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

Revision as of 04:59, 27 January 2019

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:

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

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

1968 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 25	Followed by Problem 27
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All AHSME Problems and Solutions

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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>.	+	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>.