Mental Math for Trading Interviews: Training Plan, Zetamac Benchmarks & Firm Tests

Why trading firms still test arithmetic

No trader prices an option in their head all day — the software does that. Firms test mental math anyway because it is a cheap, hard-to-fake proxy for two things they actually care about: comfort manipulating numbers under time pressure, and composure when the clock is running and you just made a mistake. A market maker quoting a two-sided price has seconds to sanity-check edge, size, and hedge ratios. If $17 \times 24$ takes you ten seconds of visible effort, the interviewer assumes the fast intuitive layer isn't there yet.

The practical consequence: mental math is a screen, not a differentiator. A great score doesn't get you the job; a weak one ends your process in round one. Your goal is to get comfortably past the bar with the minimum training time, then move on to probability and games.

The tests you'll actually face

Three formats cover almost every trading-firm arithmetic screen:

Test	Format	What's distinctive
Optiver 80 in 8	80 arithmetic questions in 8 minutes	Negative marking — wrong answers cost you points, so guessing is punished. Part of the broader Optiver online assessment.
Flow Traders math test	Short timed arithmetic test	Heavy on fractions, decimals, and percentage conversions rather than raw multiplication.
Zetamac-style screens	120-second sprint, add/subtract/multiply/divide	The de facto community benchmark; several firms use tests that feel very similar. Verbal mental math also shows up live in interviews at firms like SIG (see the SIG assessment guide).

On Zetamac default settings, the rough consensus from candidate forums (r/quant, WSO) is: below 40 means you're not ready to apply, 45–55 is a workable baseline, 55–70 is competitive for most prop shops, and 70+ means arithmetic will never be the reason you're cut, even at the top market makers. These are community-reported bands, not official cutoffs — firms don't publish thresholds.

The core toolkit, with a worked example

Five tools do most of the work. Memorize squares to $25^2$, learn the decimal forms of $\tfrac{1}{6}$ through $\tfrac{1}{16}$ (Flow-style tests live here: $\tfrac{1}{8}=0.125$, $\tfrac{1}{12}=0.08\overline{3}$, $\tfrac{1}{16}=0.0625$), swap percentages ($16\%$ of $25$ = $25\%$ of $16$ = $4$), and use the two multiplication patterns below. Our speed tricks reference has the full list.

Anchor and adjust. Pick a nearby round number, then correct:

$$68 \times 74 = 68 \times 75 - 68 = 5100 - 68 = 5032$$

where $68 \times 75$ is fast because $75 = \tfrac{3}{4} \times 100$, so $68 \times 75 = 51 \times 100$. Compare that with grinding out $68 \times 70 + 68 \times 4$ — also correct, but two multiplications and a carry instead of one clean move.

Difference of squares. When two numbers straddle a midpoint, use $(a-b)(a+b) = a^2 - b^2$:

$$62 \times 58 = 60^2 - 2^2 = 3600 - 4 = 3596$$

Overshoot division. For something like $1656 \div 24$, overshoot with a round multiple and walk back: $24 \times 70 = 1680$, and $1680 - 1656 = 24$, which is exactly one unit of 24, so the answer is $70 - 1 = 69$. This turns division — most people's slowest operation — into one multiplication and one subtraction.

A four-week training plan

1. Week 1 — accuracy, no timer. Drill untimed until you're above 95% accuracy. Memorize the squares and reciprocal tables. Speed built on sloppy technique plateaus early.
2. Week 2 — timed sprints, error log. Two or three 120-second sessions daily, 15–20 minutes total. Write down every miss. Most people discover 70% of their errors come from two operation types (usually subtraction borrows and two-digit division).
3. Week 3 — harder ranges and penalty scoring. Widen the number ranges and score yourself with negative marking to simulate Optiver conditions. Under a $+1/-1$ scheme, an attempt with accuracy $p$ has expected value $2p - 1$: guessing below 50% accuracy actively destroys your score, and steeper penalties push the breakeven higher. Skipping is a skill — practice it.
4. Week 4 — full simulations. Run complete 8-minute tests at interview intensity, at the time of day your real test is scheduled.

Daily short sessions beat weekend marathons — arithmetic speed is retrieval fluency, and retrieval consolidates with spacing, not volume.

The traps that cap your score

• Grinding only default Zetamac settings. You end up fast at one question distribution and stall around 55–60. Vary ranges and operations; our Zetamac comparison covers exactly where the free tool stops helping.
• Ignoring negative marking until test day. A 65-Zetamac candidate who answers everything can lose to a 55 candidate who skips intelligently.
• Skipping fractions and decimals. Raw multiplication speed doesn't transfer to a Flow-style conversion test. Drill both.
• Interface friction. Number-pad typing speed and answer-format quirks (does the field auto-submit?) are worth two or three questions per test. Practice on the real input style.

Ready to train? Run timed sprints on our arithmetic speed drill, then pressure-test the skill where it actually gets used — the market-making and trading games — and finish with a full Optiver-style assessment simulation before the real thing.

More topic guides

• The Airplane Seat Problem: Why the Answer Is 1/2 (Three Proofs)
• Bayes' Theorem in Quant Interviews
• Behavioral Interview Questions at Trading Firms (With Answer Frameworks)
• Coin Flip Questions in Quant Interviews
• C++ Low-Latency Interview Questions at HFT Firms
• Dice Questions in Quant Interviews
• Fermi Estimation Interview Questions at Trading Firms
• Gambler's Ruin in Quant Interviews
• The Kelly Criterion in Quant Interviews
• Linear Regression Interview Questions: OLS Assumptions, R² Traps & Regression to the Mean
• Machine Learning Quant Interview Questions: Overfitting, Cross-Validation & Feature Leakage
• The Market Making Game Interview: How to Answer 'Make Me a Market'
• Market Microstructure Interview Questions: Order Books, Spreads & Adverse Selection
• Markov Chains in Quant Interviews
• Martingales in Quant Interviews
• The Monty Hall Problem — and the Variants Interviews Actually Ask
• Number Sequence Tests in Trading Interviews: The 8 Pattern Types & How to Practice
• Optimal Stopping in Quant Interviews
• Options Pricing Interview Questions: Black-Scholes, Greeks & Put-Call Parity
• Quant Interview Cheat Sheet: Probability, Markov Chains, Options & Linear Algebra (Free PDF)
• Random Walks in Quant Interviews
• Statistics Interview Questions for Quant Roles: Hypothesis Testing, MLE & p-Value Traps
• Stochastic Calculus Interview Questions: Ito's Lemma, SDEs & Brownian Motion
• Time Series Interview Questions: Stationarity, ARMA & Autocorrelation Traps
• Top 50 Quant Interview Questions (With Full Solutions)
• All guides & explainers

Frequently asked questions

What is a good Zetamac score for trading interviews?

On default settings, candidate-reported consensus puts 45-55 as a workable baseline, 55-70 as competitive for most prop trading firms, and 70+ as comfortable even for top market makers like Optiver. These are community benchmarks from forums like r/quant, not official cutoffs. Firms do not publish their thresholds, so treat the bands as rough guidance.

How long does it take to get faster at mental math?

Most candidates add 15-20 points to their Zetamac score in three to six weeks of daily 15-20 minute sessions. The key is training accuracy first, keeping an error log, and spacing practice daily rather than cramming. Progress usually stalls if you only grind one question distribution.

Is Zetamac enough to prepare for the Optiver 80 in 8?

No. Zetamac has no negative marking, so it never teaches you when to skip a question, which is a core skill on the Optiver test where wrong answers cost points. You should also practice under an 8-minute format with penalty scoring, since pacing a 120-second sprint and an 8-minute test are different skills.

Can you use a calculator or paper in trading firm math tests?

Mental math screens are no-calculator by design; that is the entire point of the test. Scratch-paper policies vary by firm and by whether the test is proctored, so the safe approach is to train to do every calculation fully in your head. Verbal mental math in live interviews obviously allows neither.