Mental maths for trading interviews: what to drill and how

Almost every proprietary trading firm and many quant funds put a timed arithmetic screen in front of candidates. Optiver, IMC, Flow Traders, Da Vinci and others each run their own version, and the underlying skill is the same. This guide goes operation by operation: what gets asked, the one technique worth learning for each, and the mistakes that cost points.

Updated September 2026 · 9 minute read

Why firms test this at all

A trader on a market making desk is constantly doing small sums with a live price: half the spread, the hedge ratio, a percentage move, the P&L on a fill. None of it is difficult. All of it has to be right, immediately, while three other things are happening. A timed arithmetic test is a cheap way to see whether a candidate can do that. Treat it as a test of composure with numbers, and train it that way: repetitions under time pressure, with accuracy as the non-negotiable.

Addition and subtraction

Questions are usually two- or three-digit numbers: 347 + 286, 512 minus 178. The technique that makes these fast is working left to right, the opposite of the way you were taught on paper.

For 347 + 286: hundreds first, 300 + 200 = 500. Then tens, 40 + 80 = 120, running total 620. Then units, 7 + 6 = 13, total 633. You are only ever holding one running number.

For subtraction, use complements. 512 minus 178: take 178 up to 200 (that is 22), then 200 up to 512 (that is 312), so the answer is 334. Or round the number you are subtracting: 512 minus 180 is 332, add back the 2, 334.

Common slip: dropping a carry when the tens sum to more than 100. If a running total feels wrong, it usually is. Skip rather than stare.

Multiplication

Expect one-digit by two-digit and two-digit by two-digit: 7 × 48, 23 × 17. Two techniques cover almost everything.

Split one factor. 7 × 48 = 7 × 50 minus 7 × 2 = 350 minus 14 = 336. Always split towards a round number.

Difference of squares when the two factors sit either side of a round number. 23 × 17 = 20² minus 3² = 400 minus 9 = 391. This only works when the factors are equidistant from a nice middle, but that comes up more often than you would expect in test questions.

Underpinning both is instant recall of times tables to 12 and squares to at least 25. If 13 × 13 takes you a second of thought, that is the first thing to fix, because it feeds every other technique.

Division

Test setters like divisions with a clean answer: 156 ÷ 12, 5.4 ÷ 0.9, or a two-digit divisor giving a short decimal. Two habits help.

Simplify first. 156 ÷ 12: halve both to 78 ÷ 6 = 13. 5.4 ÷ 0.9: multiply both by 10, 54 ÷ 9 = 6.

Know the decimal shape of the common fractions. Anything over 8 ends in .125, .25, .375, .5, .625, .75 or .875. Anything over 6 ends in .1667, .333, .5, .667, .8333. Recognising the pattern turns 7 ÷ 8 into recall rather than long division.

Fractions

Adding and multiplying fractions is where accuracy usually drops, because there are more steps to fumble. For addition, find the lowest common denominator, not just any common one: 1/4 + 1/6 is 3/12 + 2/12 = 5/12. For multiplication, cancel before you multiply: 3/8 × 4/9 becomes 1/2 × 1/3 = 1/6 after cancelling the 3 and the 4. Multiplying first and simplifying after is how you end up with 12/72 and thirty seconds gone.

Most tests accept an answer in lowest terms. Some accept an equivalent fraction. Quickfire accepts any equivalent form, so the habit to build is getting the value right first and tidying second.

Percentages and decimals

Three question shapes: a percentage as a decimal (62% = 0.62), a decimal as a percentage (0.045 = 4.5%), and a percentage of a number (15% of 84). The first two are pure recall of "move the point two places". Slips come from numbers under 10% and over 100%, so drill 0.5%, 7%, 125% specifically.

For percentage-of, build from 10% and 1%. 15% of 84 is 8.4 + 4.2 = 12.6. 35% of 60 is 3 × 6 + half of 6 = 18 + 3 = 21. Never compute 15/100 × 84 as written.

Squares and roots

Learn squares to 25 cold and 26 to 32 well enough to reconstruct. For anything else, use (a + b)² from the nearest known square: 27² = 25² + 2 × 25 × 2 + 2² = 625 + 100 + 4 = 729. Roots in these tests are almost always of perfect squares you already know; if a root looks awkward, it is more likely you have misread the question.

Estimation and Fermi questions

Later interview rounds move from exact arithmetic to estimation: how many litres of blood in an adult, how many piano tuners in Chicago, what is 17% of 2,340 roughly. The skill here is different. You want a fast, defensible answer within about 10%, with the reasoning stated out loud. Round aggressively, do the arithmetic on the rounded numbers, then say which way the rounding biased you. This is exactly the skill the estimation round of a market making game tests, so it is worth practising in that form.

How to structure practice

Short daily sessions beat long occasional ones. The whole point is making the techniques automatic, and automaticity comes from frequency. Fifteen minutes a day for four weeks is more than most candidates do, and it shows.

Practise it

Every operation in this guide has its own timed drill on Quickfire, plus a mixed mock that mirrors the real tests. Free, no account needed. Sign in if you want a per-operation accuracy table to find your weak spot.

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