Difference between revisions of "1973 AHSME Problems/Problem 21"
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[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
[[Category:Intermediate Number Theory Problems]] | [[Category:Intermediate Number Theory Problems]] |
Latest revision as of 13:02, 20 February 2020
Problem
The number of sets of two or more consecutive positive integers whose sum is 100 is
Solution
If the first number of a group of consecutive numbers is , the number is . We know that the sum of the group of numbers is , so We know that and are positive integers, so we check values of that are a factor of . Of these values, the only ones that result in a positive integer is when or when , so there are sets of two or more consecutive positive integers whose sum is .
See Also
1973 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 20 |
Followed by Problem 22 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 | ||
All AHSME Problems and Solutions |