Don’t give Hank a straight answer or even a guesstimate when asked this type of ‘impossible’ brainteaser
PS Check out the complete guide to investment banking brain teasers here >
You don’t know the answer now.
Neither does Hank mind you!
This alludes to an important point; don’t start sweating when you get weird and wacked out questions like “How many pitch books would fit in a 747?”.
Although you have no idea what the answer is, you soon will if you follow our strategy.
First seek out the missing facts
- Is the plane flying or grounded?
- Do safety laws apply with respect to pitch book storage?
- Is the cargo hold empty? Etc
It may surprise you to know that when candidates ask for further information and do so intelligently and probingly like this, bankers are impressed – and more so by this than your ability to run through the subsequent math involved!
This makes sense given 1) hunting out facts and analyzing problems is half a young banker’s job, and 2) in banking we use Excel for every single calculation anyway (even 2+2!).
But don’t fall into the trap of asking too many clarifying questions, because the more info you extract the harder the problem becomes to solve.
For example, knowing whether the plane has xx cubic feet of cargo hold is helpful; but knowing whether the tail of the plane is 2 feet or 3.7 feet is not.
Instead it will only add an extra layer of complexity to the problem, so find the balance and Keep The Math Simple!
Thankfully many bankers won’t even give you additional information, preferring to leave it ambiguous in order to see how you respond to missing data – another key quality of young bankers.
Next state your assumptions
For example, “I’m assuming the seats are in the plane, the plane’s weight limit is more than enough to accommodate the pitch books, that there are no safety issues with stacking pitch books up in aisles or wherever empty space is available” etc.
This is another important point to cover.
If you’ve ever looked at a financial model you’ll know the role ‘assumptions’ play in a banker’s work. Showing you can reach sound assumptions yourself will further demonstrate you have what it takes.
Be sure you explain every step of your working out
Whether you do your working out on paper or in your head, you need to communicate it verbally to bankers as this question is as much a test of your analytical and quantitative power as it is your Steve Jobs presentation skills.
As a side note, we recommend always working out this type of brainteaser on paper if it is available, because “thinking on paper” will make life infinitely easier and crucially, bankers don’t look down on it.
Use our simple little trick to make the math easy
In banking interview you will rarely be handed a calculator, which means you may run into trouble when juggling multiple calculations and complex numbers.
Use really simple numbers like 10, 100, 1000 or anything ending in 0’s.
This is most important when you are starting out with the math and stating your assumptions, because if you begin your answer with even the most innocuous looking numbers, e.g. 7 x 100, it can turn into a complete mess 2 multiplications, 3 additions and one division later!
Hello 748 divided by 17, multiplied by 223!
Limit yourself to ‘ballpark’ figures
No matter how tempting it might seem – in pursuit of accuracy – to start saying “between 100 and 120” for example, don’t do it.
You see, the minute you attempt to bring sensitivity analysis to the table you are screwed – you will have just doubled the Math needed to work out this ulcer-inducing question!
Now it’s time to do some math
Start by breaking apart the calculations.
You will earn half your points for simply stating what calculations you will need to make. This also helps you get a clear head and stranglehold of the problem.
First, work out the planes volume that could be taken up by pitch books
Length of the plane
Identify the parts of the plane (e.g. Cockpit, 6 rows of business class-size seats, bar/toilet, tail) and a guesstimate of length for each.
In other words, don’t just guess “30 foot”.
You want to work up to it using commonsense and basic knowledge. And perhaps some insider knowledge on private planes gleaned from watching too many episodes of Entourage.
Width of the plane
Same as above. i.e. work up to the width by running through “one fat seat, wide aisle, one fat seat”.
Volume of cylinder calculations
If that eluded you, ask the bankers for the formula.
Otherwise, just do a rough rectangular volume calculation and reduce by a 1/3rd, because however crude this is at least you’ll be able to giving an answer.
Now adjust for nose (e.g. 1/10, cone or pyramid calc, but we’ll assume and justify there is no storage there to make life easy, so eliminate) and tail (e.g. 1/10, no storage, so eliminate).
Cut cylinder into 50-50 halves for seating area and cargo hold area. Remember assume, justify and get that easy math in no matter what. Who gives a shit if the actual division is 60-40?!
Adjust for space-invaders like seats, people, luggage, Hank’s 18 bottles of Glenfiddich (more assumptions, but all justified). Adjust these space-invaders as whole, otherwise it’s too hard. And adjust using a basic percentage like “20% off space already taken up”.
Now you have ‘empty’ volume for the plane.
Then work out the volume of 1 x 100 slide pitch book
Easy estimates and a rectangular volume calculation make this as Basic as Ben Stiller. At this point it’s wise to multiply the pitch book’s tiny volume by 100 and then do the plane-book division, because this will give us easy fat numbers.
Keep explaining every input number you give
Although we’ve just been spitting out input estimates above, it’s wise to explain how you arrived at each of them.
For example, you assumed the pitch book is A4 size, printed on normal paper, double-sided etc.
i.e. Although you stated your initial ‘big picture’ assumptions at the start, you still need to provide the interviewer with your reasoning for new assumptions as they crop up.
Pause to see if the numbers you are churning out make sense at a gut level
How many times this has saved us – when doing interviews or models! – is crazy.
And it’s so simple.
The only real challenge is remembering and feeling confident enough to take the 4 seconds out when you’re trying to desperately answer a crazed MD.
Although many people won’t advise this, we think it’s actually quite smart to explicitly say “Let me just do a ‘sense check’ to see if these numbers are sound”.
Far from being a turn off, bankers will now know why you are pausing and will be impressed by your business savvy.
Unfortunately not all Type A brainteasers are so easy
Instead of a concrete item like 120 slide pitch books, you could be asked about “smart phones”. And instead of a concrete idea like a plane, you could be asked about “how many are sold online?”.
In these cases everything is different.
1. This new type of brainteaser invites more clarifying questions like;
- What is a smart phone?
- What markets are we talking about (geographically, customer wise etc)?
- What time period?
2. It requires many more assumptions too.
3. Plus the math involves more levels of calculation and tighter numbers.
Thankfully though, this is a question suited to sense checks, because it’s easy to determine if your numbers are way off given you know basic stats like population counts, smart phone adoption rates, average lifespan of a smart phone and when consumers return to the market etc.
Clearly then this type of brainteaser invites more intelligent business analysis – as opposed to Hank’s question which calls for a freaking guessing game involving elementary math. Want more advice on the toughest brain teasers on Wall St? Check out this >