Problem 15 · 2024 Math Kangaroo
Hard
Number Theory
factorizationsum-constraintages
The daughter of Mary’s daughter was born today. In two years’ time the product of Mary’s age, her daughter’s age and her granddaughter’s age will be exactly 2024, and each of the three ages will be an even number. How old is Mary today?
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Answer: B — 44
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Hint 1 of 2
The granddaughter is 0 today, so in two years she is 2; that 2 is a factor of 2024.
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Hint 2 of 2
Factor 2024/2 into two even numbers that are sensible ages for a mother and her daughter.
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Approach: factor 2024 with the granddaughter's age fixed
- In two years the ages are M+2, D+2 and 2, with product 2024, so (M+2)(D+2) = 1012.
- All three ages are even, so M+2 and D+2 are both even; 1012 = 46 x 22 fits.
- Then M+2 = 46 gives Mary's current age as 44.
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