Online tests
Mental math for trading tests: the core tricks
Break-and-rebuild, round-number tricks, fractions to know cold and decimal placement: the methods that make timed arithmetic tests fast and accurate.
指南为英文，与面试语言一致。
Why speed comes from method
Timed arithmetic tests are common at trading firms, often dozens of questions in a few minutes. The fastest candidates don't calculate harder: they recognize the shape of each question and apply a trick they've practiced.
The tricks
- 1
Break and rebuild
Split one number into easy parts: 47 × 6 = 40 × 6 + 7 × 6 = 240 + 42.
- 2
Use a nearby round number
98 × 7 = 700 − 14. For numbers either side of a round one, use a difference of squares: 49 × 51 = 50² − 1.
- 3
Squares ending in 5
Take the leading digit n, multiply by n + 1, and write 25 after it: 65² → 6 × 7 = 42 → 4,225.
- 4
Multiply by 5, 25 or 125
× 5 is × 10 ÷ 2; × 25 is × 100 ÷ 4; × 125 is × 1,000 ÷ 8.
- 5
Flip percentages
x% of y = y% of x: 8% of 25 = 25% of 8 = 2. Build others from 10% and 5%: 15% of 80 = 8 + 4.
- 6
Clear the decimal before dividing
252 ÷ 1.2 = 2,520 ÷ 12.
- 7
Count decimal places
0.3 × 0.04: 3 × 4 = 12, with three decimal places in total, so 0.012.
| Fraction | Decimal | Fraction | Decimal |
|---|---|---|---|
| 1/8 | 0.125 | 1/6 | 0.1667 |
| 3/8 | 0.375 | 1/7 | 0.1429 |
| 5/8 | 0.625 | 1/9 | 0.1111 |
| 7/8 | 0.875 | 1/12 | 0.0833 |
Know these cold: they turn many divisions into a lookup.
Worked examples
例题 · Five quick ones
经代码验证47 × 6, 49 × 51, 65², 36 × 25 and 15% of 80.
查看解题过程
- 1.47 × 6 = 240 + 42 = 282.
- 2.49 × 51 = 2,500 − 1 = 2,499.
- 3.65² = 42 then 25 = 4,225.
- 4.36 × 25 = 3,600 ÷ 4 = 900.
- 5.15% of 80 = 8 + 4 = 12.
答案282, 2,499, 4,225, 900 and 12.
例题 · Decimals and division
经代码验证252 ÷ 1.2 and 0.3 × 0.04.
查看解题过程
- 1.252 ÷ 1.2 = 2,520 ÷ 12 = 210.
- 2.3 × 4 = 12 with three decimal places: 0.012.
答案210 and 0.012.
提示Before you answer, check the size and the last digit. 47 × 6 must end in 2 and sit near 50 × 6 = 300.
Common mistakes
常见错误
- Misplacing the decimal point under time pressure.
- Getting stuck on one hard question. Move on and come back.
- Guessing blindly when wrong answers cost marks. Read the test's rules first.
- Practicing only untimed. Speed is a separate skill: train with the clock running.
Online tests