14% of 14 + 28% of 28 + 92% of 96 - 15% of 85 = $x$

### Concept & Strategy This question tests raw calculation speed using squares and algebraic identities. Instead of standard percentage multiplication, recognize the patterns: $14 \times 14$ is a perfect square, $28 \times 28$ is a perfect square, and $92 \times 96$ can be solved using the base-100 multiplication shortcut. ### Step-by-Step Solution * **Given**: $14\% \text{ of } 14 + 28\% \text{ of } 28 + 92\% \text{ of } 96 - 15\% \text{ of } 85 = x$ * **Calculation**: 1. Calculate $14\% \text{ of } 14$: $$0.14 \times 14 = \frac{14^2}{100} = \frac{196}{100} = 1.96$$ 2. Calculate $28\% \text{ of } 28$: $$0.28 \times 28 = \frac{28^2}{100} = \frac{784}{100} = 7.84$$ 3. Calculate $92\% \text{ of } 96$: Using base 100: $(100 - 8) \times (100 - 4)$. Cross subtract: $92 - 4 = 88$ (or $96 - 8 = 88$). Multiply differences: $(-8) \times (-4) = 32$. Result is $8832$. Therefore, $0.92 \times 96 = 88.32$. 4. Calculate $15\% \text{ of } 85$: $$0.15 \times 85 = \frac{15 \times 85}{100} = \frac{1275}{100} = 12.75$$ 5. Combine all the values: $$x = 1.96 + 7.84 + 88.32 - 12.75$$ Add the first two terms: $1.96 + 7.84 = 9.80$ Add to the third term: $9.80 + 88.32 = 98.12$ Subtract the final term: $98.12 - 12.75 = 85.37$ ### Exam Strategy & Shortcut Memorizing squares up to 30 is non-negotiable for bank exams, instantly giving you $1.96$ and $7.84$. For the addition phase, leverage digit sum or unit digit estimation to verify options quickly, though exact calculation is fairly smooth here. Notice the decimals: $.96 + .84 = 1.80$. $1.80 + .32 = 2.12$. $2.12 - .75$ ends in $.37$. Looking at the options, three of them end in $.37$. You must estimate the integers: $1 + 7 + 88 - 12 \approx 84$. Combined with the decimal carryovers, it naturally pushes to $85.37$. ### Common Pitfall Students often waste time converting percentages into fractions (e.g., $\frac{14}{100} = \frac{7}{50}$) which complicates the math. Keep the $/100$ in the denominator and just multiply the integers in the numerator, then shift the decimal point two places left. ### Final Answer **Therefore, the correct answer is 85.37.**