Difference between revisions of "2006 AMC 10A Problems/Problem 9"

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== Problem ==
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#redirect [[2006 AMC 12A Problems/Problem 8]]
How many sets of two or more consecutive positive integers have a sum of 15?
 
 
 
<math> \mathrm{(A) \ } 1\qquad \mathrm{(B) \ } 2\qquad \mathrm{(C) \ } 3\qquad \mathrm{(D) \ } 4\qquad \mathrm{(E) \ } 5 </math>
 
== 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
 
 
 
<math>n+n+1+n+2=15</math>, and you come up with n=4. 4+5+6=15.
 
 
 
Again solve the similar equation
 
 
 
<math>n+n+1+n+2+n+3=15</math> 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 ==
 
{{AMC10 box|year=2006|ab=A|num-b=8|num-a=10}}
 
 
 
[[Category:Introductory Algebra Problems]]
 

Latest revision as of 00:13, 28 April 2008