, there’s a process you can use to structure your thoughts and analysis in case math:

1. Set your approach and describe it

Before you begin to solve the problem, tell your interviewer the approach you plan to take. This will both help you to structure your thoughts and allow your interviewer to correct any mistakes or incorrect assumptions you might have made.

If your interviewer agrees with your approach, they might indicate that they’re happy to ‘sign off’ on it, either verbally or non-verbally.

2. Calculate

The second step is to work through the required calculations correctly, confidently, and quickly. Be sure to write everything down and tell the interviewer what you’re doing, as this will help them to follow along.

3. Sense-check

After you’ve completed your calculations, pause for a moment to take a bird’s-eye view of your approach. Does your solution make sense?

If you’re trying to assess the yearly revenue of a well-established multinational law firm and your final result is just a few thousand dollars, common sense should tell you that you need to return to your calculations.

4. Interpret

Finally, you need to demonstrate to your interviewer that you can glean meaningful and – wherever possible – actionable insights from calculations. Ask yourself whether your solution supports your initial hypothesis.

Keep your work tidy and simple

Throughout this process, you should write everything down and ensure that your calculations are tidy and simple. Otherwise, you could easily become confused and you’ll be unlikely to impress your interviewer, who will be expecting you to take a professional approach to the exercise.

Here are some simple measures that can help you keep your case math work neat and organized:

• Use a fresh sheet of paper for every problem and non-trivial calculation
• Write neatly and give yourself ample space on the page
• Align your ‘equal signs’ on the page to keep your calculations tidy
• Compute one operation at a time
• Avoid multiplying percentages together, as this can often lead to errors
• Look out for when it might be wise to use a table to synthesize different units or types of data

Here’s an example of an effective page of case math calculations:

Work with your interviewer

While it might be tempting to stay silent and then impress your interviewer with the correct answer after performing your calculations, the most successful candidates involve their interviewer in the process.

This means you should:

• get upfront feedback on the approach you plan to take
• state your assumptions out loud
• ask the interviewer to provide additional information about certain data sets (although this won’t be appropriate for estimation questions)
• describe everything you’re doing as you perform your calculations

There are many benefits to working with your interviewer in this way. It allows you to react to their verbal or non-verbal feedback in real time. They may even point out errors that you’ll then have the opportunity to correct. It also demonstrates that you have the confidence to collaborate with others on these kinds of problems, and work well in a team.

You can see all of this in action in the following video, which shows a candidate working with their interviewer to solve a math problem in a case interview:

What kind of math do I need to know to ace my case interview?

To do well in case math, there’s no need for you to learn advanced math or complex corporate finance. Instead, you simply need to master the following types of calculations:

Basic operations

You learned the four basic operations at school, and they’re pivotal in case interview math.

To recap, the basic operations are:

• subtraction
• multiplication

You might already feel confident that you’ve got the four operations down. However, it’s still an excellent idea to brush up on performing these kinds of calculations – especially with a pen and paper.

This video, taken from our Case Math Course , walks you through everything you need to know about division for case interviews.

Key math concepts

Along with the four basic operations, you’ll also be required to employ many of the following key math concepts in your case math calculations:

• Percentages
• Compounding
• Weighted averages
• Probability

Business math

As consulting roles focus on improving business performance, it shouldn’t come as a surprise to learn that you’ll probably be tested on business math in a case interview. You’ll need to know how to:

• interpret financial statements (i.e. income statements, balance sheets, and cash flow reports)
• make an investment decision
• value a business
• optimize operations

This video, which is also from our Case Math Course, walks you through everything you need to know about income statements:

How to stand out in case interview math

The more proficiency and confidence you can demonstrate with math, the more you’ll impress your interviewer. Being able to work through these problems efficiently will also give you more time to work on other aspects of the case.

Here are three pro tips that can help you stand out from the crowd:

1) Keeping track of zeros

The number-one math mistake we see candidates make in case interviews is miscounting zeros. Case questions often involve large numbers, sometimes in the millions or even billions.

Because of this, it’s easy to misplace or inadvertently leave out a zero and render your entire calculation incorrect as a result. Keeping close track of your zeros is therefore crucial. We recommend using one of the following methods to do this:

• Counting the zeros in your calculation
• Using scientific notation
• Assigning letter units to zeros

2) Simplifying your calculations

Simplifying your calculations in case interview math will help you to work through the problem with greater speed and efficiency. It will also demonstrate a level of confidence to your interviewer and show that you’re more interested in the essence of the problem than in getting caught up in trivial details.

One way of simplifying calculations is by rounding numbers up or down to make them more ‘friendly’. There are typically two opportunities to do this in a case interview:

• When making assumptions about figures like population numbers
• When performing calculations, rounding numbers as you go

There are a few important points to note when it comes to rounding figures in case interviews. First, check that your interviewer is happy for you to do this. Then, as you progress through the problem, communicate any rounding assumptions you make. Finally, bear in mind that as a rule of thumb, effective rounding shouldn’t change the answer by more than 10%.

3) Memorizing frequently-used fractions

Some fraction values are used so frequently in case math that knowing them – along with their percentage value and decimal conversions – can save you significant time. We recommend memorizing the fraction and corresponding percentage and decimal values of 1/2, 1/3, all the way through to 1/10.

How to prepare for case interview math

While case interviews require candidates to demonstrate only a high-school level of math proficiency, you’ll likely need to refresh your skills in this area. Remember that you’ll be performing calculations with a pen and paper, with an interviewer looking over your shoulder.

The good news is that we’ve got everything you need to brush up on math theory and then put it to the test.

Understanding the theory

The dedicated Case Math Course in our Interview Prep Course includes 21 video lectures that cover the following areas in detail:

• The four operations: addition, subtraction, multiplication, and division
• All the key math concepts you’ll need to master, including fractions, percentages and weighted averages
• ‘Pro-tips’ for doing well in case math, including keeping track of zeros and simplifying calculations
• Business math concepts you’ll need to know, including cash flow, investments, and valuations

Putting the theory into practice

Once you’ve developed a firm grasp of the theory, you can put it into practice with the other resources in the Interview Prep Course.

As mental arithmetic is one of the case interview skills you can practice alone as part of your preparation, we’ve included a comprehensive set of calculation drills in the course. Drills are interactive exercises that pose rapid-fire questions and then provide instant feedback.

When you feel confident with your calculation skills, you can move on to our case math drills. These allow you to practice all the elements of case math, including requesting missing data, setting an approach to calculating the solution, and interpreting the results.

The final – and most important – stage of case math preparation is practicing live cases with a partner. Most candidates who go on to receive an offer from a top consulting firm like McKinsey, BCG or Bain complete at least 25 live practice sessions before their interview. At CaseCoach, we can connect you with a diverse community of fellow candidates who are all available for case interview practice in our Practice Room .

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Case Interview Math: The Insider Guide

Last Updated on March 27, 2024

Embarking on a career in consulting at leading firms demands mastery over consulting math problems. Statistically speaking, a staggering 85% of management consulting case interviews put candidates to the test with case interview math questions. At top consultancies such as McKinsey , BCG , and Bain , this expectation skyrockets to nearly 100%.

During case interviews, candidates are tasked with dissecting complex mathematical business puzzles, delving into the qualitative aspects that underpin these numbers, and ultimately crafting strategic recommendations.

These mathematical challenges often emerge as the largest hurdle for many aspiring consultants. Drawing from our extensive background in conducting interviews at McKinsey and coaching thousands of interviews on platforms such as PrepLounge and StrategyCase.com, we’ve observed that the lion’s share of mishaps during case interviews arises within this quantitative segment.

Developing math skills in consulting interviews is crucial for candidates aiming for top-tier firms. The ability to navigate these numerical problems not only sets the foundation for success in case interviews but also mirrors the analytical challenges consultants face in real-world scenarios.

This article is your ultimate guide to consulting interview preparation, with a focus on math challenges. Our insights in this expert article aim to demystify the numerical proficiency required by top-tier consulting firms, preparing you to tackle these challenges head-on with confidence and strategic insight. It includes all relevant tips for solving consulting math problems, making complex calculations manageable.

It is a critical installment in our comprehensive consulting case interview prep series:

• Overview of case interviews: what is a consulting case interview?
• How to create a case interview framework
• How to ace case interview exhibit and chart interpretation
• How to ace case interview math questions (this article)
• How to approach brainstorming questions in case interviews

Why Candidates Struggle with Case Interview Math

The conundrum of case interview math is not intrinsically tied to the difficulty of the mathematical problems themselves, which often do not surpass high school-level arithmetic. You have solved similar problems before, maybe not in a business or interview context, but in a classroom setting.

Let’s start with some positivity.

There is no need to fear quantitative problems in case interviews. The level of math required is not more complex than what you have already learned in school and you do not need a specific degree to pass the case interviews.

The true challenge emerges from the synthesis of multiple skills under the high-pressure environment of a case interview.

Logical thinking is paramount, as you must not only arrive at the correct approach but do so swiftly and efficiently. This is compounded by the need to execute calculations with potentially large numbers accurately and quickly, all while maintaining composure to manage the interviewer’s impression. Communication also plays a critical role; articulating your thought process and conclusions in a clear and concise manner is essential.

When faced with the task of juggling these aspects simultaneously, it’s common for candidates to experience panic, leading to a decrease in overall performance. However, by deconstructing these skills and mastering each individually – logical problem-solving, fast and accurate arithmetic, effective communication, and impression management – you can significantly bolster your confidence. This strategic preparation not only mitigates the fear associated with case interview math but equips you with the comprehensive skill set necessary to excel.

That being said, as with every other element in a case interview ( structuring , brainstorming , exhibit and data interpretation ), there is a very specific way of approaching case interview math, which candidates are not used to from their previous academic or professional experience. Learn how to apply business case math to real-world consulting scenarios.

Let’s get to it!

Case Math Mastery Course and Drills

Learn how to tackle case interview math questions with the insight and precision of an experienced consultant with the most comprehensive preparation program on the market. Learn from our McKinsey interviewer experience and benefit from the detailed curriculum of the guidebook and the video program as well as 40 hours of practice.

The Purpose of Case Interview Math

Numerical analysis forms the backbone of decision-making and strategic recommendations in case interviews, reflecting the real-world consulting emphasis on data-driven insights.

In the context of a business problem usually found in a case interview, quantitative analyses are conducted for two reasons.

Identifying problems and quantifying their impact

Initially, consultants are tasked with identifying underlying issues within a business context. Through quantitative analysis, they delve deep into the problem, quantifying its impact to uncover root causes and, subsequently, potential solutions.

In the condensed format of a case interview, you’re expected to mirror this investigative approach, albeit in a more abbreviated manner.

Supporting recommendations

Quantitative data underpins every business recommendation, providing a solid foundation for decision-making. In consulting practice, every suggestion or strategic plan presented to a client is supported by numerical evidence.

Similarly, during a case interview, the quantitative analyses you conduct will critically inform your final recommendations.

Test of your quantitative skills

Moreover, case interviews serve as a proving ground for your quantitative skills, simulating the analytical rigor required in consulting. I cannot remember a single day in my McKinsey career, where I was not running some form of quantitative analysis.

Therefore, honing your ability to devise strategic, logical approaches to quantitative challenges and execute precise calculations is crucial not only for acing case interviews but also for thriving as a consultant.

This skillset ensures you’re well-equipped to deliver insights that drive impactful business decisions, marking your capability to thrive in the consulting domain.

A simplified version of reality

In the case interview context, the mathematical problems presented are invariably a streamlined representation of real business challenges, often drawn from the interviewer’s direct experience with actual clients. This means that while the scenarios aim to mimic the complexities of business decision-making, the approach and calculations are deliberately simplified for the sake of brevity and clarity.

For instance, scenarios might feature fewer market segments or shorter time periods than those in actual business cases, and variables are designed to be more straightforward, allowing for easier manipulation and calculation. It’s also common practice for candidates to round numbers to simplify the process further. Unlike the exhaustive analyses that can span weeks on the job as new insights emerge, a typical math problem in a case interview is designed to be resolved within a succinct 5 to 8-minute window from start to finish. That should give you an idea of how complex it can really be.

This distilled version of reality, however, does not make the task at hand any less challenging. The dual demands of strategizing your steps and executing calculations unfold under the watchful eye of the interviewer, all within a high-pressure, calculator-free environment.

Yet, mastering the basics – quick mental arithmetic, fundamental operations (addition, subtraction, multiplication, division, percentages, and fractions), and the ability to make judicious estimates – proves invaluable. These skills equip you to tackle most interview problems effectively, without the need for advanced mathematical knowledge.

While some problems might feature a complexity that demands logical problem-solving and potentially multiple calculation steps, the essence of case interview math lies in its reduced complexity, designed to assess your analytical acumen rather than your prowess in advanced mathematics.

The myth of perfection

In the high-stakes environment of case interviews, there’s a prevalent myth that perfection is the key to success. This belief leads many to think that any mistake, particularly in math, spells automatic rejection. However, this couldn’t be further from the truth. Mistakes, whether in calculations or pacing, are not uncommon and do not necessarily jeopardize your chances of success.

It’s important to recognize that errors, to an extent, are expected. You might miscalculate, take a bit longer to arrive at an answer, or even find the interviewer stepping in to guide you. These instances, in isolation, aren’t deal-breakers. They’re often seen as part of the process, providing insights into your problem-solving approach and resilience.

The critical factor is how you handle mistakes. An isolated error or a moment of slowness doesn’t doom your interview outcome. However, repeated errors, especially if they’re indicative of a pattern within the same interview or across multiple interviews, can raise concerns. Moreover, a single mistake leading to a cascade of follow-up errors, triggered by loss of confidence or panic, can be detrimental. This reaction, rather than the initial mistake itself, can hinder your performance significantly. I have seen this hundreds of times in live settings.

One key strategy to mitigate the impact of mistakes is to excel in other aspects of the case interview. Demonstrating exceptional analytical skills, creative problem-solving, or outstanding communication can offset occasional mathematical errors. Interviewers are looking for a well-rounded skill set, so performance spikes in areas other than math can greatly enhance your overall evaluation.

Ultimately, how you respond to mistakes is crucial. Viewing them as learning opportunities rather than failures can transform your interview experience. Showing the interviewer your ability to quickly recover, correct errors, and proceed with confidence speaks volumes about your potential as a consultant. It demonstrates resilience, adaptability, and a growth mindset.

Effective Strategies for Tackling Case Interview Math Questions

Different skill levels, same problem.

Understanding the unique challenges and logic behind math questions in case interviews reveals an interesting observation:

Candidates from various academic backgrounds might find themselves revisiting basic mathematical concepts not engaged with since high school. Conversely, individuals with a strong quantitative foundation, such as engineers, may need to simplify their analytical approach to align with the straightforward nature of case interview math. This adjustment is crucial for all candidates, regardless of their initial competency levels, to adapt to the nuances of case interview calculations effectively.

Both types of backgrounds need to adapt to the specific case interview math principles and process.

Unlike traditional math problems, case interview questions prioritize the relevance and application of mathematical solutions to the business scenario at hand. The aim is not merely to arrive at precise numerical answers but to receive directionally correct results to leverage these findings and inform strategic decisions within the case’s context. Thus, achieving perfectly accurate results is less critical than developing a sound, strategic approach that yields directionally correct insights swiftly.

It’s better to get directionally correct results swiftly and interpret them correctly than getting 100% accurate results and not providing any insights into the case problem. Approach case interview math with this mantra

Adopting a mindset that embraces quantitative analysis as an integral part of every case scenario is essential. This involves not just solving the problem at hand but also considering the broader implications of your calculations on the strategic recommendations you propose. The ability to relate different numerical factors and assess their impact on the business challenge is key.

The apprehension some candidates feel towards case math can be mitigated by understanding that these calculations are designed to reflect real-world business problems in a simplified manner. Therefore, embracing the opportunity to demonstrate logical thinking and analytical prowess through these mathematical exercises is vital.

Even more so, have a quantitative angle in every case, even if the interviewer does not explicitly ask you for it. For example, try to relate numbers to each other, think about the potential quantitative impact of your recommendation, etc.

Many candidates are simply scared of digging into the mathematics of a case. Don’t be that person! rather go where no one else is going and highlight your numerical prowess at every opportunity.

As we delve further, I aim to equip you with the knowledge and strategies to confidently tackle both the structuring and calculation aspects of math questions in case interviews, ensuring you’re well-prepared to handle the quantitative analysis that underpins effective case interview performances.

My approach to every case math problem

Mastering the art of solving quantitative problems in case interviews involves a two-pronged approach: developing a universal strategy applicable across various case scenarios and executing calculations to arrive at concrete insights.

How, then, should one tackle the numerical aspects of case interviews with a structured strategy that you can always rely on? Proving essential math skills for case interviews is less daunting with my step-by-step guide.

• Listening : Engage fully, paying close attention to the information provided by your interviewer. Active listening forms the foundation of your analytical process.
• Clarification : Pause to ensure clarity around the data presented or derived from visual aids such as charts and tables. It’s crucial to confirm the accuracy of these figures and understand the objective of your analysis before proceeding.
• Strategizing : Outline a clear, logical plan for your calculations. For complex problems, don’t hesitate to request a brief moment – typically a minute or two – to organize your thoughts and structure your approach on paper.
• Articulating your strategy : Communicate your planned methodology to the interviewer. This step is vital for preemptively identifying any potential errors and ensuring alignment on the approach.
• Calculation execution : With the interviewer’s nod, carry out your calculations diligently. It’s advisable to work through this phase methodically, allowing yourself time to focus without interruption.
• Verification : Review your work to catch and correct any errors. Ensuring your numbers are reasonable and accurate is key to building a solid argument.
• Presentation of results : Share your findings in a clear, concise, and assertive manner, avoiding presenting your conclusion as a question. Highlight the most critical results, adhering to a top-down communication style as recommended by the Pyramid Principle .
• Interpretation and next steps : Beyond just presenting numbers, interpret what they mean in the context of the case. How do they influence your analysis and recommendations? Always connect your findings back to the larger case narrative, exploring their implications and forming hypotheses based on these insights. Propose next steps.

The benefit of adopting a structured approach to quantitative problems in case interviews is twofold. Firstly, it showcases to the interviewer your ability to navigate complex situations with a level-headed, systematic strategy, effectively demonstrating case leadership qualities. This organized methodology signals that you possess the poise and strategic foresight necessary to dissect and solve business challenges – a trait highly valued in consulting.

Secondly, this approach creates an optimal environment for you to perform at your peak. By delineating the processes of thinking, communicating, and calculating, you’re able to maintain a sharp focus at any given moment. This separation ensures that each step of the problem-solving process receives your undivided attention, significantly enhancing your efficiency and effectiveness.

Conversely, when candidates attempt to juggle multiple aspects simultaneously – such as solving the problem while overly concentrating on managing the interviewer’s impression – results tend to suffer. This scattered focus often leads to underperformance in case interviews, as it dilutes the clarity and precision necessary for success.

By adhering to a structured approach, you not only present yourself as a composed and capable candidate but also set the stage for demonstrating your best analytical and problem-solving skills.

Exercise caution with mental math

For those adept at mental arithmetic, a word of caution: always jot down your calculations. Relying solely on mental computations can lead to significant challenges if errors occur. Without a written record, pinpointing and rectifying mistakes becomes a daunting task, necessitating a complete reevaluation of your work. This not only hampers your ability to quickly identify where you went wrong but also prevents the interviewer from offering guidance or corrections.

Moreover, maintaining written documentation of your steps and intermediate results serves a dual purpose. It enables the interviewer to follow your thought process more effectively, providing an opportunity for intervention if necessary. Furthermore, it allows you to efficiently review your calculations, ensuring accuracy and clarity throughout the problem-solving phase.

Typical Case Interview Math Problems and Key Formulas

3 types of case math problems.

In case interviews, math problems predominantly fall into three main categories, each designed to test your analytical prowess and decision-making capabilities. Understanding these categories not only aids in your preparation but also equips you with the insight to tackle these challenges methodically.

Roughly 90% of case interview math problems can be categorized as follows, guiding you toward strategic recommendations:

• Market or segment sizing : This type of problem requires you to estimate the size of a market or a specific segment within a market. For instance, you might be asked to calculate the potential sales of sports cars in China over the next five years. Alternatively, you might be asked to estimate something, i.e. the impact of an initiative. This involves understanding key influencing variables and making reasonable assumptions to provide a well-reasoned estimate.
• Operational calculations and decisions : These problems focus on the operational aspects of a business and often involve making calculations to improve efficiency, reduce costs, or enhance productivity. A typical question might involve calculating the total time saved if the lead time for each production step is reduced by 15%. Such questions require an analysis of current operations and an understanding of how changes can impact overall performance.
• Investment and financial strategic decisions : This category involves assessing various investment options or financial strategies to determine the most beneficial course of action. For example, you might need to compare the returns of two investment options, where Investment A offers a 12% annual return and Investment B offers a 5.5% return every six months. These problems test your ability to apply financial concepts and formulas to real-world scenarios, evaluating options based on their potential returns, risks, and strategic fit with the client’s objectives.

Extending beyond these primary categories, case interview math problems may also touch upon areas such as cost-benefit analysis, pricing strategies, and financial forecasting. Each type of problem requires a blend of quantitative skills, logical reasoning, and strategic thinking, allowing you to demonstrate your comprehensive understanding of business fundamentals. As you prepare for your case interviews, focusing on these core categories will help you develop a robust footing for tackling mathematical challenges, enabling you to approach each problem.

Case math formulas

Market sizing. When it comes to market or segment sizing questions, it’s perfectly acceptable to seek clarification from your interviewer on specific figures, such as the population of a particular country. Nonetheless, arming yourself with a foundational knowledge of key statistics can streamline your analysis and enhance your efficiency during these exercises. Familiarizing yourself with essential data points, including:

• Global population
• Populations of major countries such as the US, UK, Germany, China, India
• Demographic specifics of regions pertinent to your geographic area
• Average life expectancy rates
• Typical household sizes
• General income brackets

Equipping yourself with these statistics not only speeds up your calculation process but also demonstrates your preparedness and broad understanding of global and regional demographics. For a deeper dive into tackling market sizing questions with confidence and accuracy, including common formulas and strategic approaches, be sure to explore our dedicated article on market sizing questions . This resource is crafted to further refine your skills in estimating market potential, a critical component of case interview success.

Operational calculations. Operational calculations in case interviews demand a tailored approach, requiring you to devise formulas that are directly applicable to the case’s specific context and challenges. Unlike predefined equations, these formulas need to be thoughtfully constructed on the fly, taking into account the unique aspects of the business scenario at hand. Whether it’s streamlining processes, optimizing resource allocation, or improving operational efficiency, your ability to craft and apply these custom formulas is key.

In many instances, you might find yourself tackling optimization problems. These are designed to identify the most efficient way to allocate resources or adjust processes to maximize or minimize a particular outcome, such as cost, time, or production output. Understanding the principles of optimization and how to apply them in various business contexts can significantly enhance your problem-solving toolkit.

To get started, familiarizing yourself with a couple of foundational operational formulas can prove invaluable:

• Utilization rate = Actual output / Maximum output
• Capacity = Total capacity / capacity need per unit​
• Resources needed = Demand / Supply (e.g., Employees needed per day = 80 hours of customer requests per day / 8 daily working hours per employee; 10 employees are needed per day)
• Output = Rate (per time) x Time (e.g., Rate = 5 pieces per hour, Time = 5 hours; Output for 5 hours = 25)

These formulas serve as a foundational base from which to approach operational challenges within case interviews.

To evaluate the financial impact of decisions, these few formulas are key.

• Profit = Revenue – Cost
• Revenue = Price x Quantity
• Cost = Fixed cost (the cost that cannot be changed in the short term, e.g., rent) + Variable cost (the cost that changes with the number of products produced or services rendered, e.g., material cost)
• Contribution margin = Price – Variable cost
• Profitability (Profit margin) = Profit / Revenue
• Market share = Revenue of one product / Revenue of all products (in one market)
• Total market share = Total company revenue in a market / Total market revenue
• Relative market share = Company market share / (largest) Competitor market share
• Growth rate = (New number – Old number) / Old number
• Payback period = Investment / Profit per specific time frame (e.g., annual)
• Breakeven number of sales = Investment / Profit per product
• Return on investment = (Revenue – Cost of investment) / Cost of investment = Profit / Cost of investment
• Depreciation refers to the reduction in the value of an asset over time

There are also more advanced concepts, which are common for more specialized financial case interviews, not for generalist roles:

• The NPV is the present value of the sum of future cash in and outflows over a period (t = number of time periods, e.g., years) and is used to analyze the profitability of an investment or project
• Rule of 72: To find out how long it takes for a market, company, or investment to double in size, simply divide 72 by the annual growth rate
• The CAGR shows the rate of return of an investment or a project over a certain period of years (t = the number of years), expressed as an annual percentage
• The perpetuity is an annuity that lasts forever
• The ROE measures how effectively equity is used to generate profit
• The ROA measures how effectively assets are used to generate profit
• It measures how a change in price affects the change in demand
• Gross profit = Revenue from sales – Cost of goods sold (COGS, e.g., materials)
• Operating profit = Gross profit – Operating expenses (e.g., rent) – Depreciation (the spread of an asset’s cost over its useful lifetime, e.g., of a machine) – Amortization (the spread of an intangible asset’s cost over its useful lifetime, e.g., of a patent)
• Gross profit margin = Gross profit / Revenue
• Operating profit margin = Operating profit / Revenue
• The EBITDA looks at the profitability of the core business

Case Interview Math Tips and Tricks

Keep the following tips in mind to 3x your case interview math performance and speed, while reducing the potential for errors and mistakes.

Tackle the problems aggressively

Tackle case study math questions with confidence. Consulting interviewers want to see highly driven candidates who show self-initiative and engagement. If you hesitate whenever a number pops up or make mistakes in the quantitative section of the case, interviewers will test if this is just an anomaly or happens repeatedly. Candidates who struggle with math get more quantitative challenges during the case, whereas candidates who proceed flawlessly through the initial math question(s) often get shortcuts for the remaining quantitative parts or even whole results readily delivered by the interviewer as they have collected enough positive data points about their candidate’s performance in that area.

Hence, it is important to tackle math problems aggressively and with confidence. In most of my client interviews, I notice a hesitancy once the case moves into a more quantitative direction. Many are simply scared of digging into the numerical parts of a case or of discussing things in a quantitative context. Do not be that person!

If you mess up one calculation, you should not let this have a negative impact on the next one.

Re-learn and practice basic calculus

(Re-)learn simple arithmetic operations and practice until you can perform them in your sleep. While case math is never difficult, many candidates struggle with the concept of being watched while doing these basic operations. Therefore, the better your skill to compute quickly in a stressful environment, the bigger your quantitative muscle in the interview.

Practice calculations both mentally and with pen and paper under time pressure and the vigilant eyes of friends and peers. Go through number generators and math drill exercises to work on large-number additions, subtractions, multiplications, and divisions. Work with averages, percentages, and fractions. This certainly helps to build resilience and stamina.

Consider the numerical impact in your analysis

Get a feeling for numbers, percentages, and magnitudes. You should be able to accurately and approximately estimate percentages, percentages of percentages, as well as magnitudes on the spot. This helps you to interpret results and put them into context as well as to spot more obvious mistakes.

You should always have a critical eye on the quantitative aspects of a situation, even if the interviewer does not explicitly ask you about it. For example, relate numbers to each other (e.g., “The total is x, which represents a y% increase” ) or automatically think about the potential financial impact of your recommendation (e.g., “While these measures would definitely help improve our client’s customer satisfaction, I would be curious to understand how much the implementation would actually cost.” ). In addition, put numbers you hear into perspective (e.g., “I heard you say a 12% decrease is needed to achieve our planned cost reduction. I believe that in the current market environment with increasing commodities prices, this could be a difficult undertaking.” ). By interpreting numerical results in that way, you demonstrate strong business sense and judgment. You spot the implications of your outcomes and conclude correctly by discussing the so-what? of your analysis.

Putting numbers into perspective is also a valuable skill during a sanity check (e.g., “Is it really possible that we could increase our revenue by 200 million if we currently only make 50 million? Let me check my calculations again because that doesn’t seem right.” ).

On the other hand, if you are basing your recommendation solely on the outcome of a calculation, it makes sense to also discuss qualitative arguments to demonstrate your holistic big-picture thinking. Management consulting math goes beyond simple calculations, involving strategic thinking and analysis. For instance, if you recommend choosing a supplier solely because it is cheaper than the others, you could discuss that you would also like to look at the quality of their products, the supply chain, the availability, etc. Supplement a quantitative result with qualitative factors and vice versa.

Express problems quantitatively

Instead of approaching problems purely from a qualitative side, make a habit of using equations to describe relationships, ideas, and parts of the issue tree (if appropriate). It helps your thinking, shows that you are structured in your approach, and demonstrates that you are not afraid to get your quantitative hands dirty. A brief example: “Our client’s train tracks on Route A suffer from more than 100% utilization during the peak hours, leading to delays for many trains and passengers. What ways can you think of that could improve the capacity issue?”

To investigate and improve the over-utilization of the route, you could come up with the following equation: Utilization = demand / capacity. From this equation, you can instantly see that you need to either decrease demand or increase the capacity to improve the utilization situation. Demand and Capacity could be potential top-level buckets for your issue tree. You can now list investigative areas or ideas below each to structure your problem analysis. This approach would help you to quickly isolate quantitatively where the problem is coming from and how big it is, then quantify your remedies as you go along, indicating the best levers to pull and the best course of action.

Sanity check everything

Quantitative problems come with the most potential for errors and mistakes as they involve multiple challenging steps and actions you need to go through before reaching a sensible outcome. You want to avoid mistakes in the first place, but we all know that they do happen; even on the job later on. If you cannot avoid a mistake, at least try to catch your own mistakes before the interviewer does. How can you do that?

• Do not assume that the approach you came up with on the spot is correct without double-checking or thinking it through properly (the importance of taking time) .
• Remain vigilant and aware that mistakes are common in the math section. Never communicate the outcome of a calculation before double-checking that it is at least in the right ballpark and not the result of a careless mistake (the importance of sanity checking).

This also applies (or even more so) when you think that the math seems to be relatively easy. I have seen many interviewees getting caught off guard with simple math problems since they pay less attention to them compared to more difficult examples, then falling into a trap or making avoidable mistakes.

In sum, sanity-check your approach to the problem and outcome of each (intermediate) calculation. Use your judgment to spot calculation and estimation results that seem out of line (e.g., 18.3% vs. 183%). There are eight typical error sources:

• The logic is off or too complex.
• Your calculation is wrong (e.g., forgetting to carry the one, magnitude errors).
• You use the wrong numbers for the right approach. I see this often when candidates do not have organized notes and – in the heat of the moment – plug in the wrong numbers to calculate, even though their approach is correct.
• Your assumptions are off.
• You round numbers too generously or simplify the calculations too much (more on rounding later in this chapter).
• You fail to keep track of units and compare apples and oranges (more on that next).
• You forget one or several steps of your calculation. I see this often when candidates are glad to have made it through the math section yet forget to work on the final step of their approach (e.g., adding up two numbers).
• You interpret the results in the wrong way. I see this often when candidates are happy to have finished their calculations and then jump to a conclusion without thinking first. For instance, if we are comparing several scenarios and are interested in the alternative with the best net benefit, you would want to recommend the alternative with the highest result (highest net benefit). Some candidates do not think and select the alternative with the lowest number (lowest net benefit) as they somehow confuse lower with being better in this situation, by mixing it up with costs in their mind. Always make sure to interpret your results correctly and define what your outcome should be when drafting and communicating your approach.

If you spot a mistake and have not yet communicated the faulty result, ask for more time to sanity-check the calculation or the approach. If you have already blurted out a wrong number, state “This cannot be right.”  Then, go back to think about your approach or re-do the calculation. Provide reasons why your numbers might be off. Fix the problem quickly if the interviewer does not intervene. Most importantly, do not get thrown off by a mistake, and keep your composure.

Do not go faster after a mistake. Often, follow-up mistakes occur due to your newfound sense of urgency and disappointment in your performance. From my experience, more than 50% of candidates who make a math mistake make another one in the next two minutes. Rather, slow down and take some extra time to pick yourself up! It is not necessarily over yet unless you let it impact your performance going forward.

Keep track of units

Do not lose track of your units. Is it kg or tons, is it USD or EUR, etc.?

• When receiving the brief for a math question, write down every number including its unit.
• While setting up the calculation already prepare (either mentally or preferably on paper) a space for the end result including the correct unit.
• Keep the units for your intermediate results organized and label every number.

Interviewers might use different units for different numbers to check if you are paying close attention or simply just to confuse you. Stay vigilant, play back the units to make sure you have noted them down correctly. You must track the units of the input variables, and manipulate them correctly (i.e., convert all to the same unit), to then get to the right output. Do not compare apples and oranges.

Sometimes interviewers also use multiple units for one variable. For instance, “Our client would pay USD 500 per employee per year with option #1 and USD 1000 per three employees for 10 months with option #2.” Pay close attention in such cases and convert both options to the same units before comparing them, e.g., cost per employee per year.

Use shortcuts in your approach

Set up efficient and effective calculations. Most analyses in the business world rely on multiple assumptions and reasonable estimates, therefore not requiring a 100% level of precision. Hence, most of the time, close-to-correct answers are expected. Employ shortcuts in your approach to get accurate and directionally correct answers. Less is often more.

A couple of examples:

• When drafting formulas, always look for the simplest way to get to an accurate answer. For instance, if you are asked to decide between two potential suppliers by comparing the cost of both over a 40-week period, yet all information in the brief is on a weekly basis, for your decision it is enough to calculate and compare the weekly cost for each. If for some reason you want to calculate the difference over 40 weeks, first take the difference of the weekly cost, then multiply it by 40. Alternatively, you could calculate the cost for each supplier for 40 weeks, and then calculate the difference, but you would end up with more calculation steps and more difficult calculations since larger numbers are involved.
• Think critically about what outcome is needed to support your decision. For instance, if you must find out if the profit margin of a deal for 30 aircraft is more than 10% there is no need to calculate the profit margin for all 30 units but calculating the profit margin for one aircraft is sufficient to evaluate the deal. This leaves you with smaller numbers which are easier to handle and interpret.
• When evaluating which option out of several is the best, only look at metrics that differ for every option. For instance, if the fixed cost for every option is the same, yet the variable cost and revenue are different, you would only need to consider the latter two to provide a recommendation (given that you are not asked to evaluate the total value of each option but just to pick the best).

Always explain your logic, shortcuts, and simplifications to the interviewer. They need to understand why your approach is enough to answer the question. Ninety-nine percent of the time, they will agree. Your final results won’t be 100% accurate either way and are not expected to be for most cases. Use plausible shortcuts in your approach and calculation to reach plausible numbers. The same is true for rounding.

Simplify and round numbers

Like the point above, use rounding to make your calculations easier and minimize the risk of mistakes. Ask the interviewer if it is okay to round beforehand and explain exactly how you want to do it. For instance, if you come up with a revenue number of 82.5 million, ask to use 80 million instead. State beforehand that you will trim the fat a bit; if the interviewer agrees, proceed with your calculation. Similarly, if you get 42.65 as an intermediate result say that in the following calculations, this will be rounded down to 40. Other examples include:

• 83 million Germans become 80 million
• 331 million Americans become 320 or even 300 million (by making some clever assumptions explaining why not everyone in the population should be included in your approach, e.g., by excluding certain demographic segments or areas)
• 365 days in a year become 350 or even 300 days (by making some clever assumptions about bank holidays, opening hours, weekends, etc.)
• USD 983 million in revenue becomes one billion.

The tricky part about rounding numbers is to know when it is a good time to do so. Some case math questions demand precise results. For example, if you are asked whether an investment has an ROI above 12% and you can already spot that the final result is close to that number, it would be wise to calculate with precision. Similarly, if you are comparing two alternatives or outcomes, be careful. Outcomes could be very close to each other so extensive rounding might just flip their ranking and the direction of your answer. That is why you should always ask if you can round and provide details on how you would like to do it. That way, the interviewer could provide feedback on whether rounding is a good idea or not.

On the other hand, rounding is especially helpful when 100% precise answers are not needed. For instance, when you calculate a singular outcome, i.e., not comparing multiple numbers or outcomes. You might also round if your calculations yield only directionally correct results anyway, and precise answers are not expected, for instance, when you need to rely on (multiple) assumptions in your approach. Examples would be estimating the size of a market or the impact of a measure, which come with many assumptions and degrees of uncertainty.

What are the best practices related to rounding?

You should round only within a ten percent margin, ideally less, and within five percent. Otherwise, you might skew the results, over or understate the outcome, and provide false recommendations. Think about the impact of rounding consecutive numbers. You can either get more precise results because the effects cancel each other out or magnify the blur of rounding.

For instance, if you want to calculate the revenue, which is quantity times price and the quantity is 9,500 units and the price is USD 35, you could calculate with a quantity of 10,000 and a price of USD 30. That roughly keeps you in a 10% margin of the precise result. If you round both numbers in the same direction, up or down, you would already be off by around 20% from the precise result.

To create a general rule: When you sum two numbers or multiply them, make sure to round one number up and the other one down, essentially rounding in the opposite direction. If you want to subtract or divide, make sure to round both numbers either up or down, rounding in the same direction. Lastly, whenever you deal with indivisible items, round them up to a whole. For instance, if you calculate that you would need to purchase 533.4 new cars for a taxi company to meet their demand, round it up to 534. There are no half-cars.

Take your time

The single biggest lever to improve the outcome of your quantitative analysis is to take time and perform numerical tasks on your terms. What this means is that you should not get pressured to answer or calculate on the spot but rather ask the interviewer for some time to prepare your logic and then, again, to perform your calculations. One minute is usually fine for the logic and up to three minutes are okay for the actual calculations. Of course, faster is better but faster and wrong is worse than slow, steady, and accurate.

Remember our initial discussion. You do not need to have a spike in every area of the case, yet you should avoid mistakes at all costs. A slow but accurate math answer helps you get the offer if you demonstrate spikes in other areas. A wrong but fast answer might lead to a rejection, even if you spike in other areas.

Do not feel pressured to talk to the interviewer while you are thinking or calculating. Focus on one thing at a time. Only communicate your logic, your results, or if you want, your intermediate outcomes once you are done with each step.

Watch the 0s

You would not believe how many candidates fall into this trap. Many people struggle with large numbers, simplify them by cutting zeros, and then end up losing zeros along the way or even adding some to the result. Watch out for zeros that you have trimmed or left out to facilitate your calculations. There are two best practice solutions to deal with and keep track of zeros:

• scientific notation.

For labels, add k for thousand (000), m for million (000,000), and b for billion (000,000,000) when manipulating larger numbers. That way you can simplify and keep track of your zeros.

Alternatively, by applying the scientific notation, you can trim the power of 10s and then perform simple calculations. Once you reach a conclusion you can add your zeros back. Let’s look at one example: Calculate 96 x 1,300,000.

First, just calculate 96 x 13 x 10 5 , essentially getting rid of the five zeros of the second number: 96 x 13 = 96 x 10 + 96 x 3 = 1,248

Add the 5 zeros back, which makes it to 124,800,000.

Another example, a division: 1.4bn / 70mn = (1.4 x 10 9 ) / (7 x 10 7 ) = 0.2 x 10 2 = 20

When adding the zeros back, for a multiplication you would add the superscripted numbers, for a division you would subtract one from the other.

Adopt one of the two options discussed above when practicing so it becomes second nature to you. You will never struggle with zeros again.

Case Interview Math Practice Questions

Practice case math question #1.

It’s important to understand what to expect when preparing for your case interviews.

Let’s look at the following case interview math example:

Scenario : Imagine you are a consultant working for a beverage company, “RefreshCo,” which is considering launching a new line of herbal tea products. RefreshCo aims to understand the potential market size, profitability, and key financial metrics associated with this launch to make an informed decision. Your task is to help RefreshCo by analyzing if the breakeven will be achieved within 5 years. Data provided : RefreshCo estimates the initial investment for launching the new herbal tea line at $2 million. The expected lifetime of the product in the market is 5 years. The target market size for herbal tea in Year 1 is estimated at 2 million potential purchases initially, with a 5% annual growth rate. RefreshCo aims to capture a 10% market share in Year 1, with a 10% growth in market share each subsequent year. The selling price per unit is set at $4, with the cost of goods sold (COGS) at $2.5 per unit. Fixed costs (excluding the initial investment) are estimated at $500,000 per year. Prompt for a case interview math problem

Take some time to work on this question and then come back to the solutions below.

Let’s go through the calculations for each section in detail:

Market size calculation

The market size for each year is calculated using the compound growth formula: Market size=Initial market size×(1+Growth Rate)^Years

• Year 1 : 2,000,000 (Given)
• Year 2 : 2,000,000×(1+0.05)=2,100,000
• Year 3 : 2,000,000×(1+0.05)^2=2,205,000
• Year 4 : 2,000,000×(1+0.05)^3=2,315,250
• Year 5 : 2,000,000×(1+0.05)^4=2,431,013

You could also calculate each year based on the number of the previous year.

Revenue projections

Revenue is calculated as the product of potential customers and selling price, considering the annual growth in market share.

• Year 1 Revenue : 800,000 (Calculated based on market share, which is growing by 10% every year, and the selling price)
• Year 2 Revenue : 924,000
• Year 3 Revenue : 1,067,220
• Year 4 Revenue : 1,232,639
• Year 5 Revenue : 1,423,698

Profitability analysis

Profit for each year is calculated by subtracting total costs (COGS per unit multiplied by the number of units sold plus fixed costs) from total revenue.

• Year 1 Profit : −200,000 (Revenue minus costs)
• Year 2 Profit : −153,500
• Year 3 Profit : −99,792
• Year 4 Profit : −37,760
• Year 5 Profit : 33,887

Break-even analysis

The break-even point is not reached within the 5-year period as cumulative costs exceed cumulative revenues throughout the period. Based on the calculations, RefreshCo will not achieve breakeven within the first 5 years of launching the new line of herbal tea products.

By the end of the 5th year, the cumulative profit (including the initial investment as a negative profit) is still negative, amounting to approximately -$2,457,166 .

To facilitate and speed up your calculations you could also work with shortcuts such as generous rounding or estimating the impact of the growth rate in market size and market share. The result would still be directionally correct, indicating that this is not a good business idea.

Practice case math question #2

Let’s look at another example:

Scenario : AutoPartsCo is a manufacturer specializing in automotive parts. Due to increasing demand, the company is exploring ways to optimize its production process for one of its key products: brake pads. The company operates two production lines, Line A and Line B, each with different capacities, costs, and output levels. Your task as a consultant is to analyze the provided data and recommend which production line should be optimized to maximize efficiency and reduce costs, based on average cost per unit. Data provided : Line A : Capacity: 10,000 units/month Current monthly production: 8,000 units Fixed costs: $120,000/month Variable cost per unit: $15 Line B : Capacity: 15,000 units/month Current monthly production: 12,000 units Fixed costs: $150,000/month Variable cost per unit: $12 Based on the average cost per unit, recommend which production line AutoPartsCo should focus on optimizing. Consider factors like capacity utilization and potential for cost reduction. Prompt for a case interview math problem

• For Line A and Line B, calculate the total costs (fixed costs + total variable costs) and then divide by the number of units produced to find the average cost per unit.
• Total Variable Costs for each line are calculated as the product of the variable cost per unit and the number of units produced.
• Compare the average costs per unit between Line A and Line B to determine which line is currently more cost-efficient.
• Assess the capacity utilization for each line (current production divided by total capacity) to identify potential for optimization.
• Based on the cost efficiency and capacity utilization, recommend which production line offers the best opportunity for optimization and why.

Average cost per unit:

• Line A : The average cost per unit is $30.
• Line B : The average cost per unit is $24.5.

Capacity utilization

• Both Line A and Line B have a capacity utilization rate of 80%.

Recommendation

Based on the average cost per unit, Line B is currently more cost-efficient than Line A, with a lower average cost per unit of $24.5 compared to $30 for Line A. Additionally, both production lines are operating at the same capacity utilization rate of 80%, suggesting that neither line is currently overburdened.

Considering the lower average cost per unit and equal capacity utilization, AutoPartsCo should focus on optimizing Line B . Optimizing Line B could further reduce costs and enhance efficiency, given its already lower cost base and potential for increasing production closer to its full capacity without the immediate need for significant capital investment.

This recommendation is made with the assumption that demand can absorb the increased production and that similar quality standards can be maintained across both lines. Further analysis could involve exploring ways to reduce the variable and fixed costs of Line A or increasing its production volume to improve its cost efficiency.

Mental Math Concepts and Shortcuts

Mental math for consulting requires practice and strategy. Below are some tricks to become faster, more accurate, and more comfortable with case math as well as more advanced concepts that you might encounter during interviews. The more often you employ these tricks during practice and work with certain concepts, the more it becomes second nature to you. Sometimes you might be able to combine a couple of tricks to become even faster.

While there are many specific calculation shortcuts (e.g., when multiplying a number by eleven), you should focus on a couple of shortcuts that are replicable and can be used for most situations. Don’t try to memorize many different shortcuts that only have highly isolated use cases. Internalize and use a few shortcuts well. Like everything else in consulting interviews: Do not boil the ocean.

Basic arithmetic calculations

Master quick and effective arithmetic shortcuts essential for acing Bain, BCG, and McKinsey math case interviews:

Learn these simple shortcuts and use the examples below as pointers.

Build groups of 10

When adding up numbers, build groups of numbers that add up to 10 or multiples of 10.

7 + 3 + 12 + 8 + 5 + 5 = 40

(10) + (20) + (10) = 40

Go from left to right

356 + 678 = (356 + 600) + 70 + 8 = (956 + 70) + 8 = 1026 + 8 = 1034

This is a simple way to become faster and more accurate once you have internalized it.

Subtractions

Make it to 10

When performing quick subtraction, figure out what makes it to 10.

For instance: 4 2 – 2 5

• Reverse the subtraction for the unit digit (5 – 2 = 3)
• Add the number that would make it to 10 (3 + 7 = 10); this is the units digit of the result
• Add 1 to the digit on the left of the number you are subtracting (2 + 1 = 3)
• You end up with 7 on the unit digit and 4 – 3 = 1 on the 10s place, which is 17

Let’s use another example: 3853 – 148

• Reverse the unit digit (8 – 3 = 5)
• Add the number that would make it to 10 (5 + 5 = 10)
• Add 1 to the digit on the left of the number you are subtracting (4 + 1 = 5)
• You end up with 5 on the unit digit, 5 – 5 = 0 on the 10s place, and 8 – 1 = 7 on the hundreds place, which gives you a result of 3705

With a bit of practice, the what do you need to add to make it to 10 becomes an automated habit for your subtractions: 1 + 9, 2 + 8, 3 + 7, 4 + 6, 5 + 5, 6 + 4, 7+ 3, 8 + 2, 9 + 1

You can use the same approach we’ve discussed for additions for subtractions as well:

42 – 25 = (42 – 20) – 5 = 22 – 5 = 17

Multiplications

Get rid of 0s

To make your calculations simpler, get rid of the zeros at first, adding them again at the end. For instance, if asked to calculate 34 x 36,000,000: convert it into 34 x 36m, which is 1,224, then add six zeros to that number which is 1,224,000,000

Use the label method ( “m” ) or the scientific notation (x10 6 ). If you had to multiply 3,400 times 36,000,000: convert again to 3.4k x 36m, which is 122.4, then move the comma to the right side of the 4 and add eight zeros (the sum of the zeros you got rid of in the beginning: 3 + 6), which is 122,400,000,000. Using the scientific notation, we would end up with this: (3.4 x 10 3 ) x (36 x 10 6 ) = 122.4 x 10 9 = 122,400,000,000.

Break apart multiplications by expanding them and breaking one of the terms into simpler numbers. For instance: 18 x 5 = 10 x 5 + 8 x 5 OR (20 – 2) x 5 = 20 x 5 – 10 = 90

Factor with five

Factor common numbers to simplify your calculations when dealing with multiples of 5. For instance: 17 x 5 = 17 x 10 / 2 = 85.

Another example would be 20 x 15 = 20 x 10 x 3 / 2 = 300

The most common numbers to keep in mind are: 5 = 10 / 2; 7.5 = 10 x 3 / 4; 15 = 10 x 3 / 2; 25 = 100 / 4; 50 = 100 / 2; 75 = 100 x 3 / 4

Exchange percentages

Sometimes you can exchange percentages to simplify the calculation. For instance:

60 x 13% = 0.6 x 13 or 6 x 1.3 = 7.8

Convert to yearly data

If you want to convert daily to yearly data, instead of multiplying by 365, multiply by 30 and then by 12, which would add up to 360 days. For most cases, this is close enough and can be argued for well by using certain assumptions, e.g., bank holidays, and downtimes. Always notify interviewers about your assumptions and simplifications.

Convert percentages

Convert percentages into divisions. For instance: 20% of 500 = 500 x 1 / 5 = 500 / 5 = 100

Split into 10ths

Split numbers into 10ths. For instance: 60% of 200 = 10% of 200 x 6 = 120

Apply expansion in a similar manner as described already for multiplications:

• Simple example: 35 / 5 = 30 / 5 + 5 / 5 = 6 + 1 = 7
• More complex example: 265 / 5 = 200 / 5 + 60 / 5 + 5 / 5 = 40 + 12 + 1 = 53

This can be extremely useful when trying to estimate a number as you do not need to perform all calculations up to the last digit to get to a ballpark estimate, e.g., 200 / 5 + 60 / 5 = 52 ≈ 50

Advanced case math concepts

In case interviews, calculating the average is popular since it is simple, yet demands several calculations to arrive at a result. It is a good pressure test for candidates. For example, you might be presented with a table containing data on three products, each with different production costs and the same production quantity. You might have to calculate the average production cost for one unit. The average is the sum of terms divided by the number of terms. For instance, the production cost of Product A is 5, of Product B, 10, and of Product C, 15. The average production cost is (5 + 10 + 15) / 3 = 30 / 3 = 10 for one unit.

A common variation is weighted averages . Instead of each of the data points contributing equally to the final average, some data points contribute more than others and therefore, need to be weighted differently in your calculations. If the weights add up to one, multiply each number by its weight and sum the results. If the weights do not add up to one, multiply each variable by their weight, sum the results, and then divide by the sum of the weights.

To stick with the example above, Product A might be responsible for 20% of the sales, whereas Product B and C for 30% and 50% respectively. Alternatively, it could be written as the following: There are 40 units of Product A, 60 units of Product B, and 100 units of Product C. The weighted average is: 5 x 20% + 10 x 30% + 15 x 50% = 5 x 0.2 + 10 x 0.3 + 15 x 0.5 = 1 + 3 + 7.5 = 11.5. For the second set, you could calculate it as: (5 x 40 + 10 x 60 + 15 x 100) / 200 = 11.5. Other common contexts, where you are asked to calculate averages could be growth rates, demographics, economic data, geographies and countries, product categories, business segments and units, revenue streams, prices, cost data, etc.

Fractions, ratios, percentages, and rates

Fractions, ratios, percentages, and rates are all different sides of the same coin and can help expedite your calculations.

For instance, fractions can be used to represent a number between 0 and 1. Expressing numbers as fractions and using them for additions and subtractions as well as multiplication and divisions can help you solve problems faster and more conveniently through simplification. For example, you can write 0.167 as 1/6, or 0.5 as 1/2. You can also combine fractions with large number divisions. For instance, let’s assume you want to see how much percent 400k is of 1.7m.

Write it as a fraction: 4/17 = 1/17 x 4

Now look at the division table for 1/17, which is 0.059, essentially 0.06.

1/17 x 4 = 0.06 x 4 = 0.24 or 24%

If you had calculated it more accurately by taking three times as long, you would get to 0.235 or 23.5%, rounding it up again to 24%.

As you can see, using fractions for larger number divisions can be a huge time saver. I would recommend you learn all fractions up to a divisor of 20 (e.g., 1/20) by heart, using the fraction table I shared earlier. It increases your speed and accuracy in interviews.

Ratios are comparisons of two quantities, telling you the amount of one thing in relation to another. If you have five apples and four oranges, the ratio is 5:4 and you have nine fruits in total. In case interviews, one tip is to write ratios as fractions of the total, e.g., apples are five out of a total of nine fruits, which is 5/9.

Percentages are a specific form of ratios, with the denominator always being fixed at 100. From experience, almost 80% of case interviews include some reference to or use of percentages, pun intended. Discussion points such as “Revenue increased by 15%” or “Costs are down four percent over the last six months” are common. Percentages are also useful when you want to put things into perspective, state your hypotheses, or guide your next steps. For instance, “That would translate to a 15% increase compared to our current revenue. Now, is a 15% increase realistic? What would we need to do to achieve this?”

Be careful not to mix percentage points with percentages. A percentage point or percent point is the unit for the arithmetic difference of two percentages. For example, moving up from 40% to 44% is a four-percentage point increase, but it is a 10% increase in what is being measured. Interviewers might ask for one or the other.

Rates are ratios between two related quantities in different units, where the denominator is fixed at one. If the denominator of the ratio is expressed as a single unit of one of these quantities, and if it is assumed that this quantity can be changed systematically (i.e., is an independent variable), then the numerator of the ratio expresses the corresponding rate of change in the other (dependent) variable. To make this more practical, let’s look at common rates. One common type of rate is per unit of time , such as speed or heart rate. Ratios with a non-time denominator include exchange rates, literacy rates, and many others. Case interviews might include some of the following rates:

• Growth rate: the ratio of the change of one variable over a period versus the starting level
• Exchange rate: the worth of one currency in terms of another
• Inflation rate: the ratio of the change in the general price level in a period to the starting price level
• Interest rate: the price a borrower pays for the use of the money they do not own (ratio of payment to amount borrowed)
• Price-earnings ratio: the market price per share of stock divided by annual earnings per share
• Rate of return: the ratio of money gained or lost on an investment relative to the amount of money invested
• Tax rate: the tax amount divided by the taxable income
• Unemployment rate: the ratio of the number of people who are unemployed to the number of people in the labor force
• Wage rate: the amount paid for working a given amount of time, or doing a standard amount of accomplished work (ratio of payment to time)

If you are not familiar with these or others that might come up, it is always okay to ask the interviewer for a clarification of the definition. Keep an eye on the time frames rates are expressed in. This could be annually (per annum = p.a.), quarterly, per month, etc. Often, information is provided for different time frames, divisors, or units (e.g., “the top speed of vehicle A is two miles per minute, the top speed of vehicle B is 150 miles per hour” ). Interviewers often use different units for different figures to trick you. For instance, when dealing with two different currencies, always convert all numbers to the same currency by using the exchange rate first. Otherwise, you are comparing apples and oranges. Convert to the same before conducting your analysis, calculations, or comparisons.

Growth rates

You should be able to work with growth rates, which is easy for one time period.

• (Increase of 30% in year 1): 100m x 1.3 = 130m

It gets trickier when you must calculate growth over multiple periods. You need to get the compound growth rate first.

• (Increase of 30% in year 1, 30% in year two): 100 x 1.3 x 1.3 = 100 x 1.69 = 169

The latter can be done quickly if you want to calculate growth over two to three time periods. Everything beyond that becomes tedious and lengthy. If you want to calculate growth for several periods, it is better to estimate the outcome. A shortcut is to use the growth rate and multiply it by the number of years.

• (Increase of 4% p.a. over 8 years): 4% x 8 years ≈ 32%; 100 x 1.32 = 132

If you use the exact compound annual growth rate (CAGR), you end up with roughly 137, more accurately 100 x (1+0.04)^8= 136.85. The total deviation of five or roughly 3.5% (5 / 137) due to your simplified approach is close enough. However, be aware that the divergence (the underestimation) increases with larger numbers, higher annual growth rates, and the number of years. In a case interview, you can account for that by adding between 1% and 10% to your outcome value, depending on the numbers you are dealing with. Keep it simple. Adding 5% to the 132 brings us to 138.6, even closer to the exact number.

To use the same approach with varying growth rates, sum them up. For instance:

• (Increase of 4% in year 1, 10% in year 2, 5% in year 3, 7% in year 4): 4% + 10% + 5% + 7% = 26%; 100 x 1.26 = 126

If we calculate the exact number, it is 128.5; again, the shortcut is close enough and much faster. If you add 1% or 2% you are even closer.

You can apply the same tricks to negative growth rates, keeping in mind that you are overestimating the decrease. Lastly, you can use this trick for combinations of positive and negative growth rates as well.

Expected value and outcomes

You might have to compare the impact and success of different recommendations or the expected return on investment. One way to do this is to work with probabilities and calculate the expected value (EV) for a course of action. The expected value for each recommendation is calculated by multiplying the possible outcome by the likelihood of the outcome. You can then compare the expected value of each option and make a decision that is most likely to achieve the desired outcome.

For example, if you have to decide between two projects and your analysis shows that Project A yields USD 50 million with a likelihood of 80% and Project B yields an outcome of USD 100 million with a likelihood of 30%, you will decide for Project A, with an expected value of USD 40 million (Project B: USD 30 million).

• EV(A) = 50m x 0.8 = 40m
• EV(B) = 100m x 0.3 = 30m

If you want to compare the outcome of bundles of recommendations, the expected value is calculated by multiplying each of the possible outcomes by the likelihood of each outcome and then summing all values for each bundle. Sometimes, interviewers keep it simple and set the expected outcome for each alternative to 100%. In such cases, just take the alternative with the better outcome, i.e., the one with a lower cost or the one with a bigger (net) benefit, depending on the question or goal.

Avoid the Most Common Pitfalls and Mistakes

There are several potential pitfalls you need to avoid when approaching case interview math problems.

Avoiding these common pitfalls requires thorough preparation, including practicing mental math, familiarizing oneself with quick calculation techniques, and simulating the interview environment to improve performance under pressure.

What Should You Do When You Get Stuck?

Most candidates start to panic when they don’t know how to structure a math problem. Not all is lost at this point if you stay calm and collected and have a plan to deal with the situation. So, what can you do when you get stuck and don’t know how to proceed?

Before you ask for help, think through the following checklist:

• Do I know what the objective is? What do I need to solve? If you don’t have an answer for that, clarify with the interviewer.
• Do I understand the problem and the details of the question? If you are missing some context, clarify with the interviewer.
• Do I have all the data that I need? Am I missing something, or am I confused due to a large amount of (irrelevant) data?
• What would be the simplest way to approach this? Am I approaching this from a too complex perspective? This is a big sticking point for most candidates.
• Is this similar to something I have worked on during practice?

If you are still not able to move forward, ask for help in a targeted way by offering the interviewer something in exchange. Do not say: “I don’t know what to do. Can you help me?”

Do not stay silent either. Rather explain your current understanding of the situation to the interviewer (e.g., “I believe that in this case, I would need to look at the net benefit of the decision.”).

Discuss your thinking about how you would like to solve the problem on a higher level but are currently missing one or two steps to make it work; then ask for guidance (e.g., “I need to compare the additional costs and revenues. It is clear to me how to get to the revenue numbers. For the additional costs I am not 100% certain that I am approaching this correctly, would you have any input on that” ).

Interviewers want you to succeed and a little push on the math approach does not automatically lead to a rejection unless it happens more frequently in one case or across cases or you need support in more areas of the case.

How to Prepare for Case Interview Math

General practice recommendations.

Incorporate case interview math practice into your preparation plan .

Regardless of your current quantitative reasoning skills, devote time during your case interview preparation to brush up on your mental and pen-and-paper math skills. If you are struggling with math or are dealing with a couple of insecurities in this area, there is no reason not to practice case math drills for at least two hours per day for a couple of weeks.

At the end of your preparation, shortly before your interviews, you want to be in a state where you can tackle every problem you see flawlessly and swiftly with confidence and without anxiety. Your structuring, overall problem-solving, and chart interpretation can be in the highest percentile of all candidates, but if you do not fix your math issues and insecurities, you will still be rejected.

I want to stress this point because most candidates fail due to issues with their quantitative reasoning, something that is entirely preventable with effort and time. I would even go so far as to say that if you do not feel 100% ready to tackle any section of the case, postpone your interviews if you have the chance until you feel fully ready.

There are several things you could do to get up to speed with mental and pen-and-paper math. The trick is to be confident in your ability to efficiently work through simple math and resilient enough to face external pressures in the process. If you are starting out, (re)-learn and practice basic calculus such as additions and subtractions, multiplications and divisions, averages, percentages, and fractions.

Free practice resources and habits

Get used to numerical reasoning by working with numbers you encounter in your daily life, be it the bar tab, the grocery store receipt, or figures and data you find in the news, especially business reporting. Perform simple arithmetic operations on the numbers you encounter in your head or with pen and paper. Do not use a calculator. Work on some simple business cases. For instance, while waiting at the doctor, calculate how much profit they make a month, a year, etc. The opportunities are endless.

Practice with the following free iOS and Android apps.

• Magoosh Mental Math
• Mental Math Cards Challenge
• Coolmath Games: Fun Mini-Games
• Matix Mental Math Games
• Math Games and Mental Arithmetic

Do all of this in a stressful environment. You want to build stamina and resilience to outside influences and stressors. Use the apps in the crowded and noisy subway, calculate during mock interviews with unpleasant interviewers who stress you out, in front of friends and family, or simply with time limits.

Free case interview math drill generator

Boost your case interview preparation with our Case Interview Math Drill Generator. Seamlessly create tailored math problems designed to boost your speed and accuracy and stand out in the interview process field.

You can access the tool for free here:

Our Case Interview Math Mastery Academy

Our comprehensive preparation strategy encompasses two distinct components designed to enhance your case interview readiness, regardless of your current skill level.

First, our “ Case Interview Math Mastery ” course and drills offer a multi-tiered learning experience. This program is meticulously crafted to support you at any stage of your preparation journey, from mastering basic calculations to tackling advanced numerical challenges, exhibit math problems, solving intricate business problems, and navigating full case math scenarios.

It comes with a 25-part video series and 2000 practice drills. Whether you’re starting to build your foundation or refining your skills, our course is structured to elevate your skills comprehensively.

Second, my personalized coaching sessions provide targeted guidance to further your case interview and problem-solving capabilities. With a track record of over 1,600 interviews, each receiving a five-star rating, and hundreds of offers generated for my clients, this coaching service is a testament to my commitment to excellence.

Case Interview Math Mastery (Video Course and 2,000 Exercises)

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Frequently Asked Questions: Case Interview Math

Mastering consulting firm interview math can significantly boost your chances of landing a job at top consulting firms. Preparing for case interviews at top consulting firms like McKinsey, BCG, and Bain involves mastering the art of solving quantitative problems efficiently and accurately. Understanding the basics is crucial, but candidates often have more nuanced questions about improving their performance in case interview math.

Below, we answer the most pressing questions to help you navigate the complexities of case interview math with confidence.

What specific math topics should I review to prepare for consulting case interviews? To excel in consulting case interviews, focus on reviewing arithmetic operations, percentages, ratios, basic algebra, and estimation techniques. Understanding these foundational topics is crucial for analyzing business scenarios and making data-driven decisions. Read through our comprehensive guide to management consulting math to equip yourself with the necessary concepts and learn how to prepare for case interview math with my structured approach.

How can non-quantitative background candidates improve their math skills for case interviews? Candidates from non-STEM or non-business backgrounds should start with basic arithmetic and gradually progress to more complex topics through online courses, practice problems, and math-focused case interview preparation materials. Consistent practice and application of math in real-life scenarios can also enhance proficiency. Elevate your quantitative analysis for consulting interviews by practicing with our curated examples. Practice drills for consulting interview math are essential.

Are there any common mathematical errors to avoid during consulting case interviews? Yes, common errors include incorrect rounding, magnitude errors, note-taking issues, mixing up units of measurement, and overlooking simple arithmetic mistakes. Double-checking your work and practicing mental math in stressful conditions can help avoid these pitfalls.

How do consulting firms evaluate candidates’ mathematical reasoning in case interviews? Consulting firms assess candidates’ ability to logically approach quantitative problems, perform accurate calculations under pressure, and derive meaningful insights from numerical data. Demonstrating clarity in thought process and precision in results is key.

Can you provide examples of complex case interview math problems and how to solve them? Complex case interview math problems often involve multiple steps, such as calculating market sizes, revenue growth over time, or cost optimization strategies. Breaking down the problem into smaller, manageable parts and using a structured approach to solve each part is an effective strategy. For free practice examples, please check this link here . For a professional case interview math course with 2000+ drills, please check out our Math Academy .

How important is speed in solving math problems during consulting case interviews? While directionally correct accuracy is paramount, speed is even more important in case interviews. Being able to quickly perform calculations and reach an outcome in the right ballpark allows more time for analysis and developing recommendations. Practice is essential to improve both speed and accuracy.

What are the best practices for presenting mathematical findings clearly in a case interview? Best practices include summarizing key findings succinctly, explaining the logic behind your calculations, and discussing the implications of your results in the context of the case. Use clear, concise language and structure your response logically. Advanced quantitative problem-solving in case interviews demands not just skill, but also strategic thinking.

How can I practice case interview math under realistic conditions? Simulate the interview environment by practicing math problems under timed conditions, without the use of a calculator, and ideally with a partner or professional case coach to mimic the pressure of real interviews. Online simulators and practice tests can also provide a realistic challenge. Overcoming math challenges in consulting case studies is achievable with the right mindset and tools.

What role does mental math play in consulting case interviews, and how can I improve it? Mental math is crucial for quickly estimating and calculating during discussions. Improving mental math involves regular practice with drills, learning shortcuts, and challenging yourself to do everyday calculations in your head. Mental math is also relevant when talking about strategies for acing McKinsey , BCG , and Bain math tests.

Arming yourself with these insights can dramatically improve your performance in consulting case interviews, setting you on the path to success in your consulting career.

Struggling with case interview math?

Tackling math problems in case interviews can feel overwhelming, but remember, you’re not the only one facing this hurdle. Math, especially under pressure, can be challenging, but it’s a skill that can be honed with practice and the right strategies. If you find yourself puzzled by specific problems or methodologies, don’t hesitate to share your questions below in the comment section. We are happy to help you out!

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Florian spent 5 years with McKinsey as a senior consultant. He is an experienced consulting interviewer and problem-solving coach, having interviewed 100s of candidates in real and mock interviews. He started StrategyCase.com to make top-tier consulting firms more accessible for top talent, using tailored and up-to-date know-how about their recruiting. He ranks as the most successful consulting case and fit interview coach, generating more than 500 offers with MBB, tier-2 firms, Big 4 consulting divisions, in-house consultancies, and boutique firms through direct coaching of his clients over the last 3.5 years. His books “The 1%: Conquer Your Consulting Case Interview” and “Consulting Career Secrets” are available via Amazon.

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Hacking the Case Interview

Although case interviews do not require any technical math or finance knowledge, there are basic formulas that you should know in order to do well in order to master case interview math .

This article will cover the 26 formulas you should know for case interviews. These formulas are organized into the following categories:

• Profit Formulas
• Investment Formulas
• Operations Formulas
• Market Share Formulas
• Accounting, Finance, and Economics Formulas

If you’re looking for a step-by-step shortcut to learn case interviews quickly, enroll in our case interview course . These insider strategies from a former Bain interviewer helped 30,000+ land consulting offers while saving hundreds of hours of prep time.

Profit Formulas for Case Interviews

1. Revenue = Quantity * Price

Revenue is the amount of money a company brings in from selling its products. This can be calculated by taking the number of units sold and multiplying it by the price per unit.

Example: Your company sells shirts for $20 each. Last year, your company sold 1,000 shirts. So, your total revenue last year was 1,000 * $20 = $20,000.

2. Total Variable Costs = Quantity * Variable Costs

Costs are payments that a company needs to make in order to run and operate its business. There are two different types of costs, variable costs and fixed costs.

Variable costs are costs that directly increase for each additional unit of product made. It represents the cost of raw materials needed to make the product.

Total variable costs are calculated by taking the number of units produced or sold and multiplying it by the raw material cost per product.

Example: It costs your company $5 to purchase the raw materials needed to make a shirt. If your company sold 1,000 shirts last year, the total variable costs are 1,000 * $5 = $5,000.

3. Costs = Total Variable Costs + Fixed Costs

Total costs for the company can be calculated by adding total variable costs and fixed costs.

Fixed costs are costs that do not directly increase for each additional unit of product made. They may include costs such as rent for the building or equipment needed to make the product.

Example: Your company pays annual rent of $10,000. It also leases the equipment it needs to make its shirts for $2,000 a year. Therefore, fixed costs are $10,000 + $2,000 = $12,000. Total variable costs were calculated to be $5,000 from the previous example. So, total costs are $12,000 + $5,000 = $17,000.

4. Profit = Revenue – Costs

Profit is the amount of money the company keeps after paying for all of its costs. Profit is calculated by subtracting total costs from total revenue.

Example: Last year, your shirt company generated revenues of $20,000 and had costs of $17,000. The profit last year was $20,000 - $17,000 = $3,000.

5. Profit = (Price – Variable Costs) * Quantity – Fixed Costs

This formula summarizes the previous four formulas into one concise and simplified equation.

6. Contribution Margin = Price – Variable Cost

Contribution margin represents how much money each product sold brings into the company after accounting for the cost of raw materials needed to make the product.

Example: If your company’s shirts sell for $20 and raw materials cost $5, then the contribution margin is $20 - $5 = $15 per shirt.

7. Profit Margin = Profit / Revenue

Profit margin represents the percentage of revenue that a company keeps as profit after taking into account all of its costs.

Example: Last year, your company generated $20,000 in revenue and had $17,000 in costs. Its profit was $3,000. Therefore, your company’s profit margin is $3,000 / $20,000 = 15%.

Investment Formulas for Case Interviews

8. Return on Investment = Profit / Investment Cost

Companies make investments by spending money in the hopes of earning even more money in the future as a result of the investment. Return on investment, or ROI for short, represents how much additional money a company generates relative to the size of its initial investment.

ROI is calculated by taking the profit that the company generated from the investment and dividing it by the investment cost.

Example: Your company spent $5,000 on marketing to advertise its shirts. As a result, the company generated an additional $6,000 in profits from selling shirts. This profit does not yet take into account the costs of the marketing campaign.  Therefore, the company has a net increase in profits of $1,000 from its original $5,000 investment. The ROI is $1,000 / $5,000 = 20%.

9. Payback Period = Investment Cost / Profit per Year

Payback period represents how long it would take a company to recoup the money it spent on an investment. It is usually specified in years.

Example: Your company invested in redesigning its shirts for $5,000. As a result, the company expects annual profits to increase by $1,000 for every year going forward. Therefore, the payback period for this investment is $5,000 / $1,000 = 5 years.

Operations Formulas for Case Interviews

10. Output = Rate * Time

The output of production can be calculated by taking the rate of production and multiplying it by time.

Example: The machine that your company uses to produce shirts can produce 5 shirts per hour. If the machine runs for 12 hours, then it will produce 60 shirts.

11. Utilization = Output / Maximum Output

Utilization represents how much a factory or machine is being used relative to its maximum possible output.

Example: The machine that your company uses to produce shirts can produce 5 shirts per hour. Therefore, its maximum capacity in a day is 5 shirts per hour * 24 hours = 120 shirts. If your machine is being used to only produce 60 shirts per day, then it is at 60 / 120 = 50% utilization.

Market Share Formulas for Case Interviews

12. Market Share = Company Revenue in the Market / Total Market Revenue

Market share measures the percentage of total market sales a particular company has. Market shares can range from 0%, no presence in the market, to 100%, complete dominance in the market.

Example: Your company sells shirts and generates $100M in annual revenues. The market size of shirts is $500M. Therefore, your company has a market share of $100M / $500M = 20%. 

13. Relative Market Share = Company Market Share / Largest Competitor’s Market Share

Relative market share compares a company’s market share to the largest competitor’s market share. It measures how strong of a presence a company has relative to the market leader. If the company is the market leader, relative market share measures how much of a lead they have over the next largest player.

Instead of using company market share and the largest competitor’s market share, you can use company revenue and the largest competitor’s revenue. This will give you the same answer.

Example: Your company has a 20% market share in the shirts market. Your largest competitor has a 50% market share. Therefore, your relative market share is 20% / 50% = 0.4.

Example 2: Your company is the market leader and has a 50% market share in the shirts market. Your largest competitor has a 25% market share. Therefore, your relative market share is 50% / 25% = 2.

Accounting, Finance, and Economics Formulas for Case Interviews

These formulas are much less commonly seen in case interviews than the previous formulas. You likely won’t need to use these formulas since they require more technical knowledge of accounting, finance, and economics.

However, you should still be familiar with these formulas in the small chance that one of these concepts shows up in your case interview.

14. Gross Profit = Sales – Cost of Goods Sold

Gross profit is a measure of how much money a company makes from selling its product after taking into account the costs associated with making and sellings its product. These costs are often called the cost of goods sold.

Compared to the previous profit formula, which was simply revenue minus costs, gross profit is always higher since it does not take into account all of the costs of the business.

Example: Your company sold $20,000 of shirts last year. The cost to produce these shirts was $5,000. Therefore, your gross profit is $20,000 - $5,000 = $15,000.

15. Operating Profit = Gross Profit – Operating Expenses – Depreciation – Amortization

Operating profit is calculated by taking gross profit and subtracting all operating expenses and depreciation and amortization.

Operating expenses may include rent, utilities, maintenance and repairs, advertising and marketing, insurance, and salaries and wages. So, operating profit is always less than gross profit.

Depreciation is the spreading of a fixed asset’s cost over its useful lifetime.

For example, let’s say that a company purchases a new machine for $10,000 that it expects to last for 5 years. Instead of stating that it incurred $10,000 in costs in its first year, the company may choose to state that the new machine costs $2,000 per year for the next five years.

Amortization is the spreading of an intangible asset’s cost over its useful lifetime. It is the exact same principle as depreciation except that it deals with intangible assets, or assets that aren’t physical.

For example, let’s say that a company purchases a patent for $10,000 and expects the benefits of the patent to last for 20 years. Instead of stating that it incurred $10,000 in costs in its first year, the company may choose to state that the patent costs $500 per year for the next twenty years.

Example: You sold $20,000 of shirts last year. Cost of goods is $5,000, operating expenses are $10,000, depreciation of a machine is $2,000, and amortization of a patent is $500. Therefore, your operating profit is $20,000 - $5,000 - $10,000 - $2,000 - $500 = $2,500.

16. Gross Profit Margin = Gross Profit / Revenue

This is the exact same formula as the profit margin formula except that gross profit is used. Gross profit margin measures how much money a company keeps from selling its products after taking into account cost of goods sold.

Example: Your company has a gross profit of $15,000 from $20,000 of revenue. Therefore, your gross profit margin is $15,000 / $20,000 = 75%.

17. Operating Profit Margin = Operating Profit / Revenue

This is the exact same formula as the profit margin formula except that operating profit is used. Operating profit margin measures how much money a company keeps from sellings its products after cost of goods sold, operating expenses, depreciation, and amortization is taken into account.

Example: Your company has an operating profit of $2,500 from $20,000 of revenue. Therefore, your operating profit margin is $2,500 / $20,000 = 12.5%.

18. EBITDA = Operating Profit + Depreciation + Amortization

EBITDA stands for earnings before interest, taxes, depreciation, and amortization. It is a financial metric used to measure a company’s cash flow or the amount of cash that a company has generated in a period of time.

To calculate EBITDA, start with operating profit and add back depreciation and amortization expenses.

Example: Your company has an annual operating profit of $2,500. Depreciation expenses are $2,000 and amortization expenses are $500. Therefore, your EBITDA is $2,500 + $2,000 + $500 = $5,000.

19. CAGR = (Ending Value / Beginning Value)^(1/Time Period) – 1

CAGR stands for compounded annual growth rate. It measures how quickly something is growing year after year.

Example: Your company generates $144M in annual revenue. Two years ago, your company only generated $100M. Over this time period, your CAGR was ($144M / $100M)^(1/2) - 1= 20%. In other words, your company grew by 20% each year for two years.

20. Rule of 72

The Rule of 72 is a shortcut used to estimate how long a market, company, or investment would take to double in size. To use it, simply divide 72 by the annual growth rate to get an estimate for the number of years needed to double in size.

Example: Your company is growing steadily at 9% per year. Using the Rule of 72, we’d expect it to take 72 / 9 = 8 years for your company to double in size if it maintains its current growth rate.

21. NPV = Cash Flow / [(1 + Discount Rate)^(Time Period)]

NPV stands for net present value. It measures how much future cash flow is worth today.

Receiving $1,000 right now is not the same as receiving $1,000 five years from now. If you received $1,000 right now, you could invest it and grow your money. Therefore, it is better to receive $1,000 right now than to receive the same amount in the future.

Net present value takes this into account.

Cash flow is the amount of money you expect to receive in the future. Time period is how many years in the future you will receive that amount of money. The discount rate is the return you expect to get from investing your money.

Example: You expect to receive $1,000 five years from now. You expect that you will be able to get 8% annual returns by investing in the stock market. Therefore, the net present value of your future cash flow is $1,000 / [(1 + 0.08)^5] = $680.58.  In other words, receiving $680.58 today would give you the same value as receiving $1,000 five years from now.

22. Perpetuity Formula: Present Value = Cash Flow / Discount Rate

An annuity is a fixed sum of money paid at regular intervals such as every year. Perpetuity is an annuity that lasts forever.

The present value of a perpetuity is calculated by taking the cash flow of each payment and dividing it by the discount rate.

Example: You are expecting to receive $1,000 per year for the rest of your life. You expect that you will be able to get 8% annual returns by investing in the stock market. Therefore, the present value of this perpetuity is $1,000 / 0.08 = $12,500.  In other words, receiving $12,500 today would give you the same value as receiving $1,000 each year for the rest of your life.

23. Return on Equity = Profit / Shareholder Equity

Return on equity , or ROE for shirt, measures how effectively a company is using its assets to create profits. It is calculated by taking profit and dividing by shareholder equity, which represents the net worth of a company.

In other words, shareholder equity is the value of a company’s total assets minus its total liabilities.

Example: Your company’s profit this year is $100M. Shareholder equity, or the net worth of the company is $1B. Your company has a ROE of $100M / $1B = 10%.

24. Return on Assets = Profit / Total Assets

Return on assets , or ROA for short, measures how profitable a company is relative to its total assets. In other words, it shows how efficiently a company is using its assets to generate income.

Assets can be anything that has value that can be converted into cash. This includes cash, property, equipment, inventory, and investments.

Example: Your company’s profit this year is $100M. Your company as $400M worth of assets. Your company has a ROA of $100M / $400M = 25%.

25. Price Elasticity of Demand = (% Change in Quantity) / (% Change in Price)

Elasticity is a measure of how much customer demand changes for a product given a change in the product’s price. In almost all cases, an increase in a product’s price results in a decrease in customer demand. Therefore, price elasticity of demand is usually negative.

Example: Your company has decreased its product’s price by 10%. As a result, the number of units sold has increased by 20%. Therefore, the price elasticity of demand is 20% / -10% = -2.

26. Cross Elasticity of Demand = (% Change in Quantity for Good #1) / (% Change in Price for Good #2)

Cross elasticity of demand measures how much customer demand changes for a product given a change in price of a different product.

If two products are complements, an increase in price of one product will result in a decrease in demand of the other product. Complementary products have a negative cross elasticity of demand.

If two products are substitutes, an increase in price of one product will result in an increase in demand of the other product. Substitute products have a positive cross elasticity of demand.

Example: A competitor has decreased the price of a competing product by 20%. As a result, the demand for your product has dropped by 10%. The cross elasticity of demand is -10% / -20% = 0.5.

Land Your Dream Consulting Job

Here are the resources we recommend to land your dream consulting job:

For help landing consulting interviews

• Resume Review & Editing : Transform your resume into one that will get you multiple consulting interviews

For help passing case interviews

• Comprehensive Case Interview Course (our #1 recommendation): The only resource you need. Whether you have no business background, rusty math skills, or are short on time, this step-by-step course will transform you into a top 1% caser that lands multiple consulting offers.
• Case Interview Coaching : Personalized, one-on-one coaching with a former Bain interviewer.
• Hacking the Case Interview Book   (available on Amazon): Perfect for beginners that are short on time. Transform yourself from a stressed-out case interview newbie to a confident intermediate in under a week. Some readers finish this book in a day and can already tackle tough cases.
• The Ultimate Case Interview Workbook (available on Amazon): Perfect for intermediates struggling with frameworks, case math, or generating business insights. No need to find a case partner – these drills, practice problems, and full-length cases can all be done by yourself.

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• Behavioral & Fit Interview Course : Be prepared for 98% of behavioral and fit questions in just a few hours. We'll teach you exactly how to draft answers that will impress your interviewer.

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• CBSE Class 10 Study Material

CBSE Class 10 Maths Case Study Questions for Chapter 4 Quadratic Equations (Published by CBSE)

Cbse class 10 maths case study questions for chapter 4 - quadratic equations are released by the board. solve all these questions to perform well in your cbse class 10 maths exam 2021-22..

Check here the case study questions for CBSE Class 10 Maths Chapter 4 - Quadratic Equations. The board has published these questions to help class 10 students to understand the new format of questions. All the questions are provided with answers. Students must practice all the case study questions to prepare well for their Maths exam 2021-2022.

Case Study Questions for Class 10 Maths Chapter 4 - Quadratic Equations

CASE STUDY 1:

Raj and Ajay are very close friends. Both the families decide to go to Ranikhet by their own cars. Raj’s car travels at a speed of x km/h while Ajay’s car travels 5 km/h faster than Raj’s car. Raj took 4 hours more than Ajay to complete the journey of 400 km.

1. What will be the distance covered by Ajay’s car in two hours?

 a) 2(x + 5)km

b) (x – 5)km

c) 2(x + 10)km

d) (2x + 5)km

Answer: a) 2(x + 5)km

2. Which of the following quadratic equation describe the speed of Raj’s car?

a) x 2 – 5x – 500 = 0

b) x 2 + 4x – 400 = 0

c) x 2 + 5x – 500 = 0

d) x 2 – 4x + 400 = 0

Answer: c) x 2 + 5x – 500 = 0

3. What is the speed of Raj’s car?

a) 20 km/hour

b) 15 km/hour

c) 25 km/hour

d) 10 km/hour

Answer: a) 20 km/hour

4. How much time took Ajay to travel 400 km?

Answer: d) 16 hour

CASE STUDY 2:

The speed of a motor boat is 20 km/hr. For covering the distance of 15 km the boat took 1 hour more for upstream than downstream.

1. Let speed of the stream be x km/hr. then speed of the motorboat in upstream will be

a) 20 km/hr

b) (20 + x) km/hr

c) (20 – x) km/hr

Answer: c) (20 – x)km/hr

2. What is the relation between speed ,distance and time?

a) speed = (distance )/time

b) distance = (speed )/time

c) time = speed x distance

d) speed = distance x time

Answer: b) distance = (speed )/time

3. Which is the correct quadratic equation for the speed of the current?

a) x 2 + 30x − 200 = 0

b) x 2 + 20x − 400 = 0

c) x 2 + 30x − 400 = 0

d) x 2 − 20x − 400 = 0

Answer: c) x 2 + 30x − 400 = 0

4. What is the speed of current ?

b) 10 km/hour

c) 15 km/hour

d) 25 km/hour

Answer: b) 10 km/hour

5. How much time boat took in downstream?

a) 90 minute

b) 15 minute

c) 30 minute

d) 45 minute

Answer: d) 45 minute

Also Check:

CBSE Case Study Questions for Class 10 Maths - All Chapters

Tips to Solve Case Study Based Questions Accurately

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Class 12 Maths Case Study Questions

Table of Contents

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Class 12 Maths question paper will have 1-2 Case Study Questions. These questions will carry 5 MCQs and students will attempt any four of them. As all of these are only MCQs, it is easy to score good marks with a little practice. Class 12 Maths Case Study Questions are available on the myCBSEguide App and Student Dashboard .

Why Case Studies in CBSE Syllabus?

CBSE has introduced case study questions in the CBSE curriculum recently. The purpose was to make students ready to face real-life challenges with the knowledge acquired in their classrooms. It means, there was a need to connect theories with practicals. Whatsoever the students are learning, they must know how to apply it in their day-to-day life. That’s why CBSE is emphasizing case studies and competency-based education .

Case Study Questions in Maths

Let’s have a look over the class 12 Mathematics sample question paper issued by CBSE, New Delhi. Question numbers 17 and 18 are case study questions.

Focus on concepts

If you go through each MCQ there, you will find that the theme/case study is common but the questions are based on different concepts related to the theme. It means, that if you have done ample practice on the various concepts, you can solve all these MCQs in minutes.

Easy Questions with a Practical Approach

The difficulty level of the questions is average or say easy in some cases. On the other hand, you get four options to choose from. So, you get two levels of support to get full marks with very little effort.

Practice Questions Regularly

Most of the time we feel that it’s easy and neglect it. But in the end, we have to pay for this negligence. This may happen here too. Although it’s easy to score good marks on the case study questions if you don’t practice such questions, you may lose your marks. So, we suggest students should practice at least 30-40 such questions before writing the board exam.

12 Maths Case-Based Questions

We are giving you some examples of case study questions here. We have arranged hundreds of such questions chapter-wise on the myCBSEguide App. It is the complete guide for CBSE students. You can download the myCBSEguide App and get more case study questions there.

Case Study Question – 1

• A is a diagonal matrix
• A is a scalar matrix
• A is a zero matrix
• A is a square matrix
• If A and B are two matrices such that AB = B and BA = A, then B 2 is equal to

Case Study Question – 2

• 4(x 3  – 24x 2   + 144x)
• 4(x 3 – 34x 2   + 244x)
• x 3  – 24x 2   + 144x
• 4x 3  – 24x 2   + 144x
• Local maxima at x = c 1
• Local minima at x = c 1
• Neither maxima nor minima at x = c 1
• None of these

Case Study Questions Matrices -1

Answer Key:

Case Study Questions Matrices – 2

Read the case study carefully and answer any four out of the following questions: Once a mathematics teacher drew a triangle ABC on the blackboard. Now he asked Jose,” If I increase AB by 11 cm and decrease the side BC by 11 cm, then what type of triangle it would be?” Jose said, “It will become an equilateral triangle.”

Again teacher asked Suraj,” If I multiply the side AB by 4 then what will be the relation of this with side AC?” Suraj said it will be 10 cm more than the three times AC.

Find the sides of the triangle using the matrix method and  answer the following questions:

• (a) 3  ×  3

Case Study Questions Determinants – 01

DETERMINANTS:  A determinant is a square array of numbers (written within a pair of vertical lines) that represents a certain sum of products. We can solve a system of equations using determinants, but it becomes very tedious for large systems. We will only do 2 × 2 and 3 × 3 systems using determinants. Using the properties of determinants solve the problem given below and answer the questions that follow:

Three shopkeepers Ram Lal, Shyam Lal, and Ghansham are using polythene bags, handmade bags (prepared by prisoners), and newspaper envelopes as carrying bags. It is found that the shopkeepers Ram Lal, Shyam Lal, and Ghansham are using (20,30,40), (30,40,20), and (40,20,30) polythene bags, handmade bags, and newspapers envelopes respectively. The shopkeeper’s Ram Lal, Shyam Lal, and Ghansham spent ₹250, ₹270, and ₹200 on these carry bags respectively.

• (b) Shyam Lal
• (a) Ram Lal

Case Study Questions Determinants – 02

Case study questions application of derivatives.

• R(x) = -x 2  + 200x + 150000
• R(x) = x 2  – 200x – 140000
• R(x) = 200x 2  + x + 150000
• R(x) = -x 2  + 100 x + 100000
• R'(x) > 0
• R'(x) < 0
• R”(x) = 0
• (a) -x 2  + 200x + 150000
• (a) R'(x) = 0
• (c) 257, -63

Case Study Questions Vector Algebra

• tan−1⁡(5/12)
• tan−1⁡(12/3)
• (b) 130 m/s
• (a)  tan−1⁡(5/12)
• (b) 170 m/s

More Case Study Questions

These are only some samples. If you wish to get more case study questions for CBSE class 12 maths, install the myCBSEguide App. It has class 12 Maths chapter-wise case studies with solutions.

12 Maths Exam pattern

Question Paper Design of CBSE class 12 maths is as below. It clearly shows that 20% weightage will be given to HOTS questions. Whereas 55% of questions will be easy to solve.

• No. chapter-wise weightage. Care to be taken to cover all the chapters
• Suitable internal variations may be made for generating various templates keeping the overall weightage to different forms of questions and typology of questions the same.

Choice(s): There will be no overall choice in the question paper. However, 33% of internal choices will be given in all the sections

12 Maths Prescribed Books

• Mathematics Part I – Textbook for Class XII, NCERT Publication
• Mathematics Part II – Textbook for Class XII, NCERT Publication
• Mathematics Exemplar Problem for Class XII, Published by NCERT
• Mathematics Lab Manual class XII, published by NCERT

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Case Study Based Questions – Class 10 Maths

CBSE has recently added Case Study Based Questions or CSQ in Maths, Science and Social Science. You can visit this article to get to practice the official Sample Papers released by CBSE by clicking  over here . Also do join out telegram channel to get all the updates and to participate in Quiz by  clicking here.

What is Case Study Based Questions or CSQ?

Case Study Based or CSQ are typically questions in which the paragraph or passage is given and you simply have to answer them. This questions are not very tough to solve and are introduced so that you score better marks as schools and tuition are kept closed due to the COVID Pandemic. As a result, this had to be introduced. This is resulting to us, by having 34 MCQ which is really very good for scoring 100/100 in CBSE.

How to start preparing for CSQ’s?

To start preparing for CSQ you will need to learn all the chapters very thoroughly especially all the chapters of Geometry. CSQ from Maths can include a mixture of many chapters thus preparing all the concepts is must. They will surely be helpful. After completing all your syllabus you will need to practice a lot. So scroll below to find more than 15 Case study based question.

Is it Easy, Hard or Moderate?

This questions are very simple if practiced at least 20-25 questions than you can easily score lot of good marks or you can score full in Maths!! Practice all the questions below.

How much time to give to each CSQ?

You will be getting 4 Case Study Question’s each would be having 5 sub questions out of which you have to just do 4 questions. So find the shortest and most theoretical question as theoretical questions doesn’t required much solving and it will not even take 1 min to solve. Each question should not take more than 6 min, resulting to only 24 min for 16 questions which is enough. Solving as many CSQ helps in better understanding and reducing the time for each question.

Below are more than 15 examples of CSQ’s for Maths!

1st Case Study Based Question

Shankar is having a triangular open space in his plot. He divided the land into three parts by drawing boundaries PQ and RS which are parallel to BC. Other measurements are as shown in the figure.

• What is the area of this land? i) 120 m 2 ii) 60 m 2 iii) 20 m 2 iv) 30 m 2
• What is the length of PQ? i) 2.5 m ii) 5 m iii) 6 m iv) 8 m
• The length of RS is i) 5 m ii) 6 m iii) 8 m iv) 4 m
• Area of △APQ is i) 7.5 m 2 ii) 10 m 2 iii) 3.75 m 2 iv) 5 m 2
• What is the area of △ARS? i) 21.6 m 2 ii) 10 m 2 iii) 3.75 m 2 iv) 6 m 2

2nd Case Study Based Question

There is some fire incident in the house. The fireman is trying to enter the house from the window as the main door is locked. The window is 6 m above the ground. He places a ladder against the wall such that its foot is at a distance of 2.5 m from the wall and its top reaches the window.

• Here, be the ladder and be the wall with the window. i) CA, AB ii) AB, AC iii) AC, BC iv) AB, BC
• We will apply Pythagoras Theorem to find length of the ladder. It is: i) AB 2 = BC 2 – CA 2 ii) CA 2 = BC 2 + AB 2 iii) BC 2 = AB 2 + CA 2 iv) AB 2 = BC 2 + CA 2
• The length of the ladder is              . i) 4.5 m ii) 2.5 m iii)6.5 m iv) 5.5 m
• What would be the length of the ladder if it is placed 6 m away from the wall and the window is 8 m above the ground? i) 12 m ii) 10 m iii) 14 m iv) 8 m
• How far should the ladder be placed if the fireman gets a 9 m long ladder? i) 6.7 m (approx.) ii) 7.7 m (approx.) iii) 5.7 m (approx.) iv) 4.7 m (approx.)

3rd Case Study Based Question

In the school garden Ajay(A), Brijesh(B), Chinki(C) and Deepak(D) planted their flower plants of Rose, Sunflower, Champa and Jasmine respectively as shown in the following figure. A fifth student Eshan wanted to plant her flower in this area. The teacher instructed Eshan to plant his flower plant at a point E such that CE: EB = 3 : 2.

• Find the coordinates of point E where Eshan has to plant his flower plant. i) (5, 6) ii) (6, 5) iii) (5, 5) iv) (6, 7)
• Find the area of △ECD. i) 9.5 square unit ii) 11.5 square unit iii) 10.5 square unit iv)12.5 square unit
• Find the distance between the plants of Ajay and Deepak. i) 8.60 unit ii) 6.60 unit iii) 5.60 unit iv) 7.60 unit
• The distance between A and B is: i) 5.5 units ii) 7 units iii) 6 units iv) 5 units
• The distance between C and D is: i) 5.5 units ii) 7 units iii) 6 units iv) 5 units

4rth Case Study Based Questions

SUN ROOM The diagrams show the plans for a sun room. It will be built onto the wall of a house. The four walls of the sunroom are square clear glass panels. The roof is made using

• Four clear glass panels, trapezium in shape, all the same size.
• One tinted glass panel, half a regular octagon in shape

• Find the mid-point of the segment joining the points J (6, 17) and I (9, 16).[Refer to Top View] i) ( 33/2 , 15/2 ) ii) ( 3/2 , 1/2 ) iii) ( 15/2 , 33/2 ) iv) ( 1/2 , 3/2 )
• The distance of the point P from the y-axis is; [Refer to Top View] i) 4 ii) 15 iii) 19 iv) 25
• The distance between the points A and S is: [Refer to Front View] i) 4 ii) 8 iii) 16 iv) 20
• Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1:3 internally. [Refer to Front View] i) (8.5, 2.0) ii) (2.0, 9.5) iii) (3.0, 7.5) iv) (2.0, 8.5)
• If a point (x,y) is equidistant from the Q(9,8) and S(17,8), then [Refer to Front View] i) x + y = 13 ii) x – 13 = 0 iii) y – 13 = 0 iv) x – y = 13

5th Case Study based Question

Education with vocational training is helpful in making a student self-reliant and to help and serve the society. Keeping this in view, a teacher made the following table giving the frequency distribution of a student undergoing vocational training from the training institute.

• Median class of above data: i) 20 – 24 ii) 20.5 – 24.5 iii) 19.5 – 24.5 iv) 24.5 – 29.5
• Calculate the median. i) 24.06 ii) 30.07 iii) 24.77 iv) 42.07
• The empirical relationship between mean, median, mode: i) Mode = 3 Median + 2 Mean ii) Mode = 3 Median – 2 Mean iii) Mode = 3 Mean + 2 Median iv) 3 Mode = Median – 2 Mean
• If mode = 80 and mean = 110, then find the median. i) 200 ii) 500 iii) 190 iv) 100
• The mode is the: i) middlemost frequent value ii) least frequent value iii) maximum frequent value iv) none of these

6th Case Study Based Question

Two brothers Ramesh and Pulkit were at home and have to reach School. Ramesh went to Library first to return a book and then reaches School directly whereas Pulkit went to Skate Park first to meet his friend and then reaches School directly.

• How far is School from their Home? i) 5 m ii) 3 m iii) 2 m iv) 4 m
• What is the extra distance travelled by Ramesh in reaching his School? i) 4.48 metres ii) 6.48 metres iii) 7.48 metres iv) 8.48 metres
• What is the extra distance travelled by Pulkit in reaching his School? (All distances are measured in metres as straight lines) i) 6.33 metres ii) 7.33 metres iii) 5.33 metres iv) 4.33 metres
• The location of the library is: i) (-1, 3) ii) (1, 3) iii) (3, 1) iv) (3, -1)
• The location of the Home is: i) (4, 2) ii) (1, 3) iii) (4, 5) iv) (5,4)

7th Case Study Based Question

The Class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Sapling of Gulmohar is planted on the boundary of the plot at a distance of 1m from each other. There is a triangular grassy lawn inside the plot as shown in Fig. The students have to sow seeds of flowering plants on the remaining area of the plot.

• Considering A as the origin, what are the coordinates of A? i) (0, 1) ii) (1, 0) iii) (0, 0) iv (-1, -1)
• What are the coordinates of P? i) (4, 6) ii) ( 6, 4) iii) (4, 5) iv) (5, 4)
• What are the coordinates of R? i) (6, 5) ii) (5, 6) iii) ( 6, 0) iv) (7, 4)
• What are the coordinates of D? i) (16, 0) ii) (0, 0) iii) (0, 16) iv) (16, 1)
• What are the coordinates of P if D is taken as the origin? i) (12, 2) ii) (-12, 6) iii) (12, 3) iv) (6, 10)

8th Case Study Based Question

There exist a tower near the house of Shankar. The top of the tower AB is tied with steel wire and on the ground, it is tied with string support. One day Shankar tried to measure the longest of the wire AC using Pythagoras theorem.

• In the figure, the length of wire AC is: (take BC = 60 ft) i) 75 ft ii) 100 ft iii) 120 ft iv) 90 ft
• What is the area of △ABC? i) 2400 ft 2 ii) 4800 ft 2 iii) 6000 ft 2 iv) 3000 ft 2
• What is the length of the wire PC? i) 20 ft ii) 30 ft iii) 25 ft iv) 40 ft
• What is the length of the hypotenuse in △ABC? i) 100 ft ii) 80 ft iii) 60 ft iv) 120 ft
• What is the area of a △POC? 100 ft 2 150 ft 2 200 ft 2 250 ft 2

9th Case Study Based Question

• SCALE FACTOR AND SIMILARITY SCALE FACTOR: A scale drawing of an object is the same shape as the object but a different size. The scale of a drawing is a comparison of the length used on a drawing to the length it represents. The scale is written as a ratio. SIMILAR FIGURES: The ratio of two corresponding sides in similar figures is called the scale factor. Hence, two shapes are Similar when one can become the other after a resize, flip, slide, or turn.

• A model of a boat is made on a scale of 1:4. The model is 120cm long. The full size of the boat has a width of 60cm. What is the width of the scale model? i) 20 cm ii) 25 cm iii) 15 cm iv) 240 cm
• What will affect the similarity of any two polygons? i) They are flipped horizontally ii) They are dilated by a scale factor iii) They are translated down iv) They are not the mirror image of one another
• If two similar triangles have a scale factor of a: b. Which statement regarding the two triangles is true? i) The ratio of their perimeters is 3a: b ii) Their altitudes have a ratio a: b iii) Their medians have a ratio a/2:b iv)Their angle bisector have a ration a 2 :b 2
• The shadow of a stick 5m long is 2m. At the same time, the shadow of a tree 12.5m high is: i) 3m ii)3.5m iii)4.5m iv)5m
• Below you see a student’s mathematical model of a farmhouse roof with measurements. The attic floor, ABCD in the model, is a square. The beams that support the roof are the edges of a rectangular prism, EFGHKLMN. E is the middle of AT, F is the middle of BT, G is the middle of CT, and H is the middle of DT. All the edges of the pyramid in the model have a length of 12 m.

What is the length of EF, where EF is one of the horizontal edges of the block? i) 24m ii) 3m iii) 6m iv) 10m

10th Case Study Based Question

An Aeroplan leaves an Airport and flies due north at 300 km/h. At the same time, another Aeroplan leaves the same Airport and flies due west at 400 km/h.

• Distance travelled by the first Airplane in 1.5 hours i) 450 km ii) 300 km iii) 150 km iv) 600 km
• Distance travelled by the second Airplane in 1.5 hours i) 450 km ii) 300 km iii) 150 km iv) 600 km
• Which of the following line segment shows the distance between both the airplane? i) OA ii) AB iii) OB iv) WB
• Which airplane travelled a long distance and by how many km? i) Second, 150 km ii) Second, 250 km iii) First, 150 km iv) First, 250 km
• How far apart the two airplanes would be after 1.5 hours? i) 600 km ii) 750 km iii) 300 km iv) 150 km

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Class 10 IT PYQs Ebook

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Class 10 Maths Case Study Questions PDF Download

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Are you looking for a reliable source to download Class 10 Maths case study questions in PDF format? Look no further! In this article, we will provide you with a comprehensive collection of case study questions specifically designed for Class 10 Maths Case Study Questions . Whether you are a student or a teacher, these case study questions will prove to be a valuable resource in your preparation or teaching process.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 10  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

Table of Contents

CBSE 10th Maths: Case Study Questions With Answers

Students taking the 10th board examinations will see new kinds of case study questions in class. The board initially incorporated case study questions into the board exam. The chapter-by-chapter case study question and answers are available here.

Chapterwise Case Study Questions for Class 10 Mathematics

Case study questions are an essential component of the Class 10 Mathematics curriculum. They provide students with real-world scenarios where they can apply mathematical concepts and problem-solving skills. By analyzing and solving these case study questions, students develop a deeper understanding of the subject and improve their critical thinking abilities.

The above  Case studies for Class 10 Maths  will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of schools.studyrate.in for the benefit of Class 10 students.

• Class 10th Science Case Study Questions

Benefits of Case Study Questions for Class 10 Mathematics

Case study questions offer several benefits to both students and teachers. Here are some key advantages:

• Practical Application : Case study questions bridge the gap between theory and real-life situations, allowing students to apply mathematical concepts in practical scenarios.
• Analytical Thinking : By solving case study questions, students enhance their analytical thinking and problem-solving skills.
• Conceptual Clarity : Case study questions help reinforce the fundamental concepts of mathematics, leading to improved conceptual clarity.
• Exam Preparation : Practicing case study questions prepares students for their Class 10 Mathematics exams, as they become familiar with the question formats and types.
• Comprehensive Assessment : Teachers can use case study questions to assess students’ understanding of various mathematical concepts in a comprehensive manner.

How to Use Case Study Questions Effectively

To make the most out of the case study questions, follow these effective strategies:

• Read the question carefully : Understand the given scenario and identify the mathematical concepts involved.
• Analyze the problem : Break down the problem into smaller parts and determine the approach to solve it.
• Apply relevant formulas and concepts : Utilize your knowledge of the subject to solve the case study question.
• Show your working : Clearly demonstrate the steps and calculations involved in reaching the solution.
• Check your answer : Always verify if your solution aligns with the given problem and recheck calculations for accuracy.

Tips for Solving Case Study Questions

Here are some useful tips to excel in solving case study questions:

• Practice regularly : Regular practice will enhance your problem-solving skills and familiarity with different question formats.
• Understand the concepts: Ensure you have a strong foundation in the underlying mathematical concepts related to each chapter.
• Work on time management : Practice solving case study questions within a stipulated time to improve your speed and efficiency during exams.
• Seek clarification : If you encounter any doubts or difficulties, don’t hesitate to seek guidance from your teacher or peers.

Case study questions are an invaluable resource for Class 10 Mathematics students. They provide practical application opportunities and strengthen conceptual understanding. By utilizing the chapter-wise case study questions provided in this article, students can enhance their problem-solving skills, prepare effectively for exams, and develop a deeper appreciation for the subject.

FAQs on Class 10 Maths Case Study Questions

Q1: can i download the class 10 maths case study questions in pdf format.

Yes, you can download the Class 10 Maths case study questions in PDF format from our site free of cost.

Q2: Are the case study questions aligned with the latest curriculum?

Yes, the case study questions presented in this article are designed to align with the latest Class 10 Mathematics curriculum.

Q3: How can case study questions improve my exam preparation?

Case study questions help you understand the practical application of mathematical concepts, enabling you to approach exam questions with greater confidence and clarity.

Q5: Where can I find more resources for Class 10 Mathematics preparation?

Download more resources of Class 10th Maths from schools.studyrate.in, we offer additional resources and practice materials for Class 10 Mathematics.

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Case Study Questions for Class 10 Maths Chapter 7 Coordinate Geometry

• Last modified on: 1 year ago
• Reading Time: 3 Minutes

Case Study Questions:

Question 1:

The top of a table is shown in the figure given below:

(i) The coordinates of the points H and G are respectively (a) (1, 5), (5, 1) (b) (0, 5), (5, 0) (c) (1, 5), (5, 0) (d) (5, 1), (1, 5)

(ii) The distance between the points A and B is (a) 4 units (b) 4 2 units (c) 16 units (d) 32 units

(iii) The coordinates of the mid point of line segment joining points M and Q are (a) (9, 3) (b) (5, 11) (c) (14, 14) (d) (7, 7)

(iv) Which among the following have same ordinate? (a) H and A (b) T and O (c) R and M (d) N and R

(v) If G is taken as the origin, and x, y axis put along GF and GB, then the point denoted by coordinate (4, 2) is (a) H (b) F (c) Q (d) R

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Case Study Class 10 Maths Questions and Answers (Download PDF)

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Case Study Class 10 Maths

If you are looking for the CBSE Case Study class 10 Maths in PDF, then you are in the right place. CBSE 10th Class Case Study for the Maths Subject is available here on this website. These Case studies can help the students to solve the different types of questions that are based on the case study or passage.

CBSE Board will be asking case study questions based on Maths subjects in the upcoming board exams. Thus, it becomes an essential resource to study. 

The Case Study Class 10 Maths Questions cover a wide range of chapters from the subject. Students willing to score good marks in their board exams can use it to practice questions during the exam preparation. The questions are highly interactive and it allows students to use their thoughts and skills to solve the given Case study questions.

Download Class 10 Maths Case Study Questions and Answers PDF (Passage Based)

Download links of class 10 Maths Case Study questions and answers pdf is given on this website. Students can download them for free of cost because it is going to help them to practice a variety of questions from the exam perspective.

Case Study questions class 10 Maths include all chapters wise questions. A few passages are given in the case study PDF of Maths. Students can download them to read and solve the relevant questions that are given in the passage.

Students are advised to access Case Study questions class 10 Maths CBSE chapter wise PDF and learn how to easily solve questions. For gaining the basic knowledge students can refer to the NCERT Class 10th Textbooks. After gaining the basic information students can easily solve the Case Study class 10 Maths questions.

Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

How to Solve Case Study Based Questions Class 10 Maths?

In order to solve the Case Study Based Questions Class 10 Maths students are needed to observe or analyse the given information or data. Students willing to solve Case Study Based Questions are required to read the passage carefully and then solve them. 

While solving the class 10 Maths Case Study questions, the ideal way is to highlight the key information or given data. Because, later it will ease them to write the final answers. 

Case Study class 10 Maths consists of 4 to 5 questions that should be answered in MCQ manner. While answering the MCQs of Case Study, students are required to read the paragraph as they can get some clue in between related to the topics discussed.

Also, before solving the Case study type questions it is ideal to use the CBSE Syllabus to brush up the previous learnings.

Features Of Class 10 Maths Case Study Questions And Answers Pdf

Students referring to the Class 10 Maths Case Study Questions And Answers Pdf from Selfstudys will find these features:-

• Accurate answers of all the Case-based questions given in the PDF.
• Case Study class 10 Maths solutions are prepared by subject experts referring to the CBSE Syllabus of class 10.
• Free to download in Portable Document Format (PDF) so that students can study without having access to the internet.

Benefits of Using CBSE Class 10 Maths Case Study Questions and Answers

Since, CBSE Class 10 Maths Case Study Questions and Answers are prepared by our maths experts referring to the CBSE Class 10 Syllabus, it provided benefits in various way:-

• Case study class 10 maths helps in exam preparation since, CBSE Class 10 Question Papers contain case-based questions.
• It allows students to utilise their learning to solve real life problems.
• Solving case study questions class 10 maths helps students in developing their observation skills.
• Those students who solve Case Study Class 10 Maths on a regular basis become extremely good at answering normal formula based maths questions.
• By using class 10 Maths Case Study questions and answers pdf, students focus more on Selfstudys instead of wasting their valuable time.
• With the help of given solutions students learn to solve all Case Study questions class 10 Maths CBSE chapter wise pdf regardless of its difficulty level.

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Home » Extras » Class 10 Maths Competency Based Questions 2024-25: Download PDF

Class 10 Maths Competency Based Questions 2024-25: Download PDF

Class 10 Maths Competency Based Questions are available for download here on aglasem.com. These Class 10 Competency Based Questions include MCQs, fill in the blanks, short answer questions, long answer questions, and answer key from the Maths curriculum and need you to apply understanding a little beyond the 10th class Maths textbook. For CBSE students, understanding and mastering these questions is crucial for success in Maths exam. Here you will understand what Competency Based Questions for Maths are, how they differ from traditional questions, and get tips on tackling these questions. You can also download Class 10 Competency Based Questions Maths PDF .

Class 10 Maths Competency Based Questions 2024-25

Here you can access a wide array of CBSE Competency Based Questions for the Maths subject. The PDF includes Multiple Choice Questions, Fill in the Blanks, Short Answer Questions, and Long Answer Questions, along with the answer key for class 10 Maths. The Competency Based Questions for Class 10 Maths can be found here.

Class 10 Maths Competency Focused Practice Questions Download Link – Click Here to Download 10 Maths CBQ PDF

Class 10 Maths Competency Based Questions PDF

The complete pdf for competency focused practice questions for Maths is as follows.

What are Maths Competency Based Questions?

These are designed to evaluate a student’s understanding of concepts of Maths, their ability to apply knowledge in real-life situations, and their critical thinking skills. Unlike traditional questions that may focus on rote learning or memorization, Competency Focused Questions require students to demonstrate a deeper comprehension of the subject matter (Maths). These questions measure various competencies in the Maths subject, such as problem-solving, logical reasoning, creativity, and subject-specific skills.

For Class 10 Competency Based Questions of Maths , students are expected to think beyond the Maths textbook and demonstrate their skills in a way that aligns with real-world applications.

• Class 10 Competency Based Questions

In addition to Maths, the Competency Focused Questions for all subjects for students in 10th standard are as follows.

• Social Science

Other Classes CBQ Download Links

Similarly the class wise CBQ practice question bank for school board are as follows.

• Class 3 Competency Based Questions
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• Class 5 Competency Based Questions
• Class 6 Competency Based Questions
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Class 10 Maths Competency Questions  – An Overview

The highlights of this educational resource are as follows.

Competency Based Questions are revolutionizing the way students approach their studies. By focusing on the core competencies required by the CBSE board, students in Class 10 can develop the skills necessary to excel academically and beyond. Whether you are dealing with Class 10 Maths Competency Based Questions or any other subject, remember to focus on understanding, application, and critical thinking.

Start practicing today, and make these questions a core part of your study strategy. The more you engage with these questions, the more confident you’ll become in your ability to tackle any challenge that comes your way!

If you have any queries on 10th Maths Specimen Paper 2025, then please ask in comments below.

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• Visualizing Solid Shapes Class 7 Case Study Questions Maths Chapter 13

Last Updated on September 7, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 13 Visualizing Solid Shapes. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Visualizing Solid Shapes

An ice-cream cart has an ice-candy drawn on all sides, except the top and the bottom

Q. 1. Which geometric shape does the ice-cream container resemble? (a) Cuboid (b) Cylinder (c) Cone (d) Pyramid

Ans. Option (a) is correct. Explanation: Cuboid

Q. 2. How many ice-candies are drawn on the cart? (a) 1 (b) 2 (c) 4 (d) 6

Ans. Option (c) is correct. Explanation: There are 4 ice-candies drawn on the cart.

• Symmetry Class 7 Case Study Questions Maths Chapter 12
• Exponents and Powers Class 7 Case Study Questions Maths Chapter 11
• Algebraic Expressions Class 7 Case Study Questions Maths Chapter 10
• Perimeter and Area Class 7 Case Study Questions Maths Chapter 9
• Rational Numbers Class 7 Case Study Questions Maths Chapter 8
• Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
• Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
• Lines and Angles Class 7 Case Study Questions Maths Chapter 5
• Simple Equations Class 7 Case Study Questions Maths Chapter 4
• Data Handling Class 7 Case Study Questions Maths Chapter 3

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Plane figures and solid shapes
• Faces, edges and vertices of solid shapes
• Nets for building 3-D shapes
• Drawing solids on a flat surface
• Visualising different section of a solid

Plane figures are of two-dimensions and solid figures are of three-dimensions. In a solid figure, the corners are the vertices, the line segments are its edges and its flat surface are its faces.

A net is an arrangement of plane figures connected at their edges, lying in the same plane, that can be folded to make a three-dimensional solid.

Figures drawn on paper are called plane figure. Solid figures are those figures which occupy space.

Case study questions from the above given topic may be asked.

Plane figures are 2-dimensional, while solids are 3-dimensional. Visualising solid shapes is a very useful skill. You should be able to see ‘hidden’ parts of the solid shape.

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Frequently Asked Questions (FAQs) on Visualizing Solid Shapes Case Study

Q1: what are solid shapes.

A1: Solid shapes are three-dimensional figures that have length, breadth, and height. Common examples of solid shapes include cubes, cuboids, cones, and cylinders. Unlike two-dimensional shapes, these objects occupy space and can be viewed from different perspectives.

Q2: What is the difference between 2D and 3D shapes?

A2: 2D shapes have only two dimensions—length and breadth—and can be drawn on flat surfaces, like squares or circles. In contrast, 3D shapes have three dimensions—length, breadth, and height—like cubes or spheres. While 2D shapes can be represented easily on paper, 3D shapes are visualized as solid objects that occupy space.

Q3: What are oblique and isometric sketches?

A3: An oblique sketch is a simple way to represent a 3D object on a 2D plane. It gives a distorted view because one side is drawn at an angle. An isometric sketch , on the other hand, provides a more accurate representation of a solid object, with all dimensions to scale, giving a clearer idea of how the object looks from different angles

Q4: How can we visualize cross-sections of solids?

A4: Cross-sections are the shapes you get when you slice a solid object along a plane. For example, cutting a cylinder horizontally would give a circular cross-section, while cutting a cube horizontally or vertically would give a square cross-section.

Q5: How are shadows of 3D objects formed?

A5: Shadows of 3D objects depend on the shape of the object and the angle of light. For example, a cube can cast a square or rectangular shadow, while a cylinder can cast a circular or rectangular shadow based on how light falls on it. Visualizing shadows helps in understanding how 3D objects interact with light​.

Q6: What are polyhedrons?

A6: Polyhedrons are three-dimensional shapes with flat faces. Each face is a polygon, and the edges of the polygons meet at vertices. Common examples of polyhedrons include cubes (with square faces) and pyramids (with triangular faces). A polyhedron is named based on the shape and number of its faces.

Q7: How do you calculate the number of faces, edges, and vertices of a solid shape?

A7: For polyhedrons, the relationship between the number of faces (F), edges (E), and vertices (V) is given by Euler’s formula: V − E + F = 2 This formula helps in identifying the structure of a polyhedron. For example, a cube has 8 vertices, 12 edges, and 6 faces, satisfying Euler’s formula.

Q10: Are there any online resources or tools available for practicing Visualizing Solid Shapes case study questions?

A10: We provide case study questions for CBSE Class 7 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

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