Difference between revisions of "2006 AMC 10A Problems/Problem 9"
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[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 08:46, 24 October 2007
Problem
How many sets of two or more consecutive positive integers have a sum of 15?
Solution
At a first glance, you should see that 7+8=15.
But are there three consecutive integers that add up to 15? Solve the equation
, and you come up with n=4. 4+5+6=15.
Again solve the similar equation
to determine if there are any four consecutive integers that add up to 15. This comes out with the non-integral solution 9/4. Further speculation shows that 1+2+3+4+5 = 15.
So the answer is (C). 3
See Also
| 2006 AMC 10A (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 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 | ||
| All AMC 10 Problems and Solutions | ||
