MENTAL MATH FOR QUANT INTERVIEWS

Why quant firms test mental math

Trading is a stream of small numerical decisions made under time pressure: sizing, spreads, odds, quick expected-value checks. Firms test mental math because it's a cheap, hard-to-fake proxy for numerical fluency — how comfortable your brain is manipulating numbers without a calculator. The famous market-maker math screens run at paces around six seconds per question, which means you cannot compute your way through with school methods. You need technique plus reps.

The core techniques

1. Work left to right

School arithmetic works right to left with carrying. Mental arithmetic is faster left to right, because you produce the most significant digits first and can often stop early. For 487 + 258: think 400+200 = 600, 80+50 = 130 → 730, 7+8 = 15 → 745. With practice this becomes one continuous motion rather than three steps.

2. Use complements for subtraction

Subtracting near a round number is easier as an addition. 702 − 458: 458 is 42 short of 500, and 702 is 202 past 500, so the answer is 202 + 42 = 244. Complements to 10, 100, and 1000 should be instant recall.

3. Factor and regroup multiplication

• Break into round parts: 45 × 12 = 45 × 10 + 45 × 2 = 450 + 90 = 540.
• Use nearby round numbers: 49 × 17 = 50 × 17 − 17 = 850 − 17 = 833.
• Halve and double: 24 × 35 = 12 × 70 = 840. Whenever one factor is even and the other ends in 5, this is nearly always fastest.
• Squares as anchors: memorize squares to 25, then use (a+b)(a−b) = a² − b². 23 × 17 = 20² − 3² = 400 − 9 = 391.

4. Make fraction–decimal–percentage conversions reflexive

Quant questions constantly move between representations. The conversions worth knowing cold: halves through twelfths (1/6 ≈ 16.7%, 1/7 ≈ 14.3%, 1/8 = 12.5%, 1/9 ≈ 11.1%, 1/11 ≈ 9.09%, 1/12 ≈ 8.33%), plus the fact that dividing by 5 is multiplying by 2 and shifting the decimal, and dividing by 25 is multiplying by 4 and shifting twice.

5. Estimate first, then refine

On multiple-choice OAs, a fast order-of-magnitude estimate often eliminates all but one answer. 38 × 17: "roughly 40 × 17 = 680, minus 2 × 17 = 34, so 646." The estimate (≈680) alone may be enough to pick the right option before you finish the exact computation.

What speeds should you target?

Based on the publicly described paces of quant math screens, these are reasonable readiness benchmarks at ~90%+ accuracy:

If you're well above these times today, that's normal — nearly everyone starts slow. Speed compounds quickly with daily timed practice.

A 4-week training plan

• Week 1 — Foundations: untimed accuracy work on left-to-right methods; memorize squares to 25, tables to 20, and the fraction table. Finish each day with one 5-minute timed set to establish a baseline.
• Week 2 — Timed volume: two 10–15 minute timed sessions daily, one addition/subtraction, one multiplication/ division. Push pace until accuracy sits near 85–90%.
• Week 3 — Mixed pressure: mixed-operation timed sets so you stop getting to "choose" your question type — exactly like a real OA. Add percentage and fraction questions.
• Week 4 — Simulation: full-length OA-style simulations with skip discipline and a wrong-answer penalty, plus a light daily warm-up. See the full OA preparation guide for test-day execution.

The principle behind all four weeks: speed is trained at the edge of failure. Comfortable practice maintains ability; slightly-too-fast practice builds it. This is exactly why Variance's drills are adaptive — the difficulty follows your edge automatically.

Small habits that add up

• Compute tips, splits, and unit prices in your head — never reach for the phone calculator.
• When you see a number (a price, a stat, a timestamp), factor it or square-check it out of habit.
• Do a 5-minute drill at the same time every day; consistency beats volume.
• Test yourself with real quant practice questions weekly to check the skills transfer.