1. Sample business case: A factory`s falling profitability

A recruiter tells you the profitability of a factory is declining, and asks you why. Though you do not have any further information at hand, you can say the following:

"Well, we know that: Profit = Total Revenue - Total Cost. So either the revenues are falling, or the costs are rising. We also know that: Revenues = Price * Quantity, and we know that: Costs = Fixed Costs + (Quantity*Variable Cost)."

You would be right on track here, without knowing anything about the business. The recruiter might be impressed by this approach and asks you what options you have to increase the profitability.

"To increase profitability, we either must increase revenues or cut costs. To start off with revenues: we can either increase the price, or sell more of the products. Perhaps there are also other ways to generate more revenues, for example by renting out an empty factory hall? To cut costs: maybe we can cut on our fixed costs by tearing down the empty factory hall!? Another option would be to produce more efficiently, whereby we would need to purchase less to produce our stock."

The key here is to be creative but stick to a logical break-down of the problem. Even though the recruiter didn`t mention an empty factory hall, he/she would definitely admire your out-of-the-box thinking to come up with such an alternative. The recruiter might go on giving you more specific information about the business, testing your mathematics capabilities and leading you deeper into the case.

2. Sample guesstimate: How much beer is consumed at home in Germany each week?

You will need to use many assumptions and rounded numbers to come to an answer here - don`t expect too much help from the interviewer.

Germany has a population of around 80 million people.

Approximately 70 million would be adults, of which maybe 60 million drink alcohol (again, just guess these figures! Recruiters don`t expect you to know populations etc, but want to test your ability to make assumptions and calculations!)

Of these 60 million, maybe 40 million drink beer. An average person consumes 2 beers per week, giving us 80 million beers total per week. An average person goes out for drinks once every two weeks. We need to consider that he/she would drink more outside of house (on average) than inside on an evening. I assume that for every 3 beers that one drinks outside of his/her home, one would drink one beer at home. Therefore 25% of 80 million beers give us: 20 million beers per week are consumed at home in Germany.

3. Sample brainteaser: five-liter and three-liter jug

Brainteasers assess your creativity and your ability to ask the right questions. They are often very unstructured, making it difficult to practice them.

Example:

You have a five-liter jug and a three-liter jug. You need exactly four liters of water and you an unlimited source of water available. How do you do this?

Answer: fill the three-liter jug with water and pour it into the five-liter jug. Repeat this process again. The five-liter jug only has two liters left in this second round, leaving exactly one liter in the three-liter jug. Empty the five-liter jug, and pour the remaining one liter in the five-liter jug. Now fill up the three-liter jug and pour into the five-liter jug - this gives you exactly four liters!