Why Mental Math Matters in Quant Interviews
Every options market-making firm - SIG, Optiver, IMC, Akuna, Belvedere, Flow Traders - tests mental arithmetic, often as the first filter. The Optiver trader test in particular is famous for asking 50 to 80 mental math questions in two minutes; pass rates are below 10%. The reason is straightforward: floor traders genuinely need to do two-digit multiplications and percentage calculations in seconds, and the test is a reasonable proxy for that ability.
This guide covers the techniques that actually work for the most common question patterns, plus 50 drill questions you can work through. For firm-specific context on which firms test mental math hardest, see our SIG interview, Optiver interview and IMC trading interview guides.
Core Techniques
Two-digit multiplication: the standard form
To multiply two two-digit numbers AB × CD:
- Compute (A×C) hundreds
- Add (A×D + B×C) tens
- Add (B×D) units
Example: 47 × 36 = (4×3)·100 + (4×6 + 7×3)·10 + (7×6) = 1200 + 450 + 42 = 1692.
Two-digit multiplication: the difference of squares
When numbers are close, use (a^2 - b^2 = (a-b)(a+b)):
- 17 × 23 = (20-3)(20+3) = 400 - 9 = 391
- 47 × 53 = (50-3)(50+3) = 2500 - 9 = 2491
- 28 × 32 = (30-2)(30+2) = 900 - 4 = 896
Squaring numbers ending in 5
(N5^2 = N(N+1)·100 + 25):
- (35^2 = 3·4·100 + 25 = 1225)
- (75^2 = 7·8·100 + 25 = 5625)
- (95^2 = 9·10·100 + 25 = 9025)
Multiplication by 11
Insert the sum of adjacent digits between them:
- 35 × 11 = 3, (3+5), 5 = 385
- 67 × 11 = 6, (6+7=13), 7 → 7,3,7 + carry → 737
- For longer numbers: 234 × 11 = 2, (2+3), (3+4), 4 = 2574
Percentages
For "X% of N", swap if easier: 24% of 50 = 50% of 24 = 12.
For "X is what % of N": think in fractions first. 8 of 32 = 1/4 = 25%. 15 of 60 = 1/4 = 25%. 7 of 35 = 1/5 = 20%.
Square roots
Memorise:
- 1²=1, 2²=4, 3²=9, 4²=16, 5²=25
- 6²=36, 7²=49, 8²=64, 9²=81, 10²=100
- 11²=121, 12²=144, 13²=169, 14²=196, 15²=225
- 16²=256, 17²=289, 18²=324, 19²=361, 20²=400
- 25²=625, 30²=900, 50²=2500
Division
For "N / 7" (or other awkward divisors), think in known multiples. 245 / 7: 7×30=210, 7×35=245, so 35.
For percentages: 38% ≈ 38/100. To divide by 100 use the comma; to divide by 7, multiply by ~0.143.
Drill Set 1: Multiplication (15 questions)
| # | Question | Answer | Technique |
|---|---|---|---|
| 1 | 13 × 17 | 221 | Diff of squares: (15^2 - 4 = 221) |
| 2 | 24 × 26 | 624 | Diff of squares: (25^2 - 1 = 624) |
| 3 | 38 × 42 | 1596 | Diff of squares: (40^2 - 4 = 1596) |
| 4 | 47 × 53 | 2491 | Diff of squares: (50^2 - 9) |
| 5 | 19 × 21 | 399 | Diff of squares: (20^2 - 1) |
| 6 | 65 × 75 | 4875 | (70^2 - 25) |
| 7 | 27 × 33 | 891 | (30^2 - 9) |
| 8 | 14 × 28 | 392 | (14 × 30 - 14 × 2) |
| 9 | 35 × 11 | 385 | Add adjacent digits |
| 10 | 67 × 11 | 737 | Add adjacent digits with carry |
| 11 | 25² | 625 | (2·3·100 + 25) |
| 12 | 45² | 2025 | (4·5·100 + 25) |
| 13 | 75² | 5625 | (7·8·100 + 25) |
| 14 | 95² | 9025 | (9·10·100 + 25) |
| 15 | 17 × 23 | 391 | (20^2 - 9) |
Drill Set 2: Percentages (15 questions)
| # | Question | Answer | Quick path |
|---|---|---|---|
| 1 | 25% of 80 | 20 | 80/4 |
| 2 | 15% of 60 | 9 | 10% + 5% = 6 + 3 |
| 3 | 75% of 240 | 180 | 3/4 of 240 |
| 4 | 12% of 50 | 6 | Swap: 50% of 12 = 6 |
| 5 | 35% of 200 | 70 | 35 × 2 |
| 6 | 8% of 250 | 20 | Swap: 250/8 × 8 = 20 |
| 7 | 24% of 50 | 12 | Swap: 50% of 24 = 12 |
| 8 | 18 is what % of 60? | 30% | 18/60 = 3/10 |
| 9 | 9 is what % of 36? | 25% | 9/36 = 1/4 |
| 10 | 21 is what % of 70? | 30% | 21/70 = 3/10 |
| 11 | 60 is what % of 80? | 75% | 60/80 = 3/4 |
| 12 | 14 is what % of 56? | 25% | 14/56 = 1/4 |
| 13 | 35 is what % of 140? | 25% | 35/140 = 1/4 |
| 14 | 240 increased by 15% | 276 | 240 + 36 |
| 15 | 80 decreased by 20% | 64 | 80 × 0.8 |
Drill Set 3: Division (10 questions)
| # | Question | Answer | Quick path |
|---|---|---|---|
| 1 | 240 / 16 | 15 | 240/8/2 = 30/2 |
| 2 | 144 / 9 | 16 | Use known: (9 × 16 = 144) |
| 3 | 196 / 14 | 14 | (196 = 14^2) |
| 4 | 117 / 13 | 9 | (13 × 9 = 117) |
| 5 | 169 / 13 | 13 | (169 = 13^2) |
| 6 | 1000 / 25 | 40 | × 4 = 4000/100 |
| 7 | 750 / 15 | 50 | × 2 = 1500/30 |
| 8 | 480 / 12 | 40 | 480/12 = 40 |
| 9 | 384 / 16 | 24 | Halve twice from 384/4 = 96 |
| 10 | 567 / 7 | 81 | (7 × 80 = 560), +7 = 81 |
Drill Set 4: Square Roots and Special (10 questions)
| # | Question | Answer | Technique |
|---|---|---|---|
| 1 | √169 | 13 | Memorise |
| 2 | √196 | 14 | Memorise |
| 3 | √225 | 15 | Memorise |
| 4 | √324 | 18 | (18^2 = 324) |
| 5 | √400 | 20 | Memorise |
| 6 | √625 | 25 | (25^2) |
| 7 | √900 | 30 | Memorise |
| 8 | √1024 | 32 | Memorise (powers of 2) |
| 9 | √1369 | 37 | (37^2 = 1369) |
| 10 | √2401 | 49 | Memorise (49²) |
How to Train
Daily routine. 30 minutes per day on Zetamac for 4-6 weeks. Set the timer to 2 minutes and aim for steady improvement. Most people start at 15-20 correct in 2 minutes; the target for a serious Optiver/SIG candidate is 50+ in 2 minutes.
Vary the operations. Don't drill only multiplication. Practice mixed arithmetic (add, subtract, multiply, divide, percentages) because the actual interview will jump between operations rapidly.
Practice fractions to decimals. Top firms test these directly. Memorise:
- 1/3 = 0.333, 2/3 = 0.667
- 1/7 = 0.143, 2/7 = 0.286, 3/7 = 0.429
- 1/8 = 0.125, 3/8 = 0.375, 5/8 = 0.625, 7/8 = 0.875
- 1/9 = 0.111, 2/9 = 0.222, 4/9 = 0.444
Practice large round numbers. "7000 × 0.6" should come instantly (4200). "350 × 0.4" instantly (140).
For broader interview prep, see our quant interview questions hub and quant probability interview questions.
Practise the questions Quant Mental Math Questions: 50 Drills and Techniques 2026 actually asks
Reading about the interview is one thing - sitting one is another. Quantt's interactive coding tests are modelled on the same problem types that show up in firms like Jane Street, Citadel, Hudson River and Optiver. Run real Python in the browser, get instant feedback, and benchmark yourself against the bar.
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