Zetamac and Mental Math for Quant Interviews: The Complete Guide

You have a finance degree. You can price a variance swap. You have worked through Hull chapter by chapter. Then Optiver asks you to multiply 47 by 83 and you have six seconds to answer. The first wall in quant interviews is not a brainteaser or a probability puzzle. It is arithmetic. The kind you learned in third grade and apparently never practiced since.

Zetamac is the drill the quant interview community has converged on, and it will get you most of the way there. Not all the way.

Why Trading Firms Test Raw Arithmetic Speed

These tests come from market-making firms, not quant research shops. The distinction matters.

A market maker is continuously quoting bid-ask prices. The profit is the spread, and it only materializes if the quoted price creates a favorable expected value before the market moves. A trader who needs 30 seconds to verify that 0.625 divided by 150 is approximately 0.004 cannot work that desk. They need someone who can.

The test is also cheap screening. Optiver receives tens of thousands of applications. A five-section online assessment that eliminates 80% of candidates before any human reviews a resume is an efficient first filter. Fast arithmetic correlates well enough with trainability and quantitative instinct that the test has stuck around for decades.

Systematic research firms like Two Sigma, D.E. Shaw, and AQR are a different world. They want statistical modeling and coding. Nobody at those firms asks you to multiply two-digit numbers under a timer. If you are targeting a research role, this guide does not apply.

Inside the Optiver 80-in-8

Optiver's arithmetic test is the most discussed and most referenced mental math screen in finance. Eighty questions in eight minutes, averaging six seconds per question. Multiple choice, four options. No calculator. Pen and paper are allowed, though at six seconds per question you will need a paper strategy that actually helps rather than costs you time.

What the questions look like:

67 × 43
0.014 × 0.0004
1/8 × 560
0.625 ÷ 150
3/153 as a decimal
8.5 × 14.4
8 ÷ 0.4

Notice what is on that list: integers, decimals, fractions, and fraction-to-decimal conversions. This is exactly where Zetamac-only candidates get surprised.

Scoring: +1 correct, -1 incorrect, -1 skipped. That last part is the one people miss. Blind guessing among four options has an expected value of exactly zero. Skipping has an expected value of -1. You are better off guessing when you have no idea and need the seconds elsewhere, because skipping guarantees a loss.

Passing threshold: approximately 55-56 correct to advance. To be competitive rather than just surviving, 70 or above. These numbers come from community reports across Wall Street Oasis and Reddit, not official Optiver data. Treat them as directionally accurate.

Delivery: Online and unsupervised, typically within a 72-hour window to complete the full five-section assessment. Failing any single section ends the process.

How Other Firms Compare

Optiver is the most famous but not the only firm that puts arithmetic speed at the top of its filter stack.

Firm	Format	Scale
Optiver	80 questions, 8 minutes, multiple choice, includes fractions and decimals	+1/-1 scoring
Akuna Capital	80 questions, 8 minutes, free response (no multiple choice), integers and decimals, no fractions	No calculator, no pen and paper
Flow Traders	60 questions, 6 minutes, basic arithmetic including fractions and decimals	Separate 26-question sequences section
SIG	Mental arithmetic embedded in a 60-75 minute cognitive assessment	Approximately 25% of trader evaluation weight
IMC Trading	50-80 arithmetic questions as part of online assessment	Two-digit multiplication under 3 seconds is an advantage
Citadel Securities	50 questions mixing logic and arithmetic, 12 minutes	Mental math is roughly 25% of trader screen
Jane Street	Arithmetic embedded in interview rounds, not a standalone speed test	3-5 questions per round, interviewer asks your confidence level after each answer

Firm-specific format differences matter more than generic prep. Akuna is free response with no fractions, so Zetamac-only training works fine there. Jane Street integrates arithmetic into conversation. The interviewer asks for your confidence level after each answer, making reasoning as important as the result. Two Sigma, HRT (engineering track), DRW, and Renaissance have no meaningful arithmetic speed gate.

What Is Zetamac

Zetamac (arithmetic.zetamac.com) is a free browser-based arithmetic drill. A problem appears, you type the answer, press Enter, the next loads. Your score is correct answers in the time window. Default: 2-minute timer, all four operations, integers only.

It became the standard community benchmark not because any firm endorses it, but because it is free, fast to start, and close enough in format that candidates can compare scores across forums. Nobody designated it the official tool. It just won.

Community score benchmarks:

Zetamac score (2-minute default)	What it signals
Under 20	Foundational work needed on number facts
20-30	Building phase, arithmetic is not yet automatic
30-40	Approaching interview-relevant territory
40-50	Competitive for most firms that have arithmetic screens
50-60	Strong preparation level
60+	Elite range, likely comfortable on Optiver's test

One documented prep log describes going from Zetamac 20 to 85+ over several months and finishing Optiver's real test with a minute to spare. Another records a baseline of 50, a peak of 60, and an Optiver internship offer. Neither is a precise conversion chart, but the direction holds.

The major limitation: Zetamac uses integers only. Optiver, Flow Traders, and SIG include fractions and decimals. Zetamac 60 does not mean Optiver-ready if you have never drilled fraction-to-decimal conversions. That is separate work and has to be done separately.

The Fraction Gap

This is the part that trips up the most well-prepared candidates.

You need fraction-to-decimal conversions cold:

1/2  = 0.5    1/6  ≈ 0.167   1/9  ≈ 0.111
1/3  ≈ 0.333  1/7  ≈ 0.143   1/12 ≈ 0.083
1/4  = 0.25   1/8  = 0.125   1/16 = 0.0625
1/5  = 0.2

When you see 1/8 × 560, the fast path is recognizing 1/8 = 0.125, so 0.125 × 560 = 70. If you pause to do long division for 1/8, you have burned two seconds on a six-second problem. That is a budget you do not have.

For decimal multiplication like 0.014 × 0.0004: strip the zeros, multiply the significands (14 × 4 = 56), count decimal places (3 + 4 = 7 total, answer is 0.0000056). That becomes pattern recognition after practice. Without practice, it becomes a four-second death spiral while the clock runs.

Zetamac does not train this. Dedicate separate sessions to it.

Techniques That Actually Transfer

Most candidates rely on brute repetition. That works, but a few strategies compress the timeline significantly.

Left-to-right decomposition for multiplication: For 47 × 8, compute 40 × 8 = 320, then 7 × 8 = 56, then add. For two-digit × two-digit like 43 × 67, decompose one factor: 43 × 70 - 43 × 3 = 3010 - 129 = 2881. Multiply-then-subtract-the-overshoot is faster than running columnar long multiplication in your head.

Complement subtraction: Instead of computing 73 - 48 the hard way, think "48 to 50 is 2, 50 to 73 is 23, total 25." You are always adding toward a round anchor instead of borrowing across columns.

Fraction recognition for division: 0.625 ÷ 150 is faster if you recognize 0.625 = 5/8, so the problem becomes 5 / (8 × 150) = 5/1200 ≈ 0.00417. The shortcut only exists if you have drilled the fraction-decimal table until it is automatic.

Before any of this, make number facts automatic. Multiplication tables through 12, addition combinations over 10, and fraction-to-decimal conversions. These are the atoms of every calculation. If you hesitate on 7 × 8, no shortcut compensates for it.

Tools Worth Using Beyond Zetamac

mathtrainer.org: Structured difficulty across 100 levels. Better than Zetamac for beginners because the difficulty scales with you. Reach level 80 before treating yourself as first-round ready.

TradingInterview.com: Has an Optiver-specific mode with +1/-1 scoring and a problem mix that includes fractions and decimals. Candidates who have cleared the real test describe it as the closest available simulation. This is the one to use in the final month.

Everythingquant.com: Optiver and Akuna practice modes with authentic timing and penalty scoring. Use this in the final two weeks to get comfortable with the clock pressure.

Matiks: Multiplayer mental math. The competitive element adds pressure, which is exactly what solo Zetamac sessions cannot replicate.

Anki: Flash cards for fraction-decimal conversions and two-digit multiplication pairs. Counterintuitively effective for building the underlying number facts that every technique depends on.

Eight Weeks to Competitive

Weeks 1 to 3: Two Zetamac sessions per day, 2 minutes each. Identify which operations slow you down. Add Anki for fraction-decimal conversions. Target: 30 correct. If you are already at 30 after week one, good. If you are at 12 after week one, that is also useful information.

Weeks 4 to 6: Switch to 5-minute sessions. Add explicit decimal and fraction drills. Start using TradingInterview or Everythingquant for the realistic Optiver problem mix. Target: 50 correct on Zetamac, fluent on fraction conversions.

Weeks 7 to 8: Full Optiver practice tests with penalty scoring, two to three per week. Drill only the operation types you lost time on between tests. Target: 60+ on Zetamac, 65+ on practice tests.

Final 72 hours: Stop learning techniques. A few light sessions on reliable operations, then rest. The score is built over weeks, not in the final night. Going hard the night before does not move the needle. It just means you are tired when you sit down to take the test.

What Happens After the Arithmetic Test

Passing the arithmetic screen gets you into the process, not to an offer. Optiver's full online assessment has five sections. The arithmetic test is one gate. Candidates who pass move to a recorded video interview, then a phone screen with trading staff, then a Super Day.

A perfect arithmetic score does not override weak probability intuition or poor communication. But you do not get to demonstrate any of those skills without clearing the first filter. For a full breakdown of the rest of Optiver's process, see the Optiver phone screen guide and Optiver software engineer interview. If you are still deciding whether quant or FAANG is the right path, FAANG vs quant firm interview covers the full contrast. To practice the verbal and reasoning components that follow the arithmetic screen, SpaceComplexity offers voice-based mock interviews with rubric-based feedback.

Where Prepared Candidates Still Fail

Training Zetamac only. The integer-only limitation is real. Optiver's fraction questions cost three to four seconds each on a test with six seconds per question average. This is not a minor gap.

Optimizing speed before accuracy. Penalty scoring means a 40% hit rate at high speed has the same expected value as random guessing. Accuracy first, then speed. In that order.

Stopping at Zetamac 40. That score is the floor where you stop being immediately eliminated. Competitive candidates score 60 or above. Reaching 40 and deciding you are prepared is a category error. You have stopped losing to the bottom tier. You have not joined the tier that gets offers.

Underestimating the pressure differential. Practicing alone with no stakes is not the same as a timed test with penalty scoring. Matiks and Everythingquant's penalty modes add useful stress. Seek it out before the real test.

Ignoring firm-specific format differences. Akuna is free response with no fractions. Optiver is multiple choice with fractions and decimals. Flow Traders is 60 questions in 6 minutes, a slightly faster pace. Check the format before you spend eight weeks training for the wrong test.