Successive percentages

SAT Glossary

Percentage changes multiply, they never add: +20% then +30% is 1.20 × 1.30 = 1.56, a 56% increase, not 50%. A rise of p% followed by a fall of p% gives 1-p^2 < 1 — equal-and-opposite changes always lose, because the second percentage applies to a bigger base. Order does not matter, since multiplication commutes; the loss comes from the asymmetry of the bases.

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