When 24 is subtracted from a number, it reduces to its four-seventh. What is the sum of the digits of that number?

### Concept & Logic When a number is reduced by a certain value, the relationship can be expressed algebraically using a single variable to represent the original number. $$ x - 24 = \frac{4}{7}x $$ ### Step-by-Step Solution * **Given:** A number decreases to its four-sevenths when 24 is subtracted from it. * Let the original number be $x$. * According to the problem statement: $$ x - 24 = \frac{4}{7}x $$ * Bring variables to one side: $$ x - \frac{4}{7}x = 24 $$ * Simplify the left side: $$ \frac{3}{7}x = 24 $$ * Solve for $x$: $$ x = \frac{24 \times 7}{3} = 56 $$ * The question asks for the sum of the digits of this number: $$ 5 + 6 = 11 $$ ### Exam Strategy & Shortcut Notice that subtracting 24 reduces the number to $\frac{4}{7}$ of itself. This means the reduction of 24 is equivalent to $\frac{3}{7}$ of the number. If $\frac{3}{7}$ is 24, then $\frac{1}{7}$ is 8. The whole number (which is $\frac{7}{7}$) must be $8 \times 7 = 56$. The sum of digits is $5 + 6 = 11$. This mental math approach is much faster. ### Common Pitfall Students often solve for the unknown number ($56$) and immediately look for it in the options, forgetting that the question specifically asks for the **sum of the digits** of that number. Always re-read the final question line! ### Final Answer **Therefore, the correct answer is 11.**