2005 AMC 10B Problem 2

1. "Percent" means "out of $100$", so $x\%$ is the number $\frac{x}{100}$. For example, $20\%$ is $\frac{20}{100} = 0.2$.
2. "Of" means multiply. So "$x\%$ of $x$" is $\frac{x}{100} \cdot x = \frac{x \cdot x}{100}$.
3. The problem says this equals $4$:
$$\frac{x \cdot x}{100} = 4.$$
Multiply both sides by $100$: $x \cdot x = 400$.
4. Which positive number times itself is $400$? Since $20 \cdot 20 = 400$, we get $x = 20$.
5. Check: $20\%$ of $20$ is $0.2 \cdot 20 = 4$. Correct.

The answer is $\boxed{\textbf{(D)}\ 20}$.

Most percent word problems become easy once you translate them word by word: "percent" becomes "divide by $100$" and "of" becomes "times." After that, what is left is a short equation. Checking the answer in the original sentence catches mistakes.

Try the answer choices, since they are small. $10\%$ of $10$ is $1$, too small. $20\%$ of $20$ is $4$, which is exactly right. $40\%$ of $40$ is $16$, too big. So $x = 20$.