Inequalities (Fractions): If p/q < 1, and p and q are pos

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If p/q < 1, and p and q are positive integers, which of the following must be greater than 1 ?

A) sqrt (p/q)
B) p/q^2
C) p/2q
D) q/p^2
E) q/p

I used the "plugging-in" numbers approach to solve this. Was wondering if there was another approach to take when solving this type of question. Any input ?

My approach. p and q are positive integers ... so for p/q < 1, I assigned p=2, q=3. so p/q = 2/3. Then I went through each of the answer choices, and the only answer choice which was greater than 1 ... is E. 3/2 is greater than 1.

Any other approaches ?

Thanks.
Last edited by II on Mon May 05, 2008 1:37 am, edited 1 time in total.
Source: — Data Sufficiency |

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by simplyjat » Mon Apr 14, 2008 3:55 am
You have to understand the properties of factions.
If X is greater than on 1/X is less than one, and vice-versa.

In the question if we say X = p/q, then 1/X > 1. So pick q/p
Last edited by simplyjat on Mon Apr 14, 2008 8:18 am, edited 2 times in total.
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by II » Mon Apr 14, 2008 5:58 am
Sure ...
What do you mean by "X <1> 1"

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by simplyjat » Mon Apr 14, 2008 8:17 am
Some HTML formatting stuff, I corrected it now to 1/X > 1
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by gmat765 » Wed Apr 16, 2008 7:04 pm
Then x is smaller than 1?