Difficulty: Easy
Correct Answer: 528
Explanation:
Introduction / Context:This expression features pairs of numbers around convenient integers (16, 18) and (15, 16). Using near-square and symmetry ideas speeds up the calculation and leads to a precise estimate for the closest option.
Given Data / Assumptions:
Concept / Approach:Note 18*16 = 288; the tiny deviations keep A near 288. Also, B ≈ 16*15 = 240 with minimal adjustment. Summing gives a value around 528; detailed correction refines this by a fraction only.
Step-by-Step Solution:
A = (18 − 0.005)*(16 + 0.005) ≈ 288 + 18*0.005 − 16*0.005 − 0.005^2 ≈ 288 + 0.09 − 0.08 ≈ 288.01 B = (16 − 0.001)*(15 + 0.001) ≈ 240 + 16*0.001 − 15*0.001 − 0.001^2 ≈ 240 + 0.001 ≈ 240.001 Sum ≈ 288.01 + 240.001 ≈ 528.011 Nearest option: 528Verification / Alternative check:Direct multiplication yields about 528.011, matching the above reasoning and reinforcing 528 as closest.
Why Other Options Are Wrong:513 and 440 are far below; 818 is far above the balanced near-16 and near-18 products.
Common Pitfalls:Roughly using 18*16 + 16*15 = 528 without considering tiny corrections actually already lands on the correct neighborhood; avoid overcomplicating adjustments that change nothing at the hundreds place.
Final Answer:528
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