There is no way around it - **your case interview is going to feature math and you are going to need
to be good at it to get any consulting job, let alone an MBB one**. However, this is not to say
you need a math degree to be a consultant. In a standard case interview, the math will be **no more
complicated than what you learnt in high school**. However, consulting math is **very
different to academic math** and you won't get far approaching problems the same way you would
have done in school.

In this article, we'll first look at what makes math so important for aspiring consultants and what makes
consulting math different. We'll then run through a list of the **areas in which you need to be
proficient in**, whilst giving some tips on **"hacks"** which you can use to excel
in interview.

**Math is one of the most important elements of preparing for a consulting interview** and this
article is a great point of entry into the subject. However, it is impossible to be fully comprehensive in
any reasonable amount of space - for one thing, we're not going to reproduce your high school math textbook
here! Where appropriate, we'll point you towards useful public resources, including other articles on this
site. Generally, though, if you want a more comprehensive source, you should check out our **Consulting
Math video lesson within the MCC Academy**.
Our **Consulting Math package** is also great for
practice, along with our **free mental math
tool**. This article will get you started, but the these **additional sources will
give everything you need** to have a real chance at landing your dream consulting job.

## Consulting math calculations in principle

You might think that “math is math” and that being good at academic math - perhaps at a university level -
will mean you have nothing to fear from a consulting interview conducted at a high school level. Certainly,
it is true that being good at math in an academic context is a great advantage going into a consulting
interview. However, **the style of math used in consulting is very different from that used in
academia and takes practice to pick up**. Even a very accomplished mathematician will struggle to
impress if they do not approach problems in the way their interviewer is expecting.

In academic math, the overriding concern is accuracy. It might take a lot of complex work and much time to
get there, but what matters is that the answer is absolutely watertight. Consulting math is a very different
beast. Working consultants - and consulting interview candidates - are always under **time
pressure**. Results are what matter and **answers are required simply to be good
enough to guide business decisions, rather than being absolutely correct**. A 90%
accurate answer

*now*is a lot more useful than a 100% accurate one after a week of in-depth analysis. The additional mathematical complexity required to reach such a totally accurate, precise answer is thus not required. Rather,

**consultants will simplify their analyses in order to be more time efficient**.

Your interviewer will also attach a **special importance to mental math**. Of course, being
able to do mental math quickly shows general mental agility. However, consultants also specifically use
quick mental math in order to impress clients (and thus help justify their fees). The sharper your mental
math, the more impressed your interviewer will be. We have a brief section on mental math skills below, with
much more detailed treatment in the MCC
Academy.

## Consulting math in practice

So, now we know a little about how academic and consulting math differ. This is good knowledge to have, but
we should keep an eye on practicalities and the **nuts and bolts of how things will actually be in
your interview**. Let's get some of the most straightforward matters out of the way before we
look at consulting math in more depth:

### Perform Calculations on Paper

You will be given a piece of paper and should feel free to use it when doing calculations.

### Don't Rush with Math

The time pressure in case interviews is severe, and you cannot afford to waste time. By the same token,
though, taking **a few extra seconds to get to a correct answer** is always preferable to
producing an incorrect answer a few seconds more quickly. **Don't be afraid to take the time you
need**. "Slow is smooth and smooth is fast".

### Be Assertive during Your Case Interview

**Candidates which are not really comfortable with math tend to state their answers as
questions** - with a rise in vocal pitch towards the end of the sentence. **Interviewers
will notice** this and take note. Successful candidates will be confident and state
their answers with an air of certainty.

### Ask About Rounding when Doing Math

**Ask your interviewer** if it is okay to round numbers in your calculations. Generally,
they will be fine with this, and you can do so.

### Forget outdated, framework-based guides...

Interviewers are sick of seeing candidates miss the point and make the same old mistakes. Stand out from the crowd by learning to think like a working consultant! Get started## Fundamentals: a checklist of consulting math skills

So, which skills will you need? Here, we'll go through the **main areas which you should cover to prep
for a standard MBB interview**.

We go into much more depth on each issue - along with worked examples and "hacks" for quicker calculations - in our video lesson in the MCC Academy. Of course, though, if you really weren't paying any attention in school and are totally in the dark as to what a fraction is - there is a point where you will simply need to simply pick up a basic math textbook from your local library.

### 1. Fractions

Fractions are a convenient way to represent numbers between 0 and 1 as parts of a whole. For instance, we might write 0.5 as 1 / 2 (or simply 1/2). For your interview, you should be readily able to add/subtract and multiply/divide fractions. There are a couple of ways to manipulate fractions which will particularly facilitate your mental math:

#### Approximating Divisions

Say you have to work out 107 ÷ 13. You only have a few seconds and no calculator. Certainly,
**you won't have time for long division** - so what will you do? The interviewer is
waiting...

One specific use of fractions is in allowing us to tackle complex divisions quickly. For example, let's imagine we do indeed have to divide 107 by 13:

We know that:

Thus:

This method gives us a **good-enough answer to proceed with our analysis, with only a few
seconds work** and no need for a calculator. Success!

#### Navigating Math Problems in an Efficient Way

Fractions can also help to simplify your analysis of certain problems. Let's take the following relatively simple example:

In a company 1/3 of employees are engineers. Due to staff restructuring, 1/3 of the engineers is laid off. What fraction of the remaining employees are engineers?

Engineers laid off:

Remaining engineers:

Employees remaining in the company:

Therefore the fraction of remaining employees who are engineers is:

### 2. Ratios

Ratios are **close cousins of fractions**, and tell us how much of one thing we have in
relation to another. For instance, if we have three pens, for pencils, and one eraser, then the ratio
between them is 3:4:1.

### Join thousands of other candidates cracking cases like pros

At MyConsultingCoach we teach you how to solve cases like a consultant Get started
Many different business scenarios require an understanding of ratios. As regards solving cases, it is
**often very useful to express ratios as fractions of the whole**. For example, we can
re-express the ratio between our items of stationery above as
3
/
8
:
4
/
8
:
1
/
8
. This then allows you to address problems with a similar method to how we solved our example of
engineers in a workforce, above.

Think about how you might address the following question:

Restaurant Barbello’s profits are split among food drinks and tips in a 7:3:2 ratio. If the profit for food is 360 USD more than the one for drinks what is the total profit?

You should be able to get to an answer very quickly - certainly in under a minute. **We show you
how to do so in the MCC Academy
video lesson**.

### 3. Percentages

Similar to fractions and ratios, we can think of percentages as ratios expressed where one number is fixed at 100, or as fractions where the denominator is always 100.

Percentages are as ubiquitous in the business world as they are in interview case studies. We might be
dealing with **profits**
which are down 40%, targeting increases in **sales** or revenue by 20% or attempting to cut
**costs**
by 15%. We are especially likely to deal with percentages when working with issues around
**pricing**, such as
applying **mark-ups** on products to generate profit or offering discounts to promote
sales.

One item to note here is that **sometimes percentages will be discussed in terms of "percentage
points"**. As such, if you are informed that revenues are down by 20 percentage points - or
even just 20 points - this simply means that they have fallen by 20%.

You can test your ability to work with percentages by seeing how quickly you can work out an answer to the following:

Marta has a shop and she sells handbags for 30 EUR. She offers a 20% discount for a day. She then realises that the price is too low so she increases the price by 10%. What it is the current handbag price?

In the MCC Academy math video, we run through a method to let you answer this question in just a few seconds.

### 4. Probability

Nothing is certain in the business world, and consultants will constantly have to evaluate the
probability of different future events when they make decisions. The probability of such an event will
always be a **number between 0 (impossible) and 1 (certain)**, calculated as the number of
ways that an event can happen divided by the total number of possible outcomes. Therefore, the
probability of rolling a six on a fair dice is 1/6, as there are a total of six possible outcomes, only
one of which is a case of the event in question.

The **probability of an event not happening** is 1 minus the probability that it will. In
proper notation, this is:

You will also need to know how to **calculate the probability of multiple chance events**
all occurring in future. Luckily, in **case interview, you will only have to deal with independent
events**, where individual outcomes do not influence subsequent ones. The standard example
here is coin tosses, where the probability of heads on each new toss remains 0.5, regardless of the
results of previous tosses (despite any intuitions in line with the
gambler's fallacy). This
is as opposed to dependent events, where the outcomes of one event can influence subsequent ones. You
might recall examples of these events from school problems about taking colored balls out of vases
without replacing them - in any case, we don't need to worry about dependent events here!

**The probability of multiple independent events all happening is calculated simply as the product
of their individual probabilities**. To illustrate, the probability of heads (P(H)) on the
toss of a fair coin is 0.5. Therefore, the probability of tossing heads three times in a row is:

#### Expected Returns

Probability is especially relevant to business in **calculating expected returns**.
Here, we **weight the yield promised by an investment by the probability that it will pay
off**. This then acts as a guide to decisions about which investment opportunities should
be pursued.

Say we have $100 to invest and that we can choose between two opportunities that will pay out after one year. Option A will pay out $120 with a probability of 0.9, whereas option B promises to pay out $150, but with a probability of only 0.7.

The expected returns are:

Option A: | 0.9 x 120 = $108 |

Option B: | 0.7 x 150 = $105 |

As such, we should favour option A as yielding a greater expected return, despite option B's greater
headline payout. **We take a look how to calculate a more complex expected return in the
MCC Academy video
lesson.**

### 5. Averages

When we consider “the average” here, we will technically be referring to the arithmetic mean. We can
think of this as a measure of the **"typical" value of some series of numbers**. It is
calculated as **the sum of all the numbers in the series, divided by the number of those
numbers**. We can state this more formally as:

Averages are fairly straightforward. The **only complexities you will need to worry about arise
when the values you are averaging do not have the same weight as one another**. In such
cases, the calculations will start to look rather like those for expected returns, where appropriate
weightings are applied.

Let's take an example to see how well you can manipulate averages. How long does it take you to solve this problem? Could you do so under time pressure in a case interview?

A company has 80 employees. 25% work on average 6 hours a day, 65% 8 hours and the rest 12 hours a day. What is the average time an employee work?

We show you two different ways to solve this problem in the MCC Academy math lesson.

### 6. Rates

Rates are **ubiquitous throughout the business world in general and in consulting in
particular**. We can think about rates as a ratio or fraction where the denominator is always
1. Some rates we will typically encounter include the **interest rate, the rate of inflation,
various tax rates, rate of return on an investment and the exchange rates between
currencies**.

Rates are very common in case studies and will **generally be expressed per year (per
annum)**. Candidates can easily become confused, though, where information is

**not all provided in the same units**. As such, it is best to

**convert all such quantities into one set of units**to facilitate comparison. For instance, with a mix of monthly and annual rates, it might be best (depending on the details of the problem) to convert all the relevant figures into per annum rates.

In the MCC Academy math lesson, we work through a business case study, advising a firm whether to invest on new equipment based on an analysis of different rates. This demonstrates how central rates can be to business problems, as well as how to work with them efficiently.

### 7. Optimisation

Optimisation is of central importance in various fields, and the optimisation of complex, non-linear problems is a substantial area of academic study, with real-world applications ranging from engineering to finance.

Mercifully, though, **optimisation in consulting interviews is a pretty straightforward
affair**. Any business **problems you will be given will be linear** - their
form will resemble something like ** y = ax + b**. This means that they will be

**optimised at one of the function's boundaries**. To establish which boundary value yields the optimum, we simply need to

**work out the gradient of the function**- or, more simply, whether this gradient is positive or negative.

As such, if we are trying to maximise y for the function below, where y = 2x + 1, between x=0 and x=4, we can see that the positive gradient (upward slope) of the line means that y will be maximised for the maximum possible value of x - which is 4 in this case.

Note that, in the section on writing equations below, we also discuss a way to solve linear optimisation problems without doing any calculations or referring to a graph.

We work though **examples of optimisation in case studies in the
MCC Academy math lesson**.

Now, let's try an example of the kind of optimisation which you might have to deal with in a case interview:

Your client is Ginetto’s gelato, a shop that sells ice cream in London. They make fresh ice cream on-site every day using high quality, organic ingredients. If they have excess ice cream, they freeze it to make ice lollies that are then sold to another retailer. Making a kilo of ice cream costs Ginetto £15, and it is sold for £30. Ice lollies, however, can only be sold for £12. On any given day, the shop expects to sell 100kg of ice cream if it is sunny and only 30kg if it is rainy. In London, the probability of rain on any given day is 75%. Ginetto has asked you how much gelato they should make to maximize their profit.

This will seem like a knotty problem if you don't know what you're doing. However, in
MCC Academy, we show you how to optimise
Ginetto's ice cream production in two different ways, demonstrating **how to deal with these kinds
of interview questions in straightforward and - crucially - time efficient fashion**.

## Charts

The above pretty much covers the fundamental math you will need to reach a solution to your case. However, there are other, related skills which you will need, beyond familiarity with these basic concepts.

Some mathematical skills will be required throughout the case, not just in computing final solutions. In particular, it is likely that you will have to interpret charts as you lead the analysis. Case interviews are not like exams, where you simply receive a question and solve it without further input. Rather, there is an ongoing dialogue between the interviewer and the candidate.

### Looking for an all-inclusive, peace of mind program?

Choose our mentoring programs to get access to all our resources, a customised study plan and a dedicated experienced MBB mentor Learn moreGenerally, you will need to acquire more information in order to eventually answer the interviewer's main question. This will often be provided to you in the form of charts - meaning that you will have to be able to interpret these in order to get at the information you need.

### Chart Basics

As a starting point, you should be familiar with the kind of basic graphs and tables which you might recognise from Excel. As well as standard tables of values, you should be absolutely comfortable reading the following:

**Scatter Plots**- used to display data in up to three dimensions - the x and y axes and the size of the "bubble" for each point, where this varies.

Even these basic kinds of charts can take multiple forms, though, and it can be a more useful distinction to categorize charts by their function in conveying information rather than their specific form. As such, we can think about these charts as records of the following:

**Comparisons/Relationships** - showing a correlation or pattern - generally with a bar
or line graph. For example, demand for a product versus the age of buyers.

**Distributions** - showing how data is distributed to provide the viewer with a sense
of the mean, standard deviation, etc., generally with pie or bar charts. For example, the
bodyweights of a group of individuals.

**Trends** - quantities are shown over a period of time, so as to identify seasonal
variations, generally with a line graph. For example, weekly sales of a product over a three year
period.

**Composition** - showing how a whole is divided into parts, generally with a pie chart
or scatter plot. For example, the market share of different car producers in a geographic region.

### Charts for Consulting Case Studies: Adding Complexity

The charts you receive in case studies will typically be rather more complex than a basic pie chart or bar graph. Charts become more complex as more and more data is added to them - generally by allowing data to be encoded in additional dimensions. Given there is an indefinite number of ways for this to be done, it is impossible to give an exhaustive treatment (though we discuss case study charts in more detail in MCC Academy). Indeed, as charts become more complex and are merged with graphic design elements, there is an increasing trend in the business world towards producing fully-fledged infographics.

#### Example: Stacked bar charts

To take what is still a **relatively simple example**, we can significantly **increase
information content** by generating "stacked" bar charts, where each bar is subdivided
into constituent portions. Frequently, **even more data will be added by recording additional
values against each bar**. Below, we can see how a stacked bar chart provides information
about the specific product breakdown, which accounts for overall annual revenues for a food
retailer:

Stacked bar charts can be used to provide information about the **relationships between
elements**. For example, the chart below shows the effect of government subsidies on the
returns generated by different energy sources in Canada:

*Alternatively*, stacked bar charts can also be used to show the **differences between
elements**, as shown below. Here, we see some data showing rising demand for various
types of building in a region of England. The chart allows us to appreciate the rising demand for
buildings as well as the extent to which this might be ameliorated by existing buildings re-entering
the market.

#### Example: Complex Tables

Case studies will very often **contain complex tables which display information in multiple
dimensions**. You will need to be able to **quickly interpret these and pull out
key values**. An example is shown below. Here, we see the success of a large,
multi-channel advertising campaign, made by a new political party in order to secure public
donations.

We discuss these complex tables in **more detail in our Consulting Math lesson in
MCC Academy**. There, we
also discuss and give examples of how tables can be used to **illustrate information about
processes carried out by a client company**.

## Writing math equations

In simpler cases, you will be able to analyse scenarios verbally **and move straight to the relevant
arithmetic without having to resort to equations. However,** as cases become more complex,
working in this way becomes exponentially more difficult **- such that it soon becomes impossible to
keep track of all the variables as well as all the relationships between them.**

**In such cases, you should be able to** express the problem you are working with as an
equation. **This will allow you to move towards a solution via more complex reasoning and keeping
reliable track of more items than you can do verbally.**

**Let's look at an example of how we have to change how we work as problems become more
complex:**

Q1: I am 25 years old and my sister is 3 years older than me. What is my sister’s age?

This problem is easy to solve with basic arithmetic. Thus, the sister's age is simply 25+3=28yrs.

Q2: I am 25 years old today. 5 years before I was born, my father’s age was 19 years less than double my age 5 years ago. What is my father’s age today?

Now it is much harder to solve the problem directly as above. However, an equation makes matters easy. If we make our own age the variable we can solve as follows:

Being comfortable with equations has other benefits. In the simple, **linear optimisations**
which we looked at above, **having the relevant equation and knowing the boundary conditions is enough
to be able to optimise the function**. In the simple example we looked at, if we are trying to
maximise *y = 2x + 1* for x between 0 and 4, then the fact that the coefficient of *x* (that
is, 2) here is positive is enough for us to know that the graph will have an upward slope the function will
be maximised at the upper bound of x - which will be *x = 4* in this case. This is, **without
drawing a graph or doing any calculations!**

## Mental math drills and questions

As we noted at the start of this article, **consultants take mental math very seriously** and
you will need your calculations to be sharp in interview if you want to get a job. We **have already
noted a few "hacks"** that will help you perform some operations more quickly. However, these are
**just a small subset of a whole host of such skills** which you should be able to draw upon.

Our video lesson on consulting math in MCC Academy explains a full set of such skills. Here, we'll just take a look at a couple of these techniques to get an idea of the kind of methods consultants use day-to-day to make quick calculations - and which are invaluable in case interviews.

### X% of Y is Y% of X

What is 28% of 75? Difficult, isn't it? Well, not really. The answer will be the same as 75% of 28, which is much easier to calculate, as we should already know that 28 ÷ 4 = 7, so 75% of 28 is just 3 x 7 = 21. Easy!

### Rule of 11 - Quick Math

63 x 11 = what? **If you have to think about this for more than two seconds, you are too
slow**. Luckily, there is a rule here that can help. Specifically, if you have to multiply a
two-digit number by 11, you simply add the two digits together and place whatever the result is between
them. As such, for 63 x 11, we add 6 + 3 = 9 and put that 9 between 6 and 3 to get 693 - the correct
answer! Similarly, if we wanted to multiply 26 by 11, we would add 2 + 6 = 8, giving an answer of 286.

If you want to **learn similar techniques** to be able to calculate almost instantly that 4900
÷ 50 = 98, or that 387 ÷ 9 is 43, then you should check out the math content in
**MCC Academy**.

Note that it is tempting to think of these kinds of "tricks" as somehow "optional extras" in your case
interview prep. However, you need to keep in mind what we said earlier about **consulting math being
an entirely different beast** to the academic math you will be accustomed to. In this context,
these kinds of **quick calculation methods are core skills**, which you can expect to
need to impress your interviewer and land an MBB job.

To make sure your mental math is as sharp as it possibly can be, you should be practicing constantly right up until your interview. You will get a certain amount of practice from case practice (see our free case bank), but you should also work on math separately. Our free mental math tool is a great resource here, as are our specialist math package:

- Video Lecture on Foundations of consulting math
- Video Lecture on Applied consulting math
- Video Lecture on Advanced topics in consulting math
- Video lecture on Advanced methods in mental math
- Actionable advice on how to improve your calculation speed and accuracy
**60+ chart based questions with detailed solutions****100+ business problems with detailed solutions**- Mental math tool to improve mental calculations speed

## Takeaway

This article gives you a good idea of the math you need to cover as you prep for your case interview. It
might be a relief for some of you to find out that the mathematical concepts required are not actually
terribly complex. However, it is **crucial not to become complacent about case interview
math!** The challenge is not in the level of the math itself, but in **being able to
conduct the relevant calculations efficiently and quickly**, without the help of a calculator or
computer and without making your interviewer wait for you to painstakingly solve long divisions or the like.

Now that you know which mathematical topics you need to read up on, you should get the basics firmly
established in your mind and immediately **move strait to practice**. Our
**free mental math tool** is a
great resource here, as are our various
**math package**.

**Mental math in particular is a skill in itself**, though, and there are **specific
techniques** or "hacks" which you should learn if you want to impress in interview. The content
in this article is a great start, though the most comprehensive resource remains our **math lesson on
MCC Academy**, which takes a
detailed look at a whole range of techniques to greatly speed up your calculations.