60% of 264 is the same as

### Concept & Strategy This problem tests the concept of equivalent percentages through proportional scaling. If you divide a percentage by a certain factor, you must multiply the base number by that exact same factor to keep the total value identical. $$ (P \div x)\% \text{ of } (B \times x) = P\% \text{ of } B $$ ### Step-by-Step Solution **Given:** * The target expression is $60\%$ of $264$. **Calculation / Deduction:** * Calculate the exact numerical value of the target expression: $\frac{60}{100} \times 264 = 0.6 \times 264$ * $0.6 \times 264 = 158.4$ * Now, test each option to find the matching value: * Test Option (a): $10\%$ of $44$ $0.1 \times 44 = 4.4$ (Incorrect) * Test Option (b): $15\%$ of $1056$ $\frac{15}{100} \times 1056 = 0.15 \times 1056$ $15 \times 10.56 = 158.4$ (Correct) * Test Option (c): $30\%$ of $132$ $0.3 \times 132 = 39.6$ (Incorrect) ### Exam Strategy & Shortcut Instead of calculating $158.4$, use factor scaling. Look at the options and compare them to the original $60\%$. Option (b) uses $15\%$. How do you get from $60\%$ to $15\%$? You divide by $4$. To keep the value the same, you must multiply the base ($264$) by $4$. $264 \times 4 = 1056$. Therefore, $60\%$ of $264$ is mathematically identical to $15\%$ of $1056$. This logical deduction is much faster than brute-force decimal multiplication. ### Common Pitfall A standard error is attempting to calculate every single option fully, which consumes too much time. Another mistake is miscalculating the decimals when checking the options, especially when dealing with numbers like $1056$. ### Final Answer Therefore, the correct answer is **15% of 1056**.