Prop Firm Quantitative Tests: Complete Guide (Optiver, SIG, Jane Street, Citadel)
A comprehensive breakdown of the mental math and quantitative screens used by the major prop trading firms — what each firm tests, how hard the screens are, and exactly how to pass.
Prop Firm Quantitative Tests: Complete Guide
Every major prop trading firm screens for quantitative ability before the real interview process begins. Knowing which format to expect — and how demanding each firm's screen is — lets you concentrate your preparation where it matters.
Why Prop Firms Screen This Way
Prop firms need traders who can:
- Process numerical information faster than the competition
- Catch their own arithmetic errors before they become losing positions
- Estimate quickly enough to act before markets move
A quantitative screen filters for these skills efficiently before investing 40+ hours of interviewer time per candidate.
Firm-by-Firm Breakdown
Optiver: The 80-in-8
Format: 80 arithmetic problems in 8 minutes. One problem every 6 seconds.
What's tested:
- Multi-digit addition and subtraction (e.g., 847 + 293)
- 2×3 digit multiplication (e.g., 37 × 124)
- Division with decimals
- Percentage calculations (e.g., "17.5% of 240")
- Fractions and ratios
Pass threshold: ~60/80 correct. Top candidates score 70–80.
What makes it hard: Not the arithmetic — the pace. Most candidates who fail can do the math. They fail because they've never practiced making a commitment in 6 seconds and moving on. The test is about reflex, not ability.
Prep focus: Pure speed arithmetic under timed pressure. Unlike estimation-focused interviews, Optiver wants exact answers fast.
Jane Street: No Timed Screen, High Bar
Format: No discrete timed arithmetic test. Mental math is evaluated conversationally throughout 4–6 interview rounds.
What's tested:
- Arithmetic fluency (2-digit multiplication, fractions, decimals — tested live in conversation)
- Probability and expected value
- Market-making games (bid/ask spreads under uncertainty with incomplete information)
- Fermi estimation
- Bayesian reasoning
Pass threshold: No cutoff score. Evaluated holistically across rounds.
What makes it hard: The intellectual depth. Jane Street wants traders who reason probabilistically in real time, not just ones who are fast. A candidate who quotes a calibrated range and updates correctly on new information outperforms one who computes quickly but anchors incorrectly.
Prep focus: Probability foundations, EV calculations, Bayes' theorem, market intuition, daily estimation practice.
Susquehanna (SIG): Aptitude + Game Theory
Format: SIG uses a proctored online aptitude test, plus in-person math and reasoning rounds.
What's tested:
- Mental arithmetic (similar difficulty to Optiver, though typically less extreme on speed)
- Numerical reasoning and pattern recognition
- Probability and combinatorics
- Poker and game theory (SIG famously teaches poker to all new hires — game-theoretic thinking is core to their culture)
Pass threshold: Not published. SIG self-selects for candidates from top math, physics, and CS programs.
What makes it hard: The game theory dimension. SIG wants candidates who understand strategic reasoning under uncertainty — not just candidates who can compute quickly.
Prep focus: Probability, game theory intuition, combinatorics, and quick estimation.
Citadel and Citadel Securities: Role-Dependent
Format: Varies significantly by role.
Trading track:
- Speed mental math under time pressure
- Probability problems (conditional probability, EV)
- Market-making scenarios
- Brain teasers with quantitative components
Quantitative research track:
- Statistics and probability theory
- Coding challenges (Python, C++)
- Machine learning fundamentals
- Stochastic calculus (for some teams)
Pass threshold: Not published. Varies by role.
What makes it hard: The breadth. Citadel hires across strategies and roles, so there's no single prep path. Research roles require much deeper statistical and mathematical knowledge than trading roles.
Prep focus: Traders need speed arithmetic and probability. Researchers need statistics, linear algebra, and coding.
IMC Trading: Optiver-Comparable
Format: IMC is an Amsterdam-based firm with a culture similar to Optiver. Expect a timed arithmetic test comparable to the 80-in-8 in difficulty.
What's tested:
- Speed arithmetic
- Mental math under pressure
- Probability and market reasoning
Pass threshold: Similar to Optiver — roughly 75%+ accuracy at high speed.
What makes it hard: Same as Optiver — pace. The Amsterdam prop trading cluster (Optiver, IMC, Flow Traders) shares similar hiring standards.
Prep focus: Speed arithmetic. Blitz mode drills under strict time pressure.
DRW: Market Knowledge Over Raw Speed
Format: More conversational than test-based. Math is embedded in market discussions, not isolated.
What's tested:
- Market intuition (commodity prices, interest rates, macro)
- Contextual mental math ("you're long 100 corn futures at $4.50/bushel, corn drops to $4.30...")
- Ability to reason about risk and uncertainty
- Basic derivatives mechanics
Pass threshold: No discrete screen. DRW looks for genuine market interest.
What makes it hard: The market knowledge requirement. DRW wants candidates who read markets, not just candidates who can compute. Knowing why crude oil spread traded at a discount last year matters here.
Prep focus: Read about commodity and rates markets. Practice contextual position math (PnL, sizing, contract specs).
HRT (Hudson River Trading): Extremely Technical
Format: HRT is primarily quantitative research and engineering. The process is heavier on CS and statistics than trading arithmetic.
What's tested:
- Algorithmic problem solving
- Statistics and probability theory at depth
- Systems thinking
- Mental math is expected but not the primary screen
Pass threshold: Among the highest bars in the industry for researcher roles.
Prep focus: CS fundamentals, statistics, probability at the graduate level. For rare trading roles: probability and speed arithmetic.
Comparative Difficulty Across Skills
| Firm | Raw Speed | Probability | Market Intuition | Overall Difficulty |
|---|---|---|---|---|
| Optiver | ●●●●● | ●●○○○ | ●●○○○ | ●●●●○ |
| Jane Street | ●●●○○ | ●●●●● | ●●●●○ | ●●●●● |
| SIG | ●●●○○ | ●●●●○ | ●●●○○ | ●●●●○ |
| Citadel | ●●●○○ | ●●●●○ | ●●●○○ | ●●●●○ |
| IMC | ●●●●○ | ●●●○○ | ●●○○○ | ●●●●○ |
| DRW | ●●○○○ | ●●●○○ | ●●●●○ | ●●●○○ |
| HRT | ●●●○○ | ●●●●● | ●●○○○ | ●●●●● |
The Universal Prep Stack
Regardless of target firm, build these foundations:
Core Arithmetic (3 weeks minimum)
- 2×2 digit multiplication to under 5 seconds per problem
- Percentage calculations without a calculator
- Fraction → decimal → percent fluency
- Common squares memorized (up to 25²)
Probability (2 weeks minimum)
- Expected value in any scenario — dice, cards, bets, assets
- Conditional probability and Bayes' theorem
- Combinations and permutations (for counting problems)
- Basic option pricing intuition (binomial trees)
Market Intuition (ongoing)
Know these to order-of-magnitude accuracy:
- S&P 500 level and approximate PE ratio
- Apple, Google, Amazon market caps
- US GDP (
$27T), US federal debt ($36T), 10-year yield - Oil price, gold price, Bitcoin price
Firm-Specific Final Prep (last 2 weeks)
Optiver / IMC: Shift 80% of practice to timed arithmetic sprints. Use 6-second-per-problem timers. Accuracy under pressure.
Jane Street / SIG: Shift to probability puzzles. Practice making markets on uncertain quantities. Get comfortable with Bayesian problems.
Citadel (trading): Balanced mix of speed math and probability. Add market-making scenario practice.
DRW: Read commodity markets. Understand futures contract specs. Practice contextual position math.
Frequently Asked Questions
Which prop firm test is hardest? Optiver has the most demanding raw speed screen. Jane Street has the most demanding overall process — probability depth, market intuition, and trader game combined.
Do prop firms share test results? No. Each firm uses its own test format and doesn't share data across firms.
Can you retake the Optiver 80-in-8? Typically not for at least 6–12 months after a failed attempt.
How long does it take to prepare? Most candidates who pass Optiver's test spend 4–8 weeks of daily practice (30–60 min/day). Jane Street preparation is ongoing — market intuition takes months to build.
Practice Resources
- Fermiq daily drill — calibration across all skill areas, Elo-rated
- Blitz mode — timed sprint mode for speed arithmetic practice
- Interview prep track — structured 6-week curriculum
- Probability category
- Markets category
The firms test the same underlying skill from different angles. Build the foundation, then firm-specific prep in the final two weeks.