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

This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 116
Joined: Tue Mar 31, 2009 10:50 am
Followed by:1 members

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

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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

1) k > 3n

2) n+k > 3n

User avatar
GMAT Instructor
Posts: 1052
Joined: Fri May 21, 2010 1:30 am
Thanked: 335 times
Followed by:98 members

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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).

Image

-Patrick
  • Ask me about tutoring.

User avatar
Legendary Member
Posts: 1556
Joined: Tue Aug 14, 2012 11:18 pm
Thanked: 448 times
Followed by:34 members
GMAT Score:650

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

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]
R A H U L