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# If n and k are positive integers, is sqrt(n+k) >

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Director
Joined: 08 Feb 2007
Posts: 597
Location: New Haven, CT
If n and k are positive integers, is sqrt(n+k) >  [#permalink]

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25 Jun 2007, 12:23
00:00

Difficulty:

(N/A)

Question Stats:

93% (01:13) correct 7% (00:49) wrong based on 80 sessions

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If n and k are positive integers, is sqrt(n+k) > 2sqrt(n)?

1) k > 3n

2) n + k > 3n

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Director
Joined: 26 Feb 2006
Posts: 846

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25 Jun 2007, 12:39
lanter1 wrote:
If n and k are positive integers, is sqrt(n+k) > 2sqrt(n)?

1) k > 3n

2) n + k > 3n

A.

1: if k > 3n, sqrt (n + 3n) = 2sqrt (n). so suff.
2: if n + k > 3n or k > 2n; sqrt (n + k) could be anything. so NSF.
Manager
Joined: 05 Oct 2011
Posts: 159
Re: If n and k are positive integers, is sqrt(n+k) >  [#permalink]

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30 Nov 2011, 16:27
2
1
Rephrasing question- $$sqrt(n + k) > 2sqrt(n)$$ ?
Squaring on both sides (n , k are both positive)
$$(n+k)>4n$$?
$$k>3n$$?

(1) $$k > 3n$$ This matches our rephrased question. Sufficient.
(2) $$n + k > 3n$$

$$k>2n$$
This doesn't gives us if k is greater than 3n -- a bigger value than 2n, as K could be a value between 3n and 2n.
We can pick numbers to prove it.
n= 1, k = 2 gives NO to the question
n=1, k = 3 gives YES to the question. Insufficient.
Non-Human User
Joined: 09 Sep 2013
Posts: 9835
Re: If n and k are positive integers, is sqrt(n+k) >  [#permalink]

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04 Feb 2019, 11:58
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Re: If n and k are positive integers, is sqrt(n+k) >   [#permalink] 04 Feb 2019, 11:58
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