How do you work out how many people are wearing red on a typical Monday? Check out our solution to this curve-ball consulting interview question.

Case interviews allow you to demonstrate how you think - your ability to understand a problem, break it down into its requisite parts, analyse them and communicate a solution. In this series, we give you ten case studies to give you an idea of how to approach the case and how to walk through it with your interviewer.

You may want to consider the case question first and think about how you might structure a response before looking at the ‘answer’. Of course, bear in mind there are many ways to answer a case, so this is just one example!

For the purposes of these examples, we will only look at market sizing and business cases.

How many people wear red in Australia on a typical Monday?

For all case interviews, it is worth making sure you understand the problem in its entirety. Feel free therefore to begin the interview by asking some initial clarifying questions.

Here’s an example discussion.

You: Ok great, so when we say wearing red, does that mean any item of clothing or all red?

Interviewer: Let’s say any item of clothing.

You: Great. And if a person goes out more than once, should we count them again?

Interviewer: No, let’s count them only once.

You: First, I want to figure out how many people live in Australia, and then second, what are the chances that they are wearing red.

Interviewer: Sounds good to me.

You: Ok, so the population of Australia is roughly 20 million give or take. We will have to make some assumptions about the number of people who are going out versus staying at home. I’m going to make an assumption that 5 per cent of people stay at home, 70 per cent go out once and 25 per cent go out twice. Does that sound fair?

Interviewer: Yes, go ahead.

You: And I’m going to assume that the number of clothing pieces per person will differ depending on if they are staying at home, going out once or twice. For example, the person staying at home will likely have on two pieces of clothing, the person going out once will have five and those going out twice will have ten. I’ll also assume there is no specific preference on colour.

Interviewer: Ok.

You: Let’s analyse the number of people wearing red from each group:

- Staying at home: 5 per cent of 20 million is 1,000,000 people. Let’s assume that each person has two pieces of clothing and that the chance of having red in each piece is one out of 10 (assuming seven colours plus grey, white and black). This means we calculate 1,000,000* 2 * 1/ 10 = 200,000.
- Going out once: We said that 70 per cent of people go out once. This is 14,000,000 people. Each of these people have five pieces of clothing and the chance of having red in each is, say, 1 out of 20. I have made that assumption because it’s a Monday and most people will probably wear more neutral colours like black, white or grey instead. So, we calculate: 14, 000, 000 * 5 * 1/20 = 3, 500, 000.
- Going out twice: We have said that 25 per cent of people go out twice. 5,000,000 people have 10 pieces of clothing. The chance of having red in each piece is, say, 1/20 for the first trip (going to work); and 1/10 on the second trip (casual trip), which means 7.5 per cent. The calculations are 5,000 000 * 10 * 7.5 per cent = 3,750,000 people.

If we add these all up, that’s 200,000 + 3,500, 00 + 3,750,000, which is a total of 7.5 million people wearing red in Australia on a typical Monday.

Interviewer: Well done. This was a good way to break down the problem