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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: 52464
If n and p are positive integers, is the ratio of n to p 2 : 1?  [#permalink]

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22 Jan 2018, 22:16
00:00

Difficulty:

75% (hard)

Question Stats:

35% (01:20) correct 65% (01:07) wrong based on 62 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

_________________
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, 03:58
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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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_________________

If it helped, some kudos would be more than welcome!

King regards,

Rooigle

If n and p are positive integers, is the ratio of n to p 2 : 1? &nbs [#permalink] 23 Jan 2018, 03:58
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