2002 AMC 12B Problems/Problem 10
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Contents
Problem
How many different integers can be expressed as the sum of three distinct members of the set ?
Solution 1
Subtracting 10 from each number in the set, and dividing the results by 3, we obtain the set . It is easy to see that we can get any integer between and inclusive as the sum of three elements from this set, for the total of integers.
Solution 2
The set is an arithmetic sequence of numbers each more than a multiple of . Thus the sum of any three numbers will be a multiple of . All the multiples of from to are possible, totaling to integers.
See also
2002 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 9 |
Followed by Problem 11 |
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All AMC 12 Problems and Solutions |
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