Mental Math Drills for Trading Interviews: How to Pass the Test

Mental Math Drills for Trading Interviews: How to Pass the Test

The mental math test is the gatekeeper at most quant trading firms. Jane Street, Optiver, SIG, Akuna, IMC, Citadel Securities, and most market makers use timed mental-math screens early in the interview process. The format is consistent: 60–80 questions, 8 minutes, no calculator, no scratch paper, and a pass bar around 70–85% correct. Below the bar, your interview ends regardless of how strong your other skills are. This guide covers what the test actually looks like, the techniques that get you above the bar, and a practice schedule that works.

What the Test Actually Looks Like

The variants differ across firms but the question types are similar:

• Multiplication: “47 × 8”, “23 × 19”, “125 × 16”
• Division: “144 / 12”, “240 / 15”, “672 / 24”
• Percentages: “15% of 280”, “37% of 200”, “what’s 36 as a percentage of 240”
• Decimals and fractions: “3.5 / 0.5”, “12.5 + 7.75”, “7/8 – 3/4”
• Comparisons: “which is larger: 48% or 12/25?”, “which fraction is closest to 0.4: 3/8 or 5/12?”
• Mixed: “compute (47 × 4) – (15 × 12)”

Difficulty escalates: early questions are easy enough to do in 3–5 seconds; later ones might need 10–15 seconds even with practice. The format rewards consistency over peak performance.

Why Trading Firms Test This

Three reasons:

• Practical relevance: traders and market makers compute prices, P&L, and percentages constantly. While modern trading uses computers, fluency with arithmetic translates to fluency with markets.
• Filter signal: mental math is correlated with general numerical aptitude and with the ability to focus under time pressure. Both matter for trading.
• Hard to fake: you can’t bluff your way through a timed math test. Either you can do it or you can’t.

The Core Techniques

Multiplication: Distribute and Round

For 47 × 8: don’t try to multiply directly. Decompose: (50 × 8) – (3 × 8) = 400 – 24 = 376. Round-to-nearest-easy-number, multiply, then adjust.

For 23 × 19: closest easy form is (23 × 20) – 23 = 460 – 23 = 437. Or (20 × 19) + (3 × 19) = 380 + 57 = 437.

For 125 × 16: 125 × 16 = 125 × 8 × 2 = 1000 × 2 = 2000. Notice 125 = 1000/8 patterns.

Useful identity: (a + b)(a – b) = a² – b². So 19 × 21 = (20 – 1)(20 + 1) = 400 – 1 = 399. Useful when numbers are equidistant from a round value.

Division: Estimate and Refine

For 672 / 24: 24 × 30 = 720, too high; 24 × 28 = 24 × 30 – 24 × 2 = 720 – 48 = 672. Answer: 28.

For 240 / 15: 15 × 16 = 240. Answer: 16.

Strategy: guess the answer to within 10%, multiply back, refine. Faster than long division mental gymnastics.

Percentages: Convert to Easy Forms

15% of 280: 10% is 28; 5% is 14; total 42. Or: 15% = 3/20 = 3 × 14 = 42.

37% of 200: 200 × 37 / 100 = 2 × 37 = 74. (37% of 200 = 37 × 2 since 200 = 2 × 100.)

36 as a percentage of 240: 36/240 = 3/20 = 15%. Reduce the fraction first, then convert.

Useful equivalents to memorize:

• 1/8 = 12.5%
• 1/7 ≈ 14.3%
• 1/6 ≈ 16.7%
• 1/5 = 20%
• 1/4 = 25%
• 1/3 ≈ 33.3%
• 3/8 = 37.5%
• 2/5 = 40%
• 3/7 ≈ 42.9%
• 5/8 = 62.5%
• 2/3 ≈ 66.7%
• 3/4 = 75%
• 5/6 ≈ 83.3%
• 7/8 = 87.5%

Recognizing these immediately saves seconds per question.

Squaring Two-Digit Numbers

For 23² use (20+3)² = 400 + 2(60) + 9 = 400 + 120 + 9 = 529.

For 28² use (30-2)² = 900 – 120 + 4 = 784.

For numbers ending in 5: 25² = 625, 35² = 1225, 45² = 2025, 55² = 3025, 65² = 4225, 75² = 5625, 85² = 7225, 95² = 9025. Pattern: drop the 5, multiply n(n+1), append 25. So 65² = 6×7=42, append 25 → 4225.

Decimal Operations

3.5 / 0.5: multiply numerator and denominator by 2 → 7 / 1 = 7.

12.5 + 7.75: 12 + 7 = 19; 0.5 + 0.75 = 1.25; total 20.25.

0.4 × 0.25: think of as fractions, 2/5 × 1/4 = 2/20 = 1/10 = 0.1.

Fraction Comparisons

“Which is larger: 48% or 12/25?” Convert: 12/25 = 48/100 = 48%. Equal.

“Which is closest to 0.4: 3/8 or 5/12?” 3/8 = 0.375; 5/12 ≈ 0.417. Distance from 0.4: 0.025 vs 0.017. Answer: 5/12.

Strategy: convert both to decimals to 2–3 places, then compare.

The Practice Schedule

The single most effective tool: Zetamac arithmetic game (free at arithmetic.zetamac.com). 2-minute drills, configurable difficulty. Standard “trading” settings: addition 2-99, multiplication 2-12 by 2-99, division 1-12 by 1-99, subtraction 0-99 from 0-99.

Week 1: Run Zetamac twice daily, 2 minutes each. Don’t worry about score; build the habit. Goal: hit 30+ questions correct in 2 minutes.

Weeks 2–3: Three sessions daily. Track scores. Goal: 50+ correct in 2 minutes by end of week 3.

Weeks 4–6: Vary difficulty. Add 5-minute “performance” sessions where you push for personal best. Goal: 65+ correct in 2 minutes.

Weeks 7–8: Approaching interview readiness. Practice harder Zetamac configurations (multiplication 2-99 × 2-99, longer divisions). Goal: 75+ correct in 2 minutes at standard settings.

Most candidates need 4–8 weeks of daily practice to go from “barely passing” to “comfortably above bar.” Skip a week and you’ll feel the rust.

Test-Day Tactics

• Don’t get stuck on one problem. If a question takes > 15 seconds, skip it (if allowed) or guess and move on. Total score matters more than any individual question.
• Trust your instincts on rounding. “37% of 200” should be reflexive: roughly 75. Don’t second-guess yourself.
• Verbalize internally. Saying numbers internally as you compute them (sub-vocalization) helps focus.
• Sleep and caffeine. Mental math performance is sensitive to fatigue. The night before matters.
• Warm up first. Run 1–2 Zetamac drills 10–30 minutes before the test. Going in cold underperforms.

Common Mistakes

• Trying to compute exactly when estimation suffices. “What’s 17.3% of 412?” The answer to within 1% is what’s needed; don’t grind to three decimal places.
• Memorizing answers instead of techniques. Question banks are large; the test will give you problems you haven’t memorized. Focus on technique fluency.
• Practicing only easy problems. Comfort zone doesn’t build the skills you need under stress.
• Stopping practice when you hit a “good enough” score. Skill atrophies fast without daily practice. Keep going until interview day.

Beyond Zetamac

For deeper practice:

• Trader-style mental math: Practice computing percentages of dollar amounts (“What’s 18% of $4,250?”), bid-ask midpoints, and price changes (stock at 247.32, drops 1.7%, what’s the new price?).
• Probability-adjacent arithmetic: “If something happens with probability 23/45, what’s that as a percentage?” 23/45 ≈ 51%.
• Compound calculations: “Stock returns 8% annually for 5 years; final value as multiple?” 1.08^5 ≈ 1.47.
• Mark-to-market: “I’m long 1000 shares at $42, stock now $39.50, P&L?” -$2,500.

Frequently Asked Questions

See also: Breaking Into Quant Finance and Wall Street: 2026 Guide • Probability Brainteasers for Quant Interviews • Jane Street Interview Guide