Simplification and approximation
- Simplify: \(\frac{3}{4}\) of \(\frac{8}{9}\) of 405 + 25% of 240 Answer: A. 330 Answer: (A) 330 3/4 × 8/9 × 405 = 2/3 × 405 = 270 . 25% of 240 = 60. Total = 330 . 1
- Find the value of \(\frac{0.6 \times 0.6 \times 0.6 + 0.4 \times 0.4 \times 0.4}{0.6 \times 0.6 - 0.6 \times 0.4 + 0.4 \times 0.4}\). Answer: C. 1 Answer: (C) 1 Use a³ + b³/a² - ab + b² = a + b . With a = 0.6, b = 0.4 : value = 0.6 + 0.4 = 1 . 1
- Simplify: \(48 \div 4 \times 3 - 5^2 + 7 \times 6 \div 2\) Answer: A. 32 Answer: (A) 32 BODMAS: 5² = 25 . 48 ÷ 4 × 3 = 12 × 3 = 36 . 7 × 6 ÷ 2 = 21 . So 36 - 25 + 21 = 32 . 1
- Find the value of \(\sqrt{2116} + \sqrt[3]{3375} - \sqrt{961}\). Answer: B. 30 Answer: (B) 30 √(2116) = 46 , sqrt[3]3375 = 15 , √(961) = 31 . So 46 + 15 - 31 = 30 . 1
- What will come in place of the question mark (?)?\( 45\% \text{ of } 860 - 12^2 + 17 \times 8 = ? \) Answer: C. 379 Answer: (C) 379 387 - 144 + 136 = 379 . 1
- What will come in place of the question mark (?)?\( ? \div 16 \times 4.5 = 27 \times 3 \) Answer: C. 288 Answer: (C) 288 ? = 81 × 16/4.5 = 288 . 1
- What will come in place of the question mark (?)?\( (\sqrt{2025} + \sqrt{576}) \times 4 - 99 = ? \) Answer: A. 177 Answer: (A) 177 (45 + 24) × 4 - 99 = 276 - 99 = 177 . 1
- What approximate value will come in place of the question mark (?)?\( 39.89\% \text{ of } 1499.8 - 22.03 \times 8.98 + 539.7 \div 17.96 = ? \) Answer: A. 432 Answer: (A) 432 Round: 40% of 1500 - 22 × 9 + 540 ÷ 18 = 600 - 198 + 30 = 432 (exact ≈ 430.5). 1
- What approximate value will come in place of the question mark (?)?\( (12.03)^2 + (6.98)^3 - 299.9 \div 5.02 = ? \) Answer: D. 427 Answer: (D) 427 Round: 12² + 7³ - 300 ÷ 5 = 144 + 343 - 60 = 427 (exact ≈ 425.0). 1
- What will come in place of the question mark (?)?\( 35\% \text{ of } 640 + 18^2 - 25 \times 6 = ? \) Answer: C. 398 Answer: (C) 398 224 + 324 - 150 = 398 . 1
- What will come in place of the question mark (?)?\( \left(\tfrac{3}{4} \text{ of } 896\right) \div 12 + ? = 85 \) Answer: D. 29 Answer: (D) 29 3/4 × 896 = 672;\ 672 ÷ 12 = 56;\ ? = 85 - 56 = 29 . 1
- What will come in place of the question mark (?)?\( \sqrt{1764} + 3^3 \times 4 - 15\% \text{ of } 300 = ? \) Answer: A. 105 Answer: (A) 105 42 + 108 - 45 = 105 . 1
- What approximate value will come in place of the question mark (?)?\( 24.97\% \text{ of } 799.8 + 14.02 \times 11.96 - 1260.2 \div 35.1 = ? \) Answer: D. 332 Answer: (D) 332 Round: 25% of 800 + 14 × 12 - 1260 ÷ 35 = 200 + 168 - 36 = 332 (exact value ≈ 331.5). 1
- What approximate value will come in place of the question mark (?)?\( \sqrt{624.8} \times 7.99 + 47.9\% \text{ of } 450.2 - ? = 260 \) Answer: D. 156 Answer: (D) 156 Round: 25 × 8 + 48% of 450 = 200 + 216 = 416 ; ? = 416 - 260 = 156 (exact ≈ 155.4). 1
- Find the value of \(\sqrt{1764} - \sqrt[3]{2744}\). Answer: B. 28 Answer: (B) 28 √(1764) = 42 and sqrt[3]2744 = 14 . 42 - 14 = 28 . 1
- Find the value of \(18 \div 3 \times 2 + 4^2 - 5 \times 3\). Answer: A. 13 Answer: (A) 13 BODMAS: 4² = 16 . Then left to right for ÷ and ×: 18 ÷ 3 = 6 , 6 × 2 = 12 ; 5 × 3 = 15 . 12 + 16 - 15 = 13 . 1