The skills you will need to solve consulting problems are those you learnt in secondary school. We will review them quickly and then move onto the structuring of business problems and useful ways to tackle and solve them. Our business problem package has all the training you need to revise all these concepts.

The most relevant problem type for consultants are obviously business problems. It is important to have a method to tackle these in a quick and accurate way. Most of the time instinct is enough, however, a structured approach usually improves both speed and accuracy.

We propose our method here which you should use a guideline; feel free to modify and adapt it to your way of thinking. Our method applies to a wide range of problems and not only those you solve in a case interview.

The main steps for solving the problem are the following:

- Problem identification
- Structuring the problem
- Defining a solution
- Solving
- Sanity checks

## Problem identification

The first stage is quite straightforward and should only take a few seconds. It involves identifying what kind of problem one is working on, whether it can be broken down into multiple problems or not and how difficult it will be.

## Structuring the problem

Structuring the problem is often the most critical step in the solution process. Firstly, define the goal, i.e. what we need to solve for. It is often useful to assign a variable, such as x, to the quantity we are solving for. Then, gather all the data in a structured manner, eliminating anything superfluous. Then start looking for a relationship between the current data and what you need to find. This stage is not always necessary for simple problems but it is very important for complex ones.

## Defining a solution

In this stage, one looks at all the possible course of action to solve the problems and choose the most efficient one. Most of the time for simple business problems there is only one solution and it usually involves either setting up a simple equation and solving it or applying a formula, such as the compound interest formula.

## SOLVING

Solving simple business problems is usually straightforward as the math is never too complicated. However, it is important to be fast and accurate, which is not easy. It usually boils down to how fast one is with numbers, and for this refer to our plain number section.

## SANITY CHECKS

The final part of the process, which is very important, is to check if the solution is right or not. First, one sees if the solution makes sense. If Mark has a saving account and he deposited 15k USD five years ago and now has 2m USD he is either doing something dodgy or you got your calculations wrong. A more accurate but longer way of checking if the solution is correct consists of plugging the solution back into the original equation, and see if one obtains the initial data.

**EXAMPLE**

Let’s look at a simple example to illustrate how to apply the procedure described.

*Mark is a car dealer. A new electric car has just come out but the model is not very good so he makes an average loss of 10% on selling the car. If he managed to sell them for 3300 USD more on average, he was going to make a 5% profit. What was the original cost of the car?*

## PROBLEM IDENTIFICATION

The problem is fairly straightforward profit and loss question.

## STRUCTURING THE PROBLEM

The aim of the problem is to find the cost of the vehicle, which can be defined as x. The problem relates the current loss with a potential profit scenario through the selling price.

## DEFINING A SOLUTION

The current loss is 10%. The selling price is therefore (1-0.1)*x. Increasing this price by 3300, would result in 5% profit, hence (1+0.05)*x. Expressing this as an equation

(1-0.1)*x+3500=(1.05)*x

0.9x+3500=1.05x

## SOLVING

While the equation is trivial to solve, it is important to do it in the shortest possible time. By looking at it, one can easily recognise that the 15% of x is 3500. 15% is 15/100 or 3/20. 3300/(3/20)=3300*20/3=22000 USD

## SANITY CHECKS

Is 22000 USD a reasonable price for an electric vehicle? Yes, even though it is lower than one would expect it is still sensible. Also, trying to put 22000 back into the equation, 0.9*22000+3300=23100 USD and 22000*1.05=23100 USD so the solution is correct!

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