Is sqrt(n+k) > 2*sqrt(n)?

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LulaBrazilia: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue Mar 31, 2009 10:50 amFollowed by: 1 member

by LulaBrazilia » Sun Mar 09, 2014 6:36 pm

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

1) k > 3n

2) n+k > 3n

Source: Beat The GMAT — Data Sufficiency | Sun Mar 09, 2014 6:36 pm

Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Sun Mar 09, 2014 6:47 pm

This question tests your understanding that so long as you're dealing with positive values, x>y means that x^2 > y^2. So we can square each side and rephrase the question as: is n+k > 4n? --> is n>3k?

The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Sun Mar 09, 2014 7:16 pm

n & k = +ve
sqrt(n+k) > 2*sqrt(n)
Or,
n + k > 4n
TO FIND: k > 3n

Statement 1:
k > 3n
SUFFICIENT

Statement 2:
n + k > 3n
k > 2n
INSUFFICIENT

[spoiler]{A}[/spoiler]

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