Quote from gentinex:
I recently took the Optiver numerical tests, and thought I would proivde some more info on what exactly the tests entail, for those on this forum who may be taking them in the near future.
The first test is an 80-question, 8-minute arithmetic multiple-choice test---yes, that means 6 seconds a question! I came in expecting a lot of complicated arithmetic---multiplying a pair of two- or three-digit numbers together, dividing a four-digit number by a two-digit number, etc.---but the questions were easier than that. Typical questions might be: 54 - 29 = ?, 84/6 = ?, (5/3) / ? = 4/3, 0.078/0 .006 = ?, 2/3 - ? = 1/6. Sometimes the answers are not written in reduced form, so, e.g., when you calculate an answer of 6, you'll have to read the choices and find, e.g., 72/12.
If you're American, you should note that they always use commas where we used periods for decimals---so the above example would actually have been written 0,078/0,006---and they sometimes use colons where we use bars or slashes for fractions---so 6:3 = 2. They did explain this adequately before administering the test, but I still found it slightly annoying.
The first test is scored as follows: each correct answer gets you one point. Any questions left blank at the end of the test get you zero points. Each incorrect answer or blank answer in the middle of the test (as opposed to the end of the test), penalize you one point. So it's in your best interests to work the test from start to finish, and not jump around. The passing score is usually somewhere around 54 or 55, and the passing rate is reportedly 15%.
In terms of preparing for the test, I think there's really no better way to do so than just practicing doing lots of calculations in your head, and doing them quickly---having to write calculations on paper will slow you down a lot. I myself did not use any of the given scratch paper at all, but I did see a number of unsuccessful test-takers who had written down a lot of stuff. You should be able to add and subtract any two two-digit numbers. For multiplication and division, I think that if you know how to multiply any two numbers up to 15, you should be fine, and if you're ambitious, knowing up to 25 is even better. The denominators of fractions are usually single-digit or small double-digit numbers, so be comfortable with those. For decimals, just make sure you know what's going on with decimal places: for example, 0.05 - 0.004 is 0.046, not 0.01, or 0.6 * 0.03 = 0.018.
In terms of actually doing drills, if you know how to generate random numbers from a computer or calculator, it should be pretty easy for you to come up with ways to test yourself on the topics above. One book I highly recommend reading is "How to Calculate Quickly" by Henry Sticker, which has a lot of good drills on fast calculation, although as I suggested above, I was kind of overprepared after reading this book. I really like this book because it has a very general philosophy on how to calculate anything quickly---in contrast, most books and sites I have looked at only teach you how to do very special calculations quickly, e.g., how to multiply a number by 25?, how to divide by 5?, etc. I should mention, though, that the book does have some weaknesses compared to the actual Optiver test: it doesn't discuss multiplication or division of decimals, and the drills on fraction arithmetic were a little easier than what was on the Optiver test, so I was a little slow on these areas in the actual test.
If you pass the 8-minute numerical test, you are invited to take two more numerical tests on the spot, and have a short interview with the HR people who are administering the test. I think that in general, the people who pass the first test usually don't have problems passing the second and third tests (which, in my opinion, have slightly more generous minimum passing scores). But I'll say a thing or two about the latter two tests anyways.
The second test (I have heard that the order of the last two tests may sometimes be different from what I had) is a sequences test: given a sequence of numbers, what's the next number in the sequence? Some examples: 1, 4, 9, 16, 25, ?; 6, 24, 12, 48, 24, 72, ?. It has 26 questions to be done in 30 minutes. The scoring is a little different from the first test: you're penalized one point for wrong answers, but you're not penalized at all for any blank answers, so it's fine to jump around and figure out what problems you can do. The passing score is around 12.
The third test is pretty similar to the first test in that it's arithmetical multiple-choice again, but now it's 40 questions in 10 minutes (so 15 seconds a question---I had time to check some of my answers on this one!). The scoring system is the same as the first test (work from beginning to end, and get penalized for wrong or skipped answers in between), and the passing score is around 24. The questions are sometimes a little different from the first, in that they're not all just straight calculations, but in the end, the calculations still never got that complicated. For example: what value must go in the blank so that the following equality is true: (4/?) / (?/16) = 4. Also, the answers are a little deceptive, in that now you always want to choose the simplest form of the answer: so sometimes you'll see, say, both 16/10 and 8/5 as answers, but the former answer is considered wrong.
After the three tests, you have a short interview with the test administrators, who are usually HR people. Hopefully, you know how to deal with the standard questions they ask: why trading / finance, are you competitive?, what do you like to do in your free time, etc. And if that goes all right, you're invited to their final rounds onsite. Their main operations are in Chicago, Amsterdam and Australia (Sydney I'd guess?), and they seem to be trying to get people to work in their headquarters in Amsterdam, although it seems like if you really wanted to, you could begin your employment elsewhere
