Problem 7 · 2010 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequence
I write down seven consecutive whole numbers. The sum of the smallest three is 33. What is the sum of the biggest three numbers?
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Answer: E — 45
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Hint 1 of 2
Call the smallest number n and write the seven numbers in a row.
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Hint 2 of 2
Find n from the first three, then add the last three.
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Approach: find the run from the given partial sum
- The smallest three are n, n+1, n+2 with sum 3n+3 = 33, so n = 10.
- The seven numbers are 10,11,12,13,14,15,16.
- The biggest three sum to 14+15+16 = 45.
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