Difference between revisions of "1981 AHSME Problems/Problem 16"

(Solution (Long Way))
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==Solution (Long Way)==
 
==Solution (Long Way)==
 
Convert <math>x</math> to base 10 then convert the result to base 9.
 
Convert <math>x</math> to base 10 then convert the result to base 9.
<cmath>12112211122211112222_{3} = 8847859</cmath>
+
<cmath>12112211122211112222_{3} = 2150029898</cmath>
  
<cmath>8847859 = 17574874_{9}</cmath>
+
<cmath>2150029898 = 5484584488_{9}</cmath>
  
Therefore, the answer is <math> \textbf{(A)}\ 1.</math>
+
Therefore, the answer is <math> \textbf{(E)}\ 5.</math>
  
 
-edited by coolmath34
 
-edited by coolmath34

Revision as of 16:45, 28 January 2021

Problem

The base three representation of $x$ is \[12112211122211112222\] The first digit (on the left) of the base nine representation of $x$ is

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$

Solution (Long Way)

Convert $x$ to base 10 then convert the result to base 9. \[12112211122211112222_{3} = 2150029898\]

\[2150029898 = 5484584488_{9}\]

Therefore, the answer is $\textbf{(E)}\ 5.$

-edited by coolmath34