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2010 Math Kangaroo

Problem 13

Problem 13 · 2010 Math Kangaroo Medium
Number Theory factor-pairsfactorization

My teacher says that the product of his age and the age of his father is 2010. In which year could my teacher have been born?

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Answer: C — 1980
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Hint 1 of 2
Factor 2010 and look for a pair of ages that make sense for a teacher and his father.
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Hint 2 of 2
A realistic age gap should guide which factor pair to pick.
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Approach: factor 2010 into a sensible age pair
  1. 2010 = 2 x 3 x 5 x 67.
  2. A teacher aged 30 and a father aged 67 give 30 x 67 = 2010, a believable pair.
  3. A 30-year-old in 2010 was born in 1980.
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