Problem 5 · 2010 Math Kangaroo
Easy
Arithmetic & Operations
arithmetic-serieswork-backward
On each birthday Rosa gets as many roses as she is old in years. She still has all the dried flowers and there are now 120 of them. How old is she?
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Answer: D — 15
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Hint 1 of 2
Each year she adds that year's age in roses, so the totals are 1, then 1+2, then 1+2+3, ...
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Hint 2 of 2
You need a running sum that lands on 120.
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Approach: triangular-number total
- After her n-th birthday she has 1+2+...+n roses.
- We need 1+2+...+n = 120, i.e. n(n+1)/2 = 120, so n(n+1) = 240.
- Since 15x16 = 240, she is 15.
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