If 1/Q > 1, which of the following must be true?

Looking at ­\(\frac{1}{Q} > 1 \), one notices that Q cannot be a whole number as the fraction would be smaller than 1, Q cannot be 0 as anything divided by 0 is undefined and therefore the inequality would not hold, and lastly Q cannot be negative as a negative number is never greater than a positive. Because of these things one can conclude that Q must be a positive fraction which is less than 1 for the inequality to hold. From another perspective it also means that one can cross multiply the inequality to get: \(1 > Q\) and as we have deduced that Q cannot be 0 and cannot be negative we can add this info to the inequality to make it \(1 > Q > 0\)


(A) \(1 < Q^2\) becomes \(1 < Q\). One knows that \(Q > 1\) will not hold for the inequality in the question stem. 

(B) \(\frac{1}{Q^2} > 2\) becomes \(1 > 2(Q^2)\) which becomes \(\frac{1}{\sqrt{2}} > Q\). \(\sqrt{2}\) is around \(1.4\) so we can rewrite the inequality as \(\frac{1}{\frac{14}{10}} > Q\) which becomes \(\frac{10}{14} > Q\). While this covers many of the values for Q which would make the inequality from the question stem hold, there are still many which it does not include.

(C) \(1> Q^2 \) becomes \(1 > Q\) Is pretty much what was deduced prior to looking at the answer choices.

(D) \(\frac{1}{Q^2} < 1\) becomes \(1 < Q^2\) which can be written as \(1 < Q\) Q must be greater than 1.

(E) \(Q < Q^2\) can be rewritten as \(1 < Q\) Once again, Q must be greater than 1 for this inequality to hold.


ANSWER C­