Problem 4 · 2013 Math Kangaroo
Easy
Number Theory
factorizationfactor-triples
The product of three of the numbers 2, 4, 16, 25, 50, 125 is 1000. What is the sum of those three numbers?
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Answer: C — 131
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Hint 1 of 2
1000 = 2³ · 5³, so the three chosen numbers must together supply exactly three 2's and three 5's.
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Hint 2 of 2
Look for a triple from the list whose prime factors multiply to 1000.
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Approach: match prime factors to 1000
- 1000 = 2³ · 5³.
- From the list, 2 · 4 · 125 = 1000 (that is 2 · 2² · 5³).
- Their sum is 2 + 4 + 125 = 131.
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