Difference between revisions of "1981 AHSME Problems/Problem 3"

(Problem 3)
 
(Solution)
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The least common multiple of <math>\frac{1}{x}</math>, <math>\frac{1}{2x}</math>, and <math>\frac{1}{3x}</math> is <math>\frac{1}{6x}</math>.  
 
The least common multiple of <math>\frac{1}{x}</math>, <math>\frac{1}{2x}</math>, and <math>\frac{1}{3x}</math> is <math>\frac{1}{6x}</math>.  
  
<math>\frac{1}{x}</math>=<math>\frac{6}{6x}</math>, <math>\frac{1}{2x}</math>=<math>\frac{3}{6x}</math>, <math>\frac{1}{3x}</math>=<math>\frac{2}{6x}</math>.
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<math>\frac{1}{x}</math> = <math>\frac{6}{6x}</math>, <math>\frac{1}{2x}</math> = <math>\frac{3}{6x}</math>, <math>\frac{1}{3x}</math> = <math>\frac{2}{6x}</math>.
  
<math>\frac{6}{6x}</math>+<math>\frac{3}{6x}</math>+<math>\frac{2}{6x}</math>=<math>\frac{11}{6x}</math>
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<math>\frac{6}{6x}</math> + <math>\frac{3}{6x}</math> + <math>\frac{2}{6x}</math> = <math>\frac{11}{6x}</math>
  
 
The answer is (D) <math>\frac{11}{6x}</math>.
 
The answer is (D) <math>\frac{11}{6x}</math>.

Revision as of 11:59, 21 November 2018

Solution

The least common multiple of $\frac{1}{x}$, $\frac{1}{2x}$, and $\frac{1}{3x}$ is $\frac{1}{6x}$.

$\frac{1}{x}$ = $\frac{6}{6x}$, $\frac{1}{2x}$ = $\frac{3}{6x}$, $\frac{1}{3x}$ = $\frac{2}{6x}$.

$\frac{6}{6x}$ + $\frac{3}{6x}$ + $\frac{2}{6x}$ = $\frac{11}{6x}$

The answer is (D) $\frac{11}{6x}$.