The reversal trick
x% of y = y% of x. Always. Use whichever direction is easier.
4% of 75 is awkward. 75% of 4 is obviously 3.
18% of 50 becomes 50% of 18 = 9.
This single identity is the highest-value thing in this guide, and it is underused.
Build from anchors
Compute 10%, 5% and 1%, then assemble.
35% of 240: 10% = 24, so 30% = 72; 5% = 12; total 84.
17% of 300: 10% = 30, 5% = 15, 1% = 3, so 17% = 30 + 15 + 6 = 51.
The fraction table
Memorise these. They convert awkward percentages into easy divisions:
- 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%, 7/8 = 87.5%
- 1/6 = 16.67%, 1/3 = 33.3%, 2/3 = 66.7%
- 1/7 ≈ 14.3%, 1/9 ≈ 11.1%, 1/11 ≈ 9.1%
- 1/12 ≈ 8.3%, 1/16 = 6.25%
37.5% of 64 is 3/8 of 64 = 24, instantly.
Percentage change
A rise of x% followed by a fall of x% does not return to the start - it ends lower by x^2/10000 of the original. Up 10% then down 10% leaves you at 99.
Interviewers ask this to check you are not treating percentages as additive.
Compounding approximations
For small rates, compound growth ≈ rate times periods. 3% for 4 periods is roughly 12%, actually 12.6%.
The correction: add roughly half the square of the total. For larger rates or more periods, use the rule of 72 - doubling time is about 72 divided by the percentage rate. At 8%, doubling takes about 9 years.
Practice
These come up constantly on timed screens, often disguised inside a word problem. Drill them in mental math and see cracking speed tests.