1951 AHSME Problems/Problem 36

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 (ProblemsAnswer KeyResources)
Preceded by
Problem 35
Followed by
Problem 37
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

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png