Trainers & Games
Mental Math Trainer
The trading-floor classic: answer as many arithmetic questions as you can before the clock runs out. Optiver-style 80-in-8.
Mental Math Trainer
Trading firms like Optiver famously screen candidates with a timed arithmetic test, often 80 questions in 8 minutes. Answer as many as you can before the clock runs out. Speed and accuracy both count.
Learn how it works
Five worked examples. Read a couple before you dive in, try to answer first, then reveal the solution.
Multiplying near a round number
Compute 98 × 87 quickly, without long multiplication.
Show solution
Nudge 98 up to the friendly number 100, then take the extra back:
- 98 × 87 = (100 − 2) × 87
- = 8700 − (2 × 87)
- = 8700 − 174
- = 8526
Whenever a number is just below a round one (98, 97, 995...), turn it into "round minus a little" and subtract.
Squaring a number that ends in 5
Compute 45². Then try 65².
Show solution
Any number ending in 5 squares in one step. Take the tens digit n, multiply by n+1, then just stick 25 on the end:
- 45²: n = 4, so 4 × 5 = 20 → write 20 then 25 → 2025
- 65²: n = 6, so 6 × 7 = 42 → write 42 then 25 → 4225
No multiplication of the full number needed, just n(n+1) and a "25".
Percentages by halving
What is 15% of 80?
Show solution
Break the percentage into easy pieces:
- 10% of 80 = 8 (just move the decimal)
- 5% is half of that = 4
- 15% = 10% + 5% = 8 + 4 = 12
Building percentages from 10% and 5% (and 1%) beats trying to multiply by 0.15 in your head.
Dividing by 5 the fast way
Compute 235 ÷ 5.
Show solution
Dividing by 5 is the same as multiplying by 2 and dividing by 10:
- 235 ÷ 5 = (235 × 2) ÷ 10
- = 470 ÷ 10
- = 47
Doubling then dropping a zero is much easier than long division by 5.
Successive percentage changes
A price rises 10%, then falls 10%. Is it back where it started?
Show solution
No, and this trips up a lot of people. Successive changes multiply, they don't cancel:
- up 10% → ×1.10
- down 10% → ×0.90
- combined: 1.10 × 0.90 = 0.99
So you end at 99% of the start, down 1%. Start at 100 → 110 → 99. The second 10% is taken off a bigger number, so a gain and an equal-percent loss never fully undo each other.
What you'll learn
Fast, accurate mental arithmetic under time pressure, the skill screened in trading interviews at Optiver, IMC, SIG and Flow Traders.