🇺🇸 AMC 8 ⇄ switch contest
1988 AJHSME

Problem 7

Problem 7 · 1988 AJHSME Medium
Arithmetic & Operations round-and-multiply

2.46 × 8.163 × (5.17 + 4.829) is closest to

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Answer: B — 200.
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Hint 1 of 2
The answer choices jump by 100s, so you don't need precision — you need a fast, roughly-right estimate. Glance at that sum in parentheses first: 5.17 + 4.829 is almost exactly what nice round number?
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Hint 2 of 2
Round every factor to something friendly: 2.46 ≈ 2.5, 8.163 ≈ 8, and the sum ≈ 10.
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Approach: round each factor to an easy number
  1. Spot the gift: 5.17 + 4.829 ≈ 10. Round the rest too — 2.46 ≈ 2.5 and 8.163 ≈ 8 — so the product ≈ 2.5 × 8 × 10.
  2. 2.5 × 8 = 20, then × 10 = 200.
  3. Why this transfers: when answer choices are far apart, estimating beats exact arithmetic. Round each factor to a value you can multiply in your head, and pick numbers (like 2.5 and 8) whose product is clean.
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