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Difference between revisions of "1951 AHSME Problems/Problem 36"

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==Problem==
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Which of the following methods of proving a geometric figure a locus is not correct?
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<math> \textbf{(A)}\ \text{Every point of the locus satisfies the conditions and every point not on the locus does}\\ \text{not satisfy the conditions.} </math>
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<math> \textbf{(B)}\ \text{Every point not satisfying the conditions is not on the locus and every point on the locus}\\
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\text{does satisfy the conditions.} </math>
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<math> \textbf{(C)}\ \text{Every point satisfying the conditions is on the locus and every point on the locus satisfies}\\ \text{the conditions.} </math>
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<math> \textbf{(D)}\ \text{Every point not on the locus does not satisfy the conditions and every point not satisfying}\\ \text{the conditions is not on the locus.} </math>
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<math> \textbf{(E)}\ \text{Every point satisfying the conditions is on the locus and every point not satisfying the} \\ \text{conditions is not on the locus.} </math>
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==Solution==
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Statement <math>\boxed{\textbf{(B)}}</math> is wrong because it does not imply that all points that satisfy the conditions are on the locus.
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== See Also ==
 
== See Also ==
 
{{AHSME 50p box|year=1951|num-b=35|num-a=37}}  
 
{{AHSME 50p box|year=1951|num-b=35|num-a=37}}  

Latest revision as of 14:21, 19 April 2014

Problem

Which of the following methods of proving a geometric figure a locus is not correct?

$\textbf{(A)}\ \text{Every point of the locus satisfies the conditions and every point not on the locus does}\\ \text{not satisfy the conditions.}$ $\textbf{(B)}\ \text{Every point not satisfying the conditions is not on the locus and every point on the locus}\\ \text{does satisfy the conditions.}$ $\textbf{(C)}\ \text{Every point satisfying the conditions is on the locus and every point on the locus satisfies}\\ \text{the conditions.}$ $\textbf{(D)}\ \text{Every point not on the locus does not satisfy the conditions and every point not satisfying}\\ \text{the conditions is not on the locus.}$ $\textbf{(E)}\ \text{Every point satisfying the conditions is on the locus and every point not satisfying the} \\ \text{conditions is not on the locus.}$

Solution

Statement $\boxed{\textbf{(B)}}$ is wrong because it does not imply that all points that satisfy the conditions are on the locus.

See Also

1951 AHSC (Problems • Answer Key • Resources)
Preceded by
Problem 35 		Followed by
Problem 37
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All AHSME Problems and Solutions

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