Investment Banking Brainteasers

A question that we often hear about brainteasers is "how important is the ability to make quick calculations and solve brain teasers in investment banking interviews, relative to other portions of the interview?", or, simply said "How important are brainteasers?" Brainteasers are not a major part of the interview process compared to your performance on the other parts, but they are useful for the interviewers for the following reasons:

1) It is another test of analytical ability

Banks will test you in multiple ways, but sometimes, when they have to make the choice between several very good candidates, they will ask brainteasers to see who can do better.

2) Brainteasers demonstrate how you can handle strong pressure

This is in fact the main purpose of a brainteaser. Bankers will often throw a question out of the blue, saying "What is 49*22" or "how many smaller cubes are there in a 10 by 10 cube?" just to see how you react. Some people totally loose their concentration in such stressful situation even though they can be brilliant during exams or at online tests. Brainteasers can tell the difference. Good bankers need to be able to think clearly in stressful situations, so be ready

3) They test your ability to structure your thoughts

With brainteasers, the best way is to tackle them step by step, with a clear logic in mind. Some people get confused and excited, and even though they may get to the final answer, they will look poorly organised and this will weight negatively. So how to handle brainteasers? The best way is to go step by step, slowly. Don't try to answer within 5 seconds. It is fine to say " please give me 30 seconds to organise my thoughts" and think through it. How fast you answer is the not the key. The key is how you structure your answer. Also, investment bankers do not try to be mean or harsh by asking tough questions, they are just testing your reactions. Remember that they were in your shoes before, so relax.

Lets look at a few examples of brainteaser categories:

Arithmetic Brainteasers

"If you add all the numbers from 1 to 100, what number do you get?" Its clearly impossible to add the numbers one by one, so you know that there is a trick here. If the question sounds impossible, take some time to think and to try to find the trick, there is always a trick!. The trick here is to think that the numbers from 1 to 100 can come in pairs that add up to 100. For example: 1 +99 = 100, then 2 + 98 = 100, etc, until you reach 49 + 51 = 100 and then you have 50 left on its own. Try to think how many pairs there are. There are 49 pairs, plus the 100 left alone, and the 50 in the middle left alone. So 50*100 = 5000 + 50 = 5050, that's your answer.

Another one: "what is 49*63?" The best way is to use easy numbers. 49*63 is in reality equal to 50 * 63 minus 63. 50*63 = 100*63 / 2 = 6300/2 = 3150. Deduct 63 from 3150 = 3087. You can use this "breakdown" method for pretty much every calculation. Even if you are not good at maths, you can still solve it easily this way.

Logic Brainteasers

"If it is 3:30pm , what is the angle formed in the clock between the minute hand and the hour hand" Similarly, its all about breaking down the problem and being careful. The answer is not 90 degrees, that would be too easy. Remember that the hour arm will also move as the minutes pass. The clock is a 360 degree circle. So every hour, the hour hand will move by 360/12 = 30 degrees. In half an hour, it will therefore move 15 degrees. Therefore the angle between the minute and hour arm will be 90 degrees minus the 15 degrees, or 75 degrees.

Other questions may include the "jugs of water" questions such as "You've got a 4 liter jug and a 9 liter jug. You've got a pool of water. What is the fewest number of steps it takes to come up with exactly 6 liters of water?" I also have had the "pizza" question quite a lot such as "How many cuts to I need to get exactly 16 equally-sized slices of pizza"

A very important point to note is that banker will very very rarely come up with their own brainteasers, unless you come across a particularly nasty one! That means that they will usually google a couple and change the data a bit, sometimes not changing the data all! So the best advice we can give you is to practice a few of them by going through a Google search, and you should be ready. Remember, the most important part of the interview remains on personality and motivation

Where do I find more practice? 

You can take a look at our investment banking technical guide which has an extensive section on brainteasers that you would typically get in investment banking interviews.

There are also a few cheap brainteaser guides on Amazon, and we recommend the one below (although not specific to investment banking):