Market maker desks such as Optiver, Flow Traders, IMC, and Jane Street frequently test mental arithmetic during early interview rounds. Candidates often wonder why trading firms care about fast calculations when computers execute modern trades in nanoseconds.
The purpose is not to replace computers. Mental math tests your composure, working memory, and comfort with numbers when the clock is ticking and you have to answer out loud.
1. The near-100 multiplication shortcut
When multiplying two numbers close to 100, such as 96 times 93, calculating by long multiplication is too slow. Use the base-100 difference method:
- Find the deficits from 100: 96 is minus 4, and 93 is minus 7.
- Subtract either deficit from the opposite number: 96 minus 7 equals 89 (or 93 minus 4 equals 89). This gives the first two digits.
- Multiply the two deficits: minus 4 times minus 7 equals 28.
- Combine the parts: 8,928. You can compute this in your head in two seconds flat.
2. Squaring numbers ending in 5
Any two-digit number ending in 5 follows a simple pattern:
- Take the first digit, multiply it by the next consecutive integer, and append 25 to the end.
- For 65 squared: 6 times 7 equals 42. Append 25 to get 4,225.
- For 85 squared: 8 times 9 equals 72. Append 25 to get 7,225.
3. Fractions to decimals: memorize them cold
You should never have to think about standard fraction-to-decimal conversions during an interview. Drill these until they are instinctive:
- 1/6 = 0.1667 (16.67%)
- 1/7 = 0.1428 (14.28%)
- 1/8 = 0.1250 (12.50%)
- 1/9 = 0.1111 (11.11%)
- 1/12 = 0.0833 (8.33%)
- 1/16 = 0.0625 (6.25%)
4. Expected value shortcuts in dice and cards
Trading interviews frequently present betting games where you must calculate fair value quickly:
- Average of a standard six-sided die: (1 + 6) / 2 = 3.5.
- Sum of two dice: Expected value is always 7. The probability distribution is symmetric, peaking at 7 with 6 out of 36 combinations (1/6).
- Linearity of expectation: The expected value of a sum is always the sum of the expected values, regardless of whether the variables are independent. This rule lets you bypass complicated probability trees in multi-stage problems.
Daily training routine
Building arithmetic speed requires daily consistency, not marathon weekend sessions. Spend 15 minutes each morning using speed arithmetic drills. Set a strict timer and focus on verbalizing your thought process calmly as you calculate.