Difference between revisions of "1951 AHSME Problems/Problem 17"
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Indicate in which one of the following equations <math> y</math> is neither directly nor inversely proportional to <math> x</math>: | Indicate in which one of the following equations <math> y</math> is neither directly nor inversely proportional to <math> x</math>: | ||
− | <math> \textbf{(A)}\ x | + | <math> \textbf{(A)}\ x + y = 0 \qquad\textbf{(B)}\ 3xy = 10 \qquad\textbf{(C)}\ x = 5y \qquad\textbf{(D)}\ 3x + y = 10</math> |
− | <math> \textbf{(E)}\ \frac {x}{y} | + | <math> \textbf{(E)}\ \frac {x}{y} = \sqrt {3}</math> |
== 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. | ||
− | <math> \textbf{(A)}\ x | + | <math> \textbf{(A)}\ x + y = 0\implies \frac{x}{y}=-1</math> |
− | <math>\textbf{(B)}\ 3xy | + | <math>\textbf{(B)}\ 3xy = 10\implies xy=\frac{10}{3}</math> |
− | <math>\textbf{(C)}\ x | + | <math>\textbf{(C)}\ x = 5y\implies \frac{x}{y}=5</math> |
− | <math> \textbf{(E)}\ \frac {x}{y} | + | <math> \textbf{(E)}\ \frac {x}{y} = \sqrt {3}\implies \frac {x}{y} = \sqrt {3}</math> |
− | As we can see, the only equation without a "standard" form is <math>\textbf{(D)}</math>, so our answer is <math>\boxed{\textbf{(D)}\ 3x | + | As we can see, the only equation without a "standard" form is <math>\textbf{(D)}</math>, so our answer is <math>\boxed{\textbf{(D)}\ 3x + y = 10}</math> |
== See Also == | == See Also == |
Latest revision as of 20:18, 30 April 2015
Problem
Indicate in which one of the following equations is neither directly nor inversely proportional to
:
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.
As we can see, the only equation without a "standard" form is , so our answer is
See Also
1951 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 16 |
Followed by Problem 18 | |
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