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Quant Mental Math Questions: 50 Drills and Techniques 2026

50 mental math drills for quant trader interviews, plus the techniques that actually work for two-digit multiplication, percentages.

12 min read·25 May 2026

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Why Mental Math Matters in Quant Interviews

Options market-making firms such as SIG, Optiver, IMC, Akuna, Belvedere and Flow Traders test mental arithmetic somewhere in the process, sometimes as the first filter and sometimes in the interviews. IMC's recent online tests for traders in the US and Europe, for example, are mostly reasoning puzzles and games. The Optiver trader test in particular is famous for its 80 in 8: 80 multiple-choice arithmetic questions in eight minutes, six seconds each, with a penalty for wrong answers. 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.

Did you know?

Tap a tile for a quick interview snippet — then keep going.

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

Quick quiz

Mental maths sprint

No calculator — three quick ones.

1 / 3

15% of 240?

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 for 4-6 weeks. Start on the mental math trainer, then run the 80 in 8 challenge at the Optiver pace with a +1/-1 penalty. Zetamac is still useful for extra 2-minute volume. Most people start at 15-20 correct in 2 minutes; the target for a serious Optiver/SIG candidate is 50+ in 2 minutes, or a competitive net on the full 80-in-8.

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.

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