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2014 Math Kangaroo

Problem 9

Problem 9 · 2014 Math Kangaroo Medium
Arithmetic & Operations estimate-and-pick

Which of the following products gives the biggest answer?

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Answer: B — \(55 \times 666\)
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Hint 1 of 2
Each product is a two-digit number times a three-digit number; estimate sizes instead of multiplying everything exactly.
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Hint 2 of 2
A product is largest when its two factors are most balanced; 55 × 666 has the closest-sized factors.
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Approach: compare products by balance of factors
  1. For a fixed style of factors, a product grows when the two factors are nearer in size.
  2. Quick values: 44×777 = 34188, 55×666 = 36630, 77×444 = 34188, 88×333 = 29304, 99×222 = 21978.
  3. The largest is 55 × 666 = 36630.
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