Approximation and quick calculation: Evaluate 127.007 × 7.998 + 6.05 × 4.001 and choose the closest option.

Introduction / Context:
Both products have one factor near an integer: 8 and 4. Using those nearby integers and applying small corrections yields a near-exact sum, perfect for choosing among options spaced by tens.

Given Data / Assumptions:

• P1 = 127.007 * 7.998 ≈ 127.007 * (8 − 0.002)
• P2 = 6.05 * 4.001 ≈ 6.05 * (4 + 0.001)

Concept / Approach:
Compute with the nearest integer then adjust by the tiny residual. Since both residuals are very small, the nearest hundred or ten remains stable.

Step-by-Step Solution:

Verification / Alternative check:
Direct calculation gives about 1040.008, confirming the chosen option.

Why Other Options Are Wrong:
1090, 1200, 1120: All are 80–160 away from the refined sum ~1040; too far for these tiny corrections.

Common Pitfalls:
Skipping the small −0.002 adjustment in the first product leads to ~1016.06, but the second product still keeps the sum very near 1040; the same nearest choice results.

Final Answer:
1040