Brain teasers are short riddles or word problems used by some consulting firms to test candidates’ critical thinking when faced with an abstract problem.
A train can hold 20 people. It was half full at the start of the journey. At the first station, 6 people get off. Several people get on, and the train leaves the station with no empty seats. How many people got onto the train?
Jason’s father has 4 children; Suzan, Jeffrey, Jennifer. Who is the fourth?
Do consulting companies really ask brain teasers during interviews?
Well, some firms do, but not very many.
In the past, consulting firms asked riddles to test candidates’ creativity and how they react under pressure. But most have transitioned to using more straightforward quantitative, qualitative, or situational-based questions on pre-assessment tests and cases during interviews.
Before you spend time practicing brain teasers, research your chosen firm to understand if you’re likely to face this type of question.
In this article, we’ll discuss:
- Examples of brain teasers,
- How to approach them, and
- Market sizing questions, a more common type of consulting question frequently mistaken for brain teasers.
Let’s get started!
Examples of Consulting Brain Teasers
Brain teasers aren’t set in a business context, so they give consulting firms insight into how candidates use logic and creativity to solve problems outside of the business environment. This can be important when interviewing undergraduates without extensive work experience.
They also let the firm observe how candidates react under pressure when faced with a novel problem.
While many firms are moving away from using consulting brain teasers, some have kept them in their recruiting process. For example, the Mitchell Madison Group includes 2 brain teasers alongside market-sizing and behavioral questions in each interview round. Bain has a logic brain teaser in it’s Online Assessment.
Here are a few brain teaser examples:
- Using only addition, how can you reach the number 500 by adding up eight 4s?
Brain teasers used by consulting firms often have a math component so they can assess your numeracy levels while testing your critical thinking.
Tackling this question is all about thinking about how you can arrange the number 4 to create a sum that equals 500. You know you need to use the number 4 eight times.
A little bit of rearranging, gives you the following answer:
Answer: 444 + 44 + 4 + 4 + 4 = 500
- You need to fill a 5-gallon jug with 4 gallons of water. You have a 3-gallon jug, a 5-gallon jug, and unlimited water. How do you measure exactly 4-gallons?
Again, this question takes a bit of to-ing and fro-ing. Here’s how to solve it:
Answer: Fill the 5-gallon jug and transfer the water to the 3-gallon jug. Empty out the 3-gallon jug and fill it with the remaining 2 gallons from the 5-gallon jug. This leaves 1-gallon of space in the 3-gallon jug.
Fill the 5-gallon jug and pour 1-gallon into the space in the 3-gallon jug. 4 gallons remain in the 5-gallon jug.
- A train can hold 20 people. It was half full at the start of the journey. At the first station, 6 people get off. Several people get on, and the train leaves the station with no empty seats. How many people got onto the train?
We couldn’t leave you without an answer to this question!
Answer: At the start of the journey, there were 10 empty seats. At the first station, 6 people got off, meaning there were 16 vacant seats. When the train leaves the station again, there are no empty seats which means 16 people must have boarded the train.
How to Approach Consulting Brain Teasers
Structured ThinkingWhile brain teasers can be illogical, your approach to tackling them doesn’t have to be. Firstly, try to identify the type of brain teaser you’re facing. There are some common types. We find these patterns used most frequently.
- Pattern brain teasers. These types of brain teasers give lists of data and require you to search for the pattern or trend and fill in gaps in the sequence.
- Word-play brain teasers. These use words to try and fool your brain into pursuing a logical answer. Instead, you need to look beyond the apparent meaning to find the answer.
- Illusion brain teasers. These use misleading information to try and trick you into drawing the wrong conclusion. Read and re-read these, looking for the ‘obvious’ answer. Example: How many 2-cent stamps are there in a dozen? Answer: 12. Don’t be fooled by the ‘2-cent’ bit into doing math you don’t need.
- Logic brain teasers. Unsurprisingly, logic brain teasers rely on you to think through the puzzle logically. These types of brain teasers aren’t trying to confuse you with distracting information or asking you to get creative with your answer. Example: You are shown 2 doors. Behind one is treasure, and behind the other is nothing. There is a guard in front of each door, and both know which door the treasure is behind. One guard has a black hat and the other a white hat.You can ask the guards one question to find out where the treasure is. One guard will always lie, and the other will always tell the truth, but you don’t know which is which. What question do you ask, and which guard do you ask it to? Answer: Ask either guard, “If I asked the other guard which door the treasure is behind, what would he say?” Then choose the opposite door to the answer given. The lying guard will lie about which door the other guard would choose, so you need to choose the opposite. The truthful guard will tell the truth about which the lying guard would choose (which would be a lie), so again you need to choose the opposite.
Example: What is the next number in this sequence – 0 0 1 2 2 4 3 6 4 8 5 ?
Answer: 10. There are 2 alternating sequences: 0 1 2 3 4 5 and 0 2 4 6 8 x
Pattern brain teasers are sometimes in graphic rather than written form. See the example in the Bain Online Assessment.
Creative ThinkingThe challenge with brain teasers is that the normal logical process of problem-solving sometimes needs to be disregarded. Brain teasers use illusion and misleading information to try and draw your brain into conventional answers. If you’re tackling logical or pattern brain teasers, then a structured approach to solving them works well. For other brain teasers, you need to forget what you know to be true and look for how things could be interpreted more creatively.
Practice Makes PerfectAs with case interviews, it’s really important to practice different kinds of consulting brain teasers. As you’re exposed to different types, you can start to see patterns between them and find clues about how to tackle them. This way it won’t feel like it’s the first time you’ve ever encountered a problem when you see it in an interview. You don’t need a case partner to practice brain teasers with. Just use sample questions. When practicing, don’t simply read the question and answer, but try to reason it out. Time yourself to make sure you can do them in a couple minutes, the time you’d have in an interview.
Don’t Be Afraid to Think AloudWhen you’re faced with a tricky brain teaser, verbalize what you’re thinking as you work through the problem. Thinking aloud helps the brain find order and logic between seemingly unrelated elements. Plus, talking through how you’re approaching the problem helps the interviewer to see your creativity and critical thinking skills. For consulting, this is often more important than getting the correct answer, so make sure to talk aloud as you’re working through the problem.
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Market Sizing Questions – Estimation Questions Frequently Mistaken for Brain Teasers
Consulting firms are trying to assess candidates’ structured problem-solving capabilities, and consulting brain teasers don’t demonstrate this as well as market sizing questions. But they can sound similar.
Market sizing questions are questions focused on estimating the size of a particular market either in terms of volume or revenue (typically annual sales). They are much more common and you are very likely to encounter them in interviews, either standalone or as part of a case interview.
Example: How many cell phones are sold annually in North America?
By market size, the interviewer is asking for the total amount spent on cell phones or the total number of units sold. You can clarify which with your interviewer.
Market sizing questions are sometimes part of a wider case interview that then explores whether the market is an attractive one or how to be competitive within it.
It’s unlikely you’ll know the actual answer to a market sizing question, and so you’ll have to use logic — and a little math — to approximate the market size.
Like brain teasers, consulting firms use market sizing questions to see how you approach tricky problems. They’ll assess how logical you are in tackling the problem and the judgment you use when deciding what factors are important to consider.
Plus, they’ll look at how well you communicate your thinking when tackling these types of questions.
How to Tackle a Marketing Sizing Question
Imagine you’re conducting a market growth analysis for a new client who imports roasted and ground coffee beans. You might be asked to determine how many independent coffee houses there are in New York.
Providing an estimate of how many business outlets might be interested in purchasing coffee from your client helps them assess the size of their potential market, sales, and revenue.
There are 2 main ways of tackling a market sizing case example:
- Top-down: Start with the total volume and divide down to the relevant market.
- Bottom-up: Start with a single unit and multiply up to include the relevant market.
Which approach you use depends on the information in the question and the size of the market. As a rule of thumb, the top-down approach works best for large markets, and for smaller markets, using the bottom-up method is smart.
Market Sizing Tip! Break down the market into key segments by type of customer and use these segments to inform your estimation. For example, if you’re doing a top-down estimate of the market for cell phones in North America, you might break the market into:
- Business customers
- Price-sensitive personal customers
- Functionality focused personal customers
Each of these segments would buy cell phones at a different frequency and a different price point. Breaking down the market size into segments might seem like 3x the work, but it makes it easier to get a picture of the customer and leads to a more interesting discussion about the factors they’d consider when buying the product. (In other words, this will more likely get you an invite to final round interviews!)
Alternatively, you could break down the retail market for cell phones by age group. This is particularly helpful if a teenage buyer would have substantially different product needs or budgets for the product.
Market Sizing Tip! Keep the math as simple as possible. Remember, it’s just an estimate!
Use round numbers and walk the interviewer through your calculations as you do them. This means if your approach is solid, but you make a simple calculation error, they can still give you credit.
We’ve got lots more tips about tackling Consulting Math in our article on that topic.
Do a bit of research if you know you’re likely to face a market sizing question. Having population size for the market you are interviewing in as a starting point, or ballpark figures for some significant markets, means you’re likely to make sensible assumptions rather than be out by an order of magnitude.
Here are some key numbers it might be worth knowing:
7 Steps to Answering a Market Sizing Question
- Ask for more information. Asking questions will help you get clear on exactly what the interviewer is interested in. Are they concentrating on a particular geographic location? Is there a timeframe they want you to focus on (e.g., a month of sales? a year)? Also, listen carefully to any data that’s shared on the client and their aspirations — it might offer clues about what they want to know about the market.
- Use a process for finding the answer. Don’t leap straight into calculations. Apply a structured and logical process, like breaking the market into key segments, to find the answer. Practice this with friends so you’re clear on how you’ll tackle these types of questions.
- Don’t complicate things. Use round numbers to make the math more simple.
- Use what you know. Don’t just pluck a number out of thin air. Base your numbers on facts that you know or your experience. Communicate this to your interviewer so they know that your estimate is grounded with facts.
- Get the math right. Market sizing case questions don’t require complicated calculations. But doing math under pressure can lead to silly mistakes. Practice your consulting math with friends until you feel confident you can tackle it with a sense of calm.
- Do a sanity check. Once you’ve reached your estimation, ask yourself if it makes sense. If not, go back and do a quick check on your assumptions and calculations.
- Share the “So what?” Remember to link your estimation back to what the client cares about. Explain the significance of your estimated market size for the client and their business. Is the market big enough that the client would be interested in the investment needed to enter it?
- What exactly consulting brain teasers are,
- Some different types of brain teasers and examples of each,
- How to tackle brain teasers, and
- Things to consider when faced with market sizing questions.
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