1951 AMC 12 Problem 36
Attempt Problem 36 of the 1951 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1951 AMC 12 solutions, or check the answer key.
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36.
Which of the following methods of proving a geometric figure a locus is not correct?
Every point on the locus satisfies the conditions and every
point not on the locus does not satisfy the conditions.
Every point not satisfying the conditions is
not on the locus and every point on the locus does satisfy the
conditions.
Every point satisfying the conditions is on the locus and every
point on the locus satisfies the conditions.
Every point not on the locus does not satisfy the conditions
and every point not satisfying the conditions is not on the
locus.
Every point satisfying the conditions is on the locus and every
point not satisfying the conditions is not on the locus.
Answer: B
Small hint:
A locus proof needs both implications between “on the locus” and “satisfies the conditions”
Big hint:
Use contrapositives to see whether each choice establishes both directions
Solution:
Let mean “on the locus” and mean “satisfies the conditions.” A complete proof needs both and Choice B states which is merely the contrapositive of and then repeats It never proves
Thus, the correct answer is B.