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

Question

If \frac{1}{Q} > 1 , which of the following must be true? (A) 1 < Q^2 (B) \frac{1}{Q^2} > 2 (C) 1 > Q^2 (D) \frac{1}{Q^2} < 1 (E) Q < Q^2 This is a PS Butler Question Check the links to other Butler Projects: Data Sufficiency Butler Critical Reasoning Butler Sentence Correction Butler Reading Comprehension Butler Integrated Reasoning Butler

Nidzo · Answer

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

mayankdgmat · Answer

Bunuel  I am getting Q>Q2. is there a typo in (E)?

unraveled · Answer

If \frac{1}{Q} > 1 , which of the following must be true? (A) 1 < Q^2 (B) \frac{1}{Q^2} > 2 (C) 1 > Q^2 (D) \frac{1}{Q^2} < 1 (E) Q < Q^2 \frac{1}{Q} > 1 is only possible when 0 < Q < 1 This implies that Q^2 < Q < 1(Here we can go with C straight but let's check other choices). Thus, A, D(same as A) and E are out straight. B is wrong since 1 < \frac{1}{Q^2} < infinity Hence either possibility exists. Answer C.

sayan640 · Answer

1/q - 1 >0 hence , (1-q)/ q > 0 either (1-q ) > 0 and q > 0 ; Hence , 0

K-ja · Answer

I think if Q is negative then this still holds true which cannot be the case!

Bunuel · Answer

Q cannot be negative because  \frac{1}{Q} > 1  implies  0 < Q < 1 . Next, E is not correct because  Q < Q^2  is not true for any of the values from  0 < Q < 1 . Or to put it in another way, since  0 < Q < 1 , then 0 <   Q^2 < Q  , so  Q < Q^2  is not true.

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

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