Problem 4 · 1986 AJHSME
Easy
Arithmetic & Operations
round-and-multiply
The product (1.8)(40.3 + .07) is closest to
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Answer: C — 74.
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Hint 1 of 2
The word "closest" is permission to be lazy: you don't need the exact answer, just the right ballpark. What clean numbers are these almost equal to?
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Hint 2 of 2
Round each factor to something easy *before* multiplying — the tiny .07 can't matter when the choices are spread out (7, 42, 74, 84, 737).
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Approach: estimate by rounding the factors first
- Because we only need the closest choice, round: 40.3 + .07 ≈ 40, and 1.8 stays. The 0.07 is far too small to move the answer, so don't waste effort on it.
- 1.8 × 40 = 72, and the nearest choice is 74.
- Sanity check using the spread-out choices: 1.8 is between 1 and 2, so the product must be between 40 and 80 — that instantly rules out 7, 42, 84, and 737, leaving only 74.
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