Approximation and quick calculation: Evaluate 198.001 × 25 + 112.05 × 24.998 and choose the closest option.

Introduction / Context:
When factors are very close to round numbers, tiny adjustments yield near-exact sums. Here both multipliers are near 25, making mental arithmetic efficient and reliable for the nearest option.

Given Data / Assumptions:

• Compute 198.001*25 and 112.05*24.998, then add.
• Pick the closest option.

Concept / Approach:
Use 25 = 100/4 to multiply quickly, and treat 24.998 ≈ 25 with a very small correction. Because answer choices differ by 20–250, maintaining the correction keeps the choice unambiguous.

Step-by-Step Solution:

Verification / Alternative check:
Exact calculation gives about 7751.05, still closest to 7750 compared with other options in the 7500–7570 range.

Why Other Options Are Wrong:

• 7570, 7550, 7500: All are at least ~180 away from the refined sum near 7751.
• None of these: 7750 fits best among provided choices.

Common Pitfalls:
Rounding both terms down to 25 or 24 can understate the result by ~200; keep the small correction for 24.998.

Final Answer:
7750