A prerequisite for most quant trading roles is to be able to think quickly, and thus, be able to do math quickly. If you're someone who struggles to do basic math quickly -- it's gonna be a rough ride. But the good news is that no matter how bad you are, there is almost always room for improvement.
A good way to practice your basic arithmetic skills is to visit zetamac, which prompts you simple math problems quickly. Your goal is to answer as many problems as you can quickly. Notice that because they don't penalize you for inputting wrong answers, try to not guess your answers.
One thing I hope you notice is that as you try to get faster at these simple math problems, you will start noticing tricks. Of course, you can just search how to do certain tricks, e.g. what the *11 trick is or how to add something in the form of 97 + 45 = (100 - 3) + 45 = 142, but I would highly recommend trying to figure out what tricks work for you. If you find that you aren't improving anymore, maybe then it might be worth to search up some arithmetic tricks.
The following table should give a sense of where you are. This is based off of a 120 second test, with default settings on.
| Score | Comments |
|---|---|
| 0-9 | You can do a lot better |
| 10-15 | Below average |
| 15-24 | Average |
| 25-35 | Above average |
| 35-44 | Pretty good |
| 45+ | Should be set for any interview |
Some companies like Akuna like to ask questions like
What is 17.5% of 354,
expect you to do it mentally and explain your method.
They also like to ask you a series of these questions
and then test if you can recall the questions they asked you.
Number sense is about being able to understand properties about numbers to do computation faster and be able to estimate difficult calculations fairly accurately. A good example of what number sense is about can be found at AGMath, an ancient website for sure, but if you scroll down to the bottom of this page you can find number sense worksheets. I think number sense is a natural extension from the simple arithmetic you can practice from zetamac.
Another great guide for number sense can be found by Bryant Heath.
Trading companies love testing your ability to know sequences. Some of these sequences are technically challenging, requiring you to compute things. Other times, it's just knowing some phrase in English (sorry non-native speakers)
- 1, 1, 2, 3, 5, 8, 13, (Fibonacci)
- 1, 2, 4, 8, 16 (2^n)
- 1, 6, 21, 66 (3x_{n-1}+3)
- F, S, T, F, F, S, S, E, N, T (1st, 2nd, 3rd, ...)
- M, V, E, M, J, S, U, N, P (Mercury, Venus, Earth, Mars, ...)
There are many, so check out sequences for more.
If you've ever seen an absurd question like
How many drops of water are in the Earth's oceans?
then you've encountered a Fermi question. The legend goes, that scientist Enrico Fermi once
observed the Trinity test on 16 July 1945, and conducted an experiment to
estimate the bomb's yield by dropping strips of paper into the blast wave.
He paced off the distance they were blown by the explosion, and calculated
the yield as ten kilotons of TNT; the actual yield was about 18.6 kilotons.
Fermi questions are about common sense, and how you can utilize what you can know to make seemingly unsurmountable questions more realizable. You can find a good guide on Fermi questions here and can practice in real time at this site.
If you don't know already, a lot of trading firms like to recruit from the competition math community. These are people who have spent a good deal of their life training, and thinking through very hard problems and answering them correctly in very high pressure, limited timed settings. Competition math can be special to you doing math for these trading interviews because it not only teaches you tricks to solve problems faster, but it also exposes ways to look at problems a different way and gives you a huge toolbox to use for cracking seemingly unbreakable problems.
In America, the following contests may be worth taking a look at if you're looking to get a sense of what competition math is about, and looking to practice or learn these skills.
This is the path that almost every aspiring mathematician takes to represent his/her country at the International Math Olympiad (IMO). These exams are in increasing order of difficulty. If you want to learn more about preparing these exams, I would highly recommend checking out the resources and forums at The Art of Problem Solving (AoPS). Most of the links below are going to be from AoPS.
- MathCounts: A competition for middle schoolers that usually serves of the first stepping stone for kids to enter competition math. This exam is administered at the regional, state, and national levels, and comes in a variety of exam styles, including multiple choice (Sprint), short answer (Target), team based, and even head-to-head speed (Countdown). This competition is lots of fun and I highly recommend it if you have kids interested in math or are a youngster for whatever reason browsing this guide (good for you!).
- AMC 8/10/12: A multiple choice based exam. Each exam is for a different demographic of students, e.g. AMC 8 is for 8th graders and under, and each exam has a different cutoff. The exams are used as qualification to take the AIME.
- AIME: A short answer based exam. Selection test for the US Math Olympiad.
- USA(J)MO: Selection test for the Math Olympiad Program.
- MOP: The actual test is called TST, but it's a selection test taken at MOP to determine the IMO team.
- IMO: Grand finale.
In college for undergraduates, there is a test called the Putnam, a proof-based test, that is highly regarded. Scoring in the top 500 is considered a strong achievement.