Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
26 Dec 2012, 05:31
3
This post received KUDOS
16
This post was BOOKMARKED
Question Stats:
70% (02:13) correct
30% (01:11) wrong based on 989 sessions
HideShow timer Statistics
If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\) (1) k > 3n (2) n + k > 3n
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 39640

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
26 Dec 2012, 05:36
2
This post received KUDOS
Expert's post
2
This post was BOOKMARKED



Manager
Joined: 24 Mar 2010
Posts: 113

If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
27 Jun 2014, 02:36
1
This post received KUDOS
Bunuel wrote: If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\)?
Both parts of the inequality are positive, thus we can square it, to get "is \(n+k>4n\)?" > is \(k>3n\)?
(1) k > 3n. Sufficient.
(2) n + k > 3n > \(k>2n\). Not sufficient.
Answer: A. Hi Bunuel, I don't understand why n & k are positive then two parts of the inequility \(\sqrt{n+k}>2\sqrt{n}\) are positive. What I understand is that: n, k>0 => n+k>0 => \(\sqrt{n+k}\) might be positive or negative. e.g: x=9>0 > \(\sqrt{x}\) = 3 or 3 Same thought or n! Please help me to clarify, thank you so much!
_________________
Start to fall in love with GMAT <3



Math Expert
Joined: 02 Sep 2009
Posts: 39640

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
27 Jun 2014, 02:53
LucyDang wrote: Bunuel wrote: If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\)?
Both parts of the inequality are positive, thus we can square it, to get "is \(n+k>4n\)?" > is \(k>3n\)?
(1) k > 3n. Sufficient.
(2) n + k > 3n > \(k>2n\). Not sufficient.
Answer: A. Hi Bunuel, I don't understand why n & k are positive then two parts of the inequility \(\sqrt{n+k}>2\sqrt{n}\) are positive. What I understand is that: n, k>0 => n+k>0 => \(\sqrt{n+k}\) might be positive or negative. e.g: x=9>0 > \(\sqrt{x}\) = 3 or 3 Same thought or n! Please help me to clarify, thank you so much! When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{9}=3\), NOT +3 or 3. In contrast, the equation \(x^2=9\) has TWO solutions, +3 and 3. Even roots have only nonnegative value on the GMAT.Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{64} =4\). Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 24 Mar 2010
Posts: 113

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
27 Jun 2014, 05:06
Bunuel wrote: LucyDang wrote: Bunuel wrote: If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\)?
Both parts of the inequality are positive, thus we can square it, to get "is \(n+k>4n\)?" > is \(k>3n\)?
(1) k > 3n. Sufficient.
(2) n + k > 3n > \(k>2n\). Not sufficient.
Answer: A. Hi Bunuel, I don't understand why n & k are positive then two parts of the inequility \(\sqrt{n+k}>2\sqrt{n}\) are positive. What I understand is that: n, k>0 => n+k>0 => \(\sqrt{n+k}\) might be positive or negative. e.g: x=9>0 > \(\sqrt{x}\) = 3 or 3 Same thought or n! Please help me to clarify, thank you so much! When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{9}=3\), NOT +3 or 3. In contrast, the equation \(x^2=9\) has TWO solutions, +3 and 3. Even roots have only nonnegative value on the GMAT.Odd roots will have the same sign as the base of the root. For example, \(\sqrt[3]{125} =5\) and \(\sqrt[3]{64} =4\). Hope it helps. I got it, thank you!!
_________________
Start to fall in love with GMAT <3



Intern
Joined: 07 Aug 2014
Posts: 1

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
19 Aug 2014, 07:01
Bunuel wrote: If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\)?
Both parts of the inequality are positive, thus we can square it, to get "is \(n+k>4n\)?" > is \(k>3n\)?
(1) k > 3n. Sufficient.
(2) n + k > 3n > \(k>2n\). Not sufficient.
Answer: A. How do you get to the conclusion that \(\sqrt{n+k}>2\sqrt{n}\)? Even if k > 3n it can be either n+k > 4n or n+k < 4n, since we don't know more about n. Thanks .



Math Expert
Joined: 02 Sep 2009
Posts: 39640

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
19 Aug 2014, 08:06
tobiasfr wrote: Bunuel wrote: If n and k are positive integers, is \(\sqrt{n+k}>2\sqrt{n}\)?
Both parts of the inequality are positive, thus we can square it, to get "is \(n+k>4n\)?" > is \(k>3n\)?
(1) k > 3n. Sufficient.
(2) n + k > 3n > \(k>2n\). Not sufficient.
Answer: A. How do you get to the conclusion that \(\sqrt{n+k}>2\sqrt{n}\)? Even if k > 3n it can be either n+k > 4n or n+k < 4n, since we don't know more about n.Thanks . Not sure how you get the above... Anyway, the question asks whether \(\sqrt{n+k}>2\sqrt{n}\)? After algebraic manipulations shown in my solution the question becomes: is \(k>3n\)? The first statement answers this question, which makes it sufficient.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15942

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
07 Oct 2015, 03:14
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 14 Jul 2012
Posts: 5

Manhattan GMAT Explanation Appears Wrong [#permalink]
Show Tags
07 Aug 2016, 10:16
Problem: If n and k are positive integers, is \(\sqrt{n+k}\) > 2 \(\sqrt{n}\)? (1) k > 3n (2) n + k > 3n  By squaring both sides of the equation, we are left with: n + k > 4n In its simplest form the equation is: k > 3n  According to Manhattan GMAT 12th edition, the second statement is insufficient. Perhaps I am overlooking some mathematical principle, but if one compares the following two equations one should be able to conclude if the statement is true or not. statement (2) from problem: n + k > 3n original equation squared: n + k > 4n Any help or guidance would be much appreciated.



Math Expert
Joined: 02 Sep 2009
Posts: 39640

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
07 Aug 2016, 11:37



Manager
Joined: 18 Feb 2015
Posts: 93

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
09 Dec 2016, 14:39
Hi,
If it were not given that n and k are positive integers, then taking the underroot of this expression (Underoort n+k > 2 underroot n) would have resulted in absolute value form as l n + k l > 4 l n l. Am I right?
Just wanted to make sure that I get the concept right.
Thanks for your help.
Regards, H



Intern
Joined: 05 Dec 2016
Posts: 5

If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
12 Mar 2017, 06:54
HarveyKlaus wrote: Hi,
If it were not given that n and k are positive integers, then taking the underroot of this expression (Underoort n+k > 2 underroot n) would have resulted in absolute value form as l n + k l > 4 l n l. Am I right?
Just wanted to make sure that I get the concept right.
Thanks for your help.
Regards, H Nope. It still would have given the positive value, however, we won't be sure of the sign of the n and k if the statement "they are +ve integers" isn't mentioned. \sqrt{10036} \sqrt{64} = 8



Manager
Joined: 01 Dec 2016
Posts: 112
Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
23 Mar 2017, 12:53
Careless mistake! Can someone share a link on how to reduce careless mistake please? Frustrating to miss this kind of easy questions
_________________
What was previously thought to be impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them



Manager
Joined: 01 Dec 2016
Posts: 112
Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
23 Mar 2017, 12:54
Careless mistake! Can someone share a link on how to reduce careless mistake please? Frustrating to miss this kind of easy questions
_________________
What was previously thought to be impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them



Math Expert
Joined: 02 Sep 2009
Posts: 39640

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
23 Mar 2017, 23:44
2
This post received KUDOS
Expert's post
1
This post was BOOKMARKED



Manager
Joined: 01 Dec 2016
Posts: 112
Location: Cote d'Ivoire
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]
Show Tags
23 Mar 2017, 23:57
Thanks a lot Bunnuel. Very useful
_________________
What was previously thought to be impossible is now obvious reality. In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them




Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2?
[#permalink]
23 Mar 2017, 23:57








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


2


If k and n are positive integer, is k > 1?

ganand 
4 
12 May 2017, 23:29 

4


n and k are positive integers, and when n is divided by k²

GMATPrepNow 
4 
02 Nov 2016, 12:12 

70


If k is a positive integer and n = k(k + 7k), is n divisible

Jem2905 
25 
29 Jan 2017, 16:34 

10


If n and k are positive integers, is n/k an even integer?

udaymathapati 
10 
17 Apr 2017, 03:28 

40


If n and k are positive integers, is n divisible by 6?

tarek99 
27 
15 Jun 2017, 09:01 



