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# If p/q < 1, and p and q are positive integers, which of the

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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) $$\frac{q}{p}$$
[Reveal] Spoiler: OA

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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 question

As p and q are positive, and $$\frac{p}{q }$$< 1, therefore, p < q

Step 2: Calculation
p < 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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Expert's post
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 test-makers 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.

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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   [#permalink] 10 Aug 2020, 03:48
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