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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 following must be greater than 1 ?

(A) $$\sqrt{\frac{p}{q}}$$
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p

Given:
$$p/q <1$$. Since p and q are positive integers, we can multiply by q on both sides.
The relation becomes:
$$p<q$$.

Now if we divide the entire relation by p, then:
$$p/p < q/p$$ or $$1< q/p$$

Hence $$q/p > 1$$.
+1 E.
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When we know the signs of fraction in an inequality and want to take the reciprocal here is a handy rule: flip the inequality when taking reciprocal unless both sides have different signs.
Thus we can flip the inequality in the given relation p/q<1, to get q/p>1. E it is!
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
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Not sure if it is solved this way:

$$\frac{p}{q} < 1$$,

As p and q are positive, Denominator should be greater than numerator.

Therefore, $$q>p$$

Hence, $$\frac{q}{p} > 1$$

Rgds,
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
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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) $$\sqrt{\frac{p}{q}}$$
(B) p/q^2
(C) p/2q
(D) q/p^2
(E) q/p

We can use some actual numbers to solve this problem. We see that p/q is less than 1. It follows that we have a positive proper fraction, where q is greater than p. Let's let p = 1 and q = 4; thus p/q = 1/4.

We now consider each answer choice:

Choice A: √(p/q) = √ (1/4) = ½, which is less than 1. Choice A is not correct.

Choice B: p/q^2 = 1/4^2 = 1/16, which is less than 1. Choice B is not correct.

Choice C: p/(2q) = 1/(2 x 4) = 1/8, which is less than 1. Choice C is not correct.

Choice D: q/p^2 = 4/1^2 = 4, which is greater than 1. This could be the answer.

Choice E: q/p = 4/1 = 4, which is greater than 1. This could be the answer.

Choices D and E work for the fraction ¼.
Let's now consider additional values for the original fraction p/q, such as p = 3 and q = 4.

Choice D now becomes q/p^2 = 4/3^2 = 4/9, which is less than 1. Thus, we can now eliminate Choice D.

Choice E now becomes q/p = 4/3, which is greater than 1. Thus, Choice E is correct. In fact, we can see that no matter what the values of p and q are, if p/q is less than 1, then its reciprocal, q/p will always be greater than 1.

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Hi All,

This question can be solved in a variety of different ways. Every so often, the GMAT offers a question that looks far more complex than it actually is. Each of the other explanations provided in this string is correct. Here's a fairly quick way of looking at it though…

Since P and Q are POSITIVE INTEGERS and P/Q < 1, inverting the fraction will invert the relationship…so Q/P > 1. The question ask which of the 5 options is greater than 1….

That's obviously

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Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]
Question Code: PS16828
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Re: If p/q < 1, and p and q are positive integers, which of the [#permalink]