Classic GRE Trap Scenario:
In 2020, $20\%$ of a company's workforce worked remotely. In 2023, $25\%$ of the workforce worked remotely.
Question: By what percent did the percentage of remote workers increase from 2020 to 2023?
The False Assumption:Many students calculate $25\% - 20\% = 5\%$ and choose 5%.
$5$ is the difference in percentage points, NOT the percentage change of the rate itself!
The First-Principles Calculation:Percentage change always equals $\frac{\text{New} - \text{Old}}{\text{Old}} \times 100\%$:
$$\text{Percent Increase} = \frac{25 - 20}{20} \times 100\% = \frac{5}{20} = \mathbf{25\%}$$
The share of remote workers grew by 5 percentage points, but it increased by 25% relative to its initial value!