Difference between revisions of "1968 AHSME Problems/Problem 26"

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== Solution ==
 
== Solution ==
Note that <math>S = 2(1+2+3+...+N) = N(N +10)</math>. It follows that <math>N = 1000</math>, so the sum of the digits of <math>N</math> is <math>\fbox{E}</math>.  
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Note that <math>S = 2(1+2+3+...+N) = N(N +1)</math>. It follows that <math>N = 1000</math>, so the sum of the digits of <math>N</math> is <math>\fbox{E}</math>.  
(Solution Done By FrostFox)
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== See also ==
 
== See also ==
{{AHSME box|year=1968|num-b=25|num-a=27}}   
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{{AHSME 35p box|year=1968|num-b=25|num-a=27}}   
  
 
[[Category: Intermediate Algebra Problems]]
 
[[Category: Intermediate Algebra Problems]]
 
{{MAA Notice}}
 
{{MAA Notice}}

Latest revision as of 00:53, 16 August 2023

Problem

Let $S=2+4+6+\cdots +2N$, where $N$ is the smallest positive integer such that $S>1,000,000$. Then the sum of the digits of $N$ is:

$\text{(A) } 27\quad \text{(B) } 12\quad \text{(C) } 6\quad \text{(D) } 2\quad \text{(E) } 1$

Solution

Note that $S = 2(1+2+3+...+N) = N(N +1)$. It follows that $N = 1000$, so the sum of the digits of $N$ is $\fbox{E}$.


FrostFox

See also

1968 AHSC (ProblemsAnswer KeyResources)
Preceded by
Problem 25
Followed by
Problem 27
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

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