1958 AHSME Problems/Problem 44
Problem
Given the true statements: (1) If is greater than , then is greater than (2) If is less than , then is greater than . A valid conclusion is:
Solution
(A) is not valid because does not imply (The inverse of Statement 1 is not necessarily true).
(B) is not valid because does not imply (The converse of Statement 2 is not necessarily true either).
In (C), does imply (contrapositive of Statement 2) but this does not tell us anything about and .
In (D), does imply , but the inverse of Statement 2 () is not necessarily true.
So the answer is . (Incidentally, the wording of this problem appears to be wrongly assuming that implies (and vice versa) when in reality and could be equal. However, this does not change the fact that none of the four choices follow logically from the given statements.)
See Also
1958 AHSME (Problems • Answer Key • Resources) | ||
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