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If p/q < 1, and p and q are positive integers, which of the [#permalink]
27 Jul 2020, 09:06
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If \(\frac{p}{q} < 1\), and p and q are positive integers, which of the following must be greater than 1 ? (A) \(\sqrt{\frac{p}{q}}\) (B) \(\frac{p}{q^2}\) (C) \(\frac{p}{2q}\) (D) \(\frac{q}{p^2}\) (E) \(\frac{q}{p}\)
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
27 Jul 2020, 10:06
Quote: If p/q<1, and p and q are positive integers, which of the following must be greater than 1 ? Step 1: Understanding the questionAs p and q are positive, and \(\frac{p}{q }\)< 1, therefore, p < q Step 2: Calculationp < q 1 < \(\frac{q}{ p}\) hence \(\frac{q}{p}\) is always greater than 1 E is correct
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
27 Jul 2020, 10:57
p and q are positive integers and p/q<1,
Since this is a MUST question and not the SHOULD question, I think we can assume the values. Say p=1 and q=2.
For these values, only option that makes the value >1 is E.
So, the answer should be E.



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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
27 Jul 2020, 12:26
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Carcass wrote: If \(\frac{p}{q} < 1\), and p and q are positive integers, which of the following must be greater than 1 ?
(A) \(\sqrt{\frac{p}{q}}\)
(B) \(\frac{p}{q^2}\)
(C) \(\frac{p}{2q}\)
(D) \(\frac{q}{p^2}\)
(E) \(\frac{q}{p}\) IMPORTANT: For questions like this, where you need to test each answer choice, the testmakers will often make D or E the correct answer (because they want to eat up your valuable time ). So, in these situations, always begin with E and work your way up.E. Is q/p > 1? Well, we're told that p/q < 1. Since q is a positive integer, we can multiply both sides by q to get: p < q Since p is a positive integer, we can now divide both sides by p to get: 1 < q/p So, answer choice E must be true. Answer: E
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
10 Aug 2020, 03:48
I considered smart numbers p = 2 and q = 3 since we want p/q < 1 so 2/3 is less than 1 now put values in options, only option E hold true
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Re: If p/q < 1, and p and q are positive integers, which of the
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10 Aug 2020, 03:48





