Problem 16 · 2015 Math Kangaroo
Medium
Number Theory
factor-pairs
If the whole number age of a father is multiplied by the whole number age of his son, one obtains 2015. Both are born in the 20th century. How big is the age gap between father and son?
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Answer: D — 34
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Hint 1 of 2
Factor 2015 into a product of two whole numbers, both ages of people born in the 1900s.
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Hint 2 of 2
2015 = 5 × 13 × 31; find the factor pair that gives believable father/son ages.
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Approach: match a factor pair to plausible ages
- 2015 = 5 × 13 × 31.
- The factor pair fitting a father and son both born in the 20th century is 65 × 31.
- Age gap = 65 − 31 = 34.
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