Simplification and Approximation

3385% of 56789.672 ≈ 33.85 × 56790 ≈ 34 × 57000 = 1938000. Then ? = 1938000 ÷ 34 ≈ 57000. Among options, 56500 is closest. More precisely: 33.85 × 56789.672 ≈ 1922510, then 1922510 ÷ 34 ≈ 56544, confirming 56500.

Calculate each square: (45.3)² ≈ 2052, (54.41)² ≈ 2960, (64.55)² ≈ 4167, (75.01)² ≈ 5626. Sum ≈ 2052 + 2960 + 4167 + 5626 = 14805. Then 14805 ÷ 4.08 ≈ 3628. Among options, 3700 is closest.

Following BODMAS: 5555 ÷ 42 × 361 + 64.5 = ?. 5555 ÷ 42 ≈ 132.26. 132.26 × 361 ≈ 47,745.86. Adding 64.5 gives approximately 47,810.36. Option D (47811) is the closest match. The calculation requires careful order of operations and approximation. Division first, then multiplication, then addition. The slight discrepancy is due to rounding during intermediate steps.

Calculate: 211 × 43 = 9073, 156 × 17 = 2652. So 9073 - 2652 = 6421. Now √6421 ≈ 80.1. Among options, 80 is closest.

Compute step by step: 32548 + 547 = 33095; 33095 + 864 = 33959; 33959 - 1264 = 32695; 32695 - 1875 = 30820; 30820 + 1222 = 32042; 32042 - 32 = 32010. This is approximately 32000.

Calculate: 1.24 × 6.25 = 7.75; 3.11 × 0.75 = 2.3325; 18 ÷ 4.44 ≈ 4.054; 3.25² = 10.5625. LHS = 7.75 - 2.3325 + 4.054 = 9.4715. So ? = 9.4715 + 10.5625 = 20.034 ≈ 20.

Approximate 25.1% as 25%, 5902 as 5900, 55.96 as 56, 3.82 as 4, 20 as 20. Calculate: 0.25 × 5900 = 1475. Then 1475 = ? × 56/4 × 20 = ? × 14 × 20 = ? × 280. So ? = 1475/280 ≈ 5.27, closest to 5. The answer 5 is correct.

Using approximation: 1365 ÷ 38.685 ≈ 1365 ÷ 39 ≈ 35, ? ÷ 23.789 ≈ ? ÷ 24. So 35 ≈ ? ÷ 24, giving ? ≈ 35 × 24 = 840. Precise calculation: 1365 ÷ 38.685 = 35.28, ? = 35.28 × 23.789 = 839.55 ≈ 840. Option D is correct.

To find the value of the question mark, we first calculate each term: 1/7 of 2803 is approximately 400, and 129.8% of 770.4 is approximately 1000. Adding these gives us about 1400. Since 14 × 100 = 1400, the answer is 100. This problem tests your ability to work with percentages and fractions simultaneously.

√5687 ≈ 75.41, √1245 ≈ 35.28, √689 ≈ 26.25. LHS = (75.41 × 35.28) ÷ 26.25 = 2660.5 ÷ 26.25 ≈ 101.35. Then ? = 101.35 × 13 = 1317.55 ≈ 1320.

Approximate: 47 × 562.58 ≈ 47 × 560 ≈ 26,320. Similarly, 23 × 112.23 ≈ 23 × 110 ≈ 2,530. Dividing: 26,320 ÷ 2,530 ≈ 10.4. The closest option is 10. For better approximation: 47 × 562.58 = 26,441.26 and 23 × 112.23 = 2,581.29, giving 26,441.26 ÷ 2,581.29 ≈ 10.24 ≈ 10.

Calculate: 32.69% of 3394.69 ≈ 0.3269 × 3395 ≈ 1109.7. Next, 12.68% of 169.78 ≈ 0.1268 × 170 ≈ 21.56. Sum: 1109.7 + 21.56 ≈ 1131.26. The equation is: 1131.26 = ? - 623.68. Therefore: ? = 1131.26 + 623.68 ≈ 1754.94. The closest option is 1734 (Option B).

Approximating: 187.325% ≈ 187%, 77.11% ≈ 77%, 49.22% ≈ 49%. Calculate: 1.87 × 942 ≈ 1764, 0.77 × 1442 ≈ 1110, 0.49 × 42 ≈ 21. So: 1764 - 1110 + 21 = 675. Therefore ?² ≈ 675, so ? ≈ √675 ≈ 26. Option B is correct.

Round 864.799 to 865 and 39.012 to 39, giving 865 × 39 = 33735. Round 72.899 to 73 and 14.02 to 14, giving 73 × 14 = 1022. The difference is 33735 - 1022 = 32713, which rounds to 32700. Option A (32300) is too low, while D (31000) and E (34000) are further from the actual value.

Calculate: 1/7 of 2803 = 2803/7 ≈ 400.43. Then 129.8% of 770.4 = 1.298 × 770.4 ≈ 999.78. Sum = 400.43 + 999.78 ≈ 1400.21. Then 1400.21/14 = 100.015 ≈ 100. The calculations confirm option C is correct.