Problem 15 · 2015 Math Kangaroo
Stretch
Number Theory
ages
Lucy and her mother were both born in January. Today, on 23rd March 2015, Lucy adds together her year of birth, that of her mother, her age, and that of her mother. Which answer does she get?
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Answer: C — 4030
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Hint 1 of 2
Both birthdays are in January, so by 23 March each has already had her birthday this year.
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Hint 2 of 2
For anyone, year of birth + current age equals the current year once the birthday has passed.
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Approach: year of birth plus current age equals the present year
- Since both were born in January, by 23 March 2015 each has already turned a year older this year.
- So Lucy's birth year + Lucy's age = 2015, and likewise her mother's birth year + her mother's age = 2015.
- Adding all four numbers gives 2015 + 2015 = 4030.
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