The number which exceeds 16% of it by 42 is

### Concept & Formula Every number represents 100% of itself. If a number "exceeds" a percentage of itself by a specific value, that value represents the remaining percentage gap between 100% and the given percentage. $$ \text{Number} (100\%) - \text{Percentage} (P\%) = \text{Remaining Percentage} ((100-P)\%) $$ ### Step-by-Step Solution * Let the required number be $x$. * "16% of it" can be written as $0.16x$ or $16\% \text{ of } x$. * The phrase "exceeds... by 42" means the difference between the number and its 16% is 42. * Set up the algebraic equation: $$ x - 16\% \text{ of } x = 42 $$ $$ 100\% \text{ of } x - 16\% \text{ of } x = 42 $$ $$ 84\% \text{ of } x = 42 $$ * Convert the percentage to a fraction to solve: $$ \frac{84}{100} \times x = 42 $$ * Solve for $x$: $$ x = 42 \times \frac{100}{84} $$ * Notice that 42 is exactly half of 84. $$ x = \frac{1}{2} \times 100 = 50 $$ ### Exam Strategy & Shortcut Think entirely in percentages. The number itself is 100%. It exceeds its 16% by $(100\% - 16\%) = 84\%$. So, 84% of the value is equal to 42. Notice the simple math: 42 is exactly half of 84. If $84\% = 42$, then $100\%$ must be exactly half of 100, which is 50. ### Common Pitfall The phrasing can be tricky. Students often misread this as "16% of a number is 42" and calculate $x = \frac{42}{0.16}$, or they write $0.16x + 42 = x$ and make an arithmetic error. Translating the English phrase "exceeds... by" directly to a subtraction equation ($A - B = \text{difference}$) prevents this. ### Final Answer **Therefore, the correct answer is 50.**