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# If n and p are positive integers, is the ratio of n to p 2 : 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 58411
If n and p are positive integers, is the ratio of n to p 2 : 1?  [#permalink]

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22 Jan 2018, 23:16
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Difficulty:

65% (hard)

Question Stats:

43% (01:14) correct 57% (01:06) wrong based on 74 sessions

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If n and p are positive integers, is the ratio of n to p 2 : 1?

(1) n – p < 0
(2) np = 20

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Intern
Joined: 22 Mar 2017
Posts: 28
GMAT 1: 680 Q48 V35
If n and p are positive integers, is the ratio of n to p 2 : 1?  [#permalink]

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23 Jan 2018, 04:58
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1
Bunuel wrote:
If n and p are positive integers, is the ratio of n to p 2 : 1?

(1) $$n – p < 0$$
(2) $$np = 20$$

In other words, is $$\frac{n}{p}=2$$ | $$n=2·p$$ ?

We know that:

p and n are positive integers.

S1.

$$n-p<0$$ implies that $$p>n$$ since both are positive numbers.

As such, $$n=2·p$$ cannot be possible and the answer is NO.

SUFF.

S2.

p is an integer so if we insert the condition that $$n=2·p$$ and it is true p should result in an integer.

$$n·p=20$$ | $$2·p^2=20$$ | $$p=\sqrt{10}$$ what is not an integer so the answer is NO.

SUFF.

AC: D

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King regards,

Rooigle
If n and p are positive integers, is the ratio of n to p 2 : 1?   [#permalink] 23 Jan 2018, 04:58
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# If n and p are positive integers, is the ratio of n to p 2 : 1?

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