Difference between revisions of "1951 AHSME Problems/Problem 17"
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== Solution == | == Solution == | ||
| − | {{ | + | Notice that for any directly or inversely proportional values, it can be expressed as <math>\frac{x}{y}=k</math> or <math>xy=k</math>. Now we try to convert each into its standard form counterpart. |
| + | <math> \textbf{(A)}\ x \plus{} y \equal{} 0\implies \frac{x}{y}=-1</math> | ||
| + | <math>\textbf{(B)}\ 3xy \equal{} 10\implies xy=\frac{10}{3}</math> | ||
| + | <math>\textbf{(C)}\ x \equal{} 5y\implies \frac{x}{y}=5</math> | ||
| + | <math> \textbf{(E)}\ \frac {x}{y} \equal{} \sqrt {3}\implies \frac {x}{y} \equal{} \sqrt {3}</math> | ||
| + | As we can see, the only equation without a "standard" form is <math>\textbf{(D)}</math>, so outr answer is <math>\boxed{\textbf{(D)}\ 3x \plus{} y \equal{} 10}</math> | ||
== See Also == | == See Also == | ||
Revision as of 21:51, 13 April 2013
Problem
Indicate in which one of the following equations 
is neither directly nor inversely proportional to 
:
$\textbf{(A)}\ x \plus{} y \equal{} 0 \qquad\textbf{(B)}\ 3xy \equal{} 10 \qquad\textbf{(C)}\ x \equal{} 5y \qquad\textbf{(D)}\ 3x \plus{} y \equal{} 10$ (Error compiling LaTeX. Unknown error_msg) $\textbf{(E)}\ \frac {x}{y} \equal{} \sqrt {3}$ (Error compiling LaTeX. Unknown error_msg)
Solution
Notice that for any directly or inversely proportional values, it can be expressed as 
or 
. Now we try to convert each into its standard form counterpart.
$\textbf{(A)}\ x \plus{} y \equal{} 0\implies \frac{x}{y}=-1$ (Error compiling LaTeX. Unknown error_msg)
$\textbf{(B)}\ 3xy \equal{} 10\implies xy=\frac{10}{3}$ (Error compiling LaTeX. Unknown error_msg)
$\textbf{(C)}\ x \equal{} 5y\implies \frac{x}{y}=5$ (Error compiling LaTeX. Unknown error_msg)
$\textbf{(E)}\ \frac {x}{y} \equal{} \sqrt {3}\implies \frac {x}{y} \equal{} \sqrt {3}$ (Error compiling LaTeX. Unknown error_msg)
As we can see, the only equation without a "standard" form is 
, so outr answer is $\boxed{\textbf{(D)}\ 3x \plus{} y \equal{} 10}$ (Error compiling LaTeX. Unknown error_msg)
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 16 |
Followed by Problem 18 | |
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| All AHSME Problems and Solutions | ||
