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. | 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. | ||
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<math> \textbf{(A)}\ x \plus{} y \equal{} 0\implies \frac{x}{y}=-1</math> | <math> \textbf{(A)}\ x \plus{} y \equal{} 0\implies \frac{x}{y}=-1</math> | ||
Revision as of 21:52, 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 our 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 | |
| 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 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
