Brainteasers are logical questions, often formulated as problems, which are designed for two main reasons:
First, to test the candidate’s ability to structure his or her thoughts and conduct logical reasoning. Second, to test the candidate’s ability to keep his or her composure under high pressure.
While brainteasers tend to be more common in Sales & Trading interviews, you may also encounter them during IB interviews – hence the importance of being prepared.
There are several types of brainteasers:
Let’s go through these types of questions and give you some examples.
These questions are designed to test your ability to think “on your feet”, using pure logic. Just like deductive and inductive reasoning tests, everything you need to know to answer the question is contained in the question. So don’t make any assumptions when you encounter these questions.
We provide below some examples of logical brainteasers that can be asked during IB interviews (with answers of course).
Question: There are three boxes of eggs. In each box there is either a set of big eggs, small eggs or big and small eggs mixed. The boxes are labelled LARGE, SMALL and MIXED but each box is labelled incorrectly. What is the least number of boxes you can open to know which eggs are in which box and why?
Open the LARGE box. You know it can’t be large eggs because the boxes are mislabelled. If you see eggs of different sizes, it means that this box has mixed eggs.
Therefore, the SMALL and MIXED boxes must contain big and small eggs. Since the boxes are incorrectly labelled, the SMALL box cannot contain the small eggs. Hence, the MIXED box must contain the small eggs.
This left us with the SMALL box containing the big eggs.
So the least number of boxes that you need to open to know which eggs are in which box is 1.
Question: You are given eight coins and told that one of them is counterfeit. The counterfeit one is slightly heavier than the other seven. Otherwise, the coins look identical. Using a simple balance scale, how can you determine which coin is counterfeit using the scale only twice?
Start by weighing three pieces against three others (so you leave two pieces on the side). If the weights are balanced, remove the six pieces, weigh the two pieces placed on the side against each other. The heaviest is the counterfeit one.
If one of the groups of three pieces initially measured is heavier, take two of the three heaviest groups of pieces and weigh them against each other (leaving one piece on the side).
If one of them is heavier, it is the counterfeit coin. If they are of equal weight, the third coin, the one that was put on the side, is the counterfeit one.
The questions are made to test your ability to quick math in your head on the spot, both accurately and swiftly.
Here are some examples of mental math questions:
Question: What is the sum of numbers from 1 to 100?
The trick is to notice that you can form 50 pairs of numbers, and each of these pairs sum to 101. For example, 1+100, 2+99, 3+98, 4+97, et cetera…
That means that you just have to multiply 101 by 50 to get your answer: 50×101=5050.
Question: A car travels a distance of 60 miles at an average speed of 30 mph. How fast would the car have to travel the same 60-mile distance home to average 60 mph over the entire trip?
The typical mistake here is to say 90mph. The answer is that it is impossible to average 60mph over the entire trip.
During the first part of the trip, you travel 60 miles at 30mph, which means that the duration of this first trip is 2 hours (60/30).
If you want to average 60mph over the entire trip (which is 2x 60 miles or 120 miles), you would have to make the whole 120 miles in 2 hours (120/60).
Since you’ve already traveled for 2 hours to make the first 60 miles, this is impossible.
Question: What is the angle between the hour and minute needle at 3.15?
The mistake here is to answer zero, by forgetting to account for the fact that the hour hand must adjust itself according to where the minute hand is.
At 3.15, what you can tell for sure is that the minute hand will point precisely towards 3 (perfectly horizontal), and that the hour hand will point between 3 and 4 (because 15 minutes have passed since 3).
More precisely, the hour hand will have covered one-quarter of angle between 3 and 4.
Since there are 12 hours on a watch dial, that means that between each hour you have an angle of 360/12=30 degrees. Then you just have to divide 30 by 4 to get 7.5 degrees.
These questions are designed to evaluate your ability to think in probabilistic terms, and to arrive at a logical conclusion after considering different scenarios.
Here are some examples:
Question: You have 100 balls (50 black balls and 50 white balls) and 2 buckets. How do you divide the balls into the two buckets so as to maximize the probability of selecting a black ball if 1 ball is chosen from 1 of the buckets at random?
Put a black ball in one bucket, and all the other balls in the other bucket. By doing so, you maximize your chances of drawing a black ball (you have a c.75% chance to be precise).
Here is how the math works. You have a 50% chance of selecting the bucket containing the black ball (100% chance of drawing a black ball when this bucket is selected) and a 50% chance of selecting the other bucket, containing 50 whites and 49 blacks (where the probability of drawing a black ball after selecting this bucket is c.49.5% i.e. 49 blacks divided by 99 balls).
This gives you: 50%x100%+50%x49.5%=74.75%.
Question: What is the probability that the first business day of the month is a Monday?
The key to answering this question is to think about how many days in the week are either followed by Monday, or are “Mondays”.
Obviously, Monday is Monday and it’s a business day, so we get at least 1/7. Further, both Saturday and Sunday can be counted as days that are followed by Monday, because Monday is the first business day that comes after them.
In other words, if we are on a Saturday, we know that the next business day is a Monday. Same thing for Sunday.
Hence you have 3 days out of 7 where Monday is either the next business day or the current business day (if we are on a Monday). Therefore, the answer is 3/7.
The correct answer is 3 in 7 because if the first day of the month is a Saturday, Sunday or a Monday then the first business day is a Monday.
Market sizing or “guesstimates” questions ask you to estimate a specific number by making several arbitrary assumptions. For instance, “how many toothbrushes are there in the United States” is one question you may get during an interview.
The key thing to have in mind for these market sizing questions is that the accuracy of the number you give matters much less than the reasoning you’ve used to come up with that number.
In other words, recruiters don’t really care if you’re right or not (they probably don’t know the answer themselves). They just want to see if you’re capable of making sensible assumptions and use these assumptions to make a sound estimate.
When you answer these questions, recruiters will evaluate you on several aspects, including: your ability to think logically, your mental math speed and accuracy, and the clarity of your communication.
Here are some examples of market sizing questions:
Question: How many golf clubs are there in the United States?
Possible answer structure:
Question: How many vacuum cleaners are there in Japan?
Possible answer structure:
EXPERT TIP #1: REMAIN COMPOSED AND BE LOGICAL
First, your answers matter less than your thinking. The truth is, for many of these brainteasers, nobody knows the perfect answer, and nobody cares.
By asking you these questions, recruiters just want to evaluate two things:
If you are able to keep calm no matter what, and show that your reasoning is logical and sensible, you cannot go wrong.
Even if your answer is objectively wrong but your reasoning makes sense, you will still get some credit for it.
So don’t see these questions as “pass or fail” tests (even though certain questions will have only one correct answer).
EXPERT TIP #2: ALWAYS THINK OUT LOUD
Second, every time you are answering these questions, always think out loud rather than thinking by yourself, even if you think you’ll be more effective in the latter case.
Remember, they are more interested in your reasoning than in your answer, so if you can articulate your thoughts in real-time (by speaking them out loud), you will make a positive impression.
It’s better to explain your reasoning out loud and to come up with an OK answer, than to reason secretly like a dark genius and come up with an excellent answer.
EXPERT TIP #3: USE AS MANY SENSIBLE ASSUMPTIONS AS POSSIBLE
Third, explain every assumption you make in your attempt to find a solution. Of the critical aspects of a financial analyst is to make forecasts by using a combination of several assumptions. As such, the more assumptions you use and the more sensible these assumptions are, the stronger impression you will make.
EXPERT TIP #4: ASK QUESTIONS TO THE INTERVIEWER TO HELP YOU IF NEEDED
Fourth, if you’re stuck or can’t find any angle of analysis, don’t be afraid of asking your interviewer a couple of questions to help you understand the problem better, and save time for thinking in the process.
If you ask smart questions, it can even be beneficial for your application, by showing that you are a diligent person.
It’s also perfectly fine to ask the interviewer for some time. You can for example say: “Could you give me a minute to gather my thoughts?”. It won’t reflect adversely on your application.
EXPERT TIP #5: DON’T ANSWER QUESTIONS DIRECTLY, EVEN IF YOU KNOW THE ANSWER
Fifth, if they ask you a brainteaser question that you’ve already seen, don’t answer it directly.
Your first option is to pretend you don’t know the answer and articulate the answer slowly by detailing the process that leads to your answer.
The second option is to play the card of honesty, by saying to the interviewer that you already know the answer (which can be appreciated).
If you’ve already got some brainteaser right during the interview, the second option might be a strong choice.
However, if you were asked brainteasers beforehand but couldn’t answer convincingly, option one might be preferable, because it will give you at least one good answer.
Aurelian Tran is the founder of Alpha Lane and an ex-Goldman Sachs analyst who has spent 4+ years working in the investment banking industry.
He founded Alpha Lane to help students and young professionals achieve their highest professional ambitions, by securing offers at top-tier financial institutions.
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