November 20, 2018 November 20, 2018 09:00 AM PST 10:00 AM PST The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat. November 20, 2018 November 20, 2018 06:00 PM EST 07:00 PM EST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177

If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
26 Dec 2012, 04:31
Question Stats:
73% (01:17) correct 27% (01:37) wrong based on 1604 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: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
26 Dec 2012, 04:36




Manager
Joined: 24 Mar 2010
Posts: 87

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
27 Jun 2014, 01:36
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: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
27 Jun 2014, 01:53
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: Ultimate GMAT Quantitative Megathread  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: 87

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
27 Jun 2014, 04:06
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, 06:01
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: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
19 Aug 2014, 07:06
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: Ultimate GMAT Quantitative Megathread  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: 18 Feb 2015
Posts: 85

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
09 Dec 2016, 13:39
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

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
12 Mar 2017, 05:54
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: 111
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, 11:54
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 considered 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: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
23 Mar 2017, 22:44



Manager
Joined: 01 Dec 2016
Posts: 111
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, 22:57
Thanks a lot Bunnuel. Very useful
_________________
What was previously considered 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



Intern
Joined: 03 Jun 2012
Posts: 5
Concentration: General Management, Marketing
GPA: 3.8
WE: Information Technology (Computer Software)

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
19 Jul 2017, 18:58
Hi Bunuel,
I couldn't understand the 2nd part.
The objective is the check if k>3n (after simplification). From option 2 we find K>2n , so it's also sufficient to answer that K is not greater than 3n.
Please explain.



Math Expert
Joined: 02 Sep 2009
Posts: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
19 Jul 2017, 20:59



Intern
Joined: 20 Apr 2015
Posts: 25
Concentration: Technology, Leadership
GPA: 3.9

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
08 Aug 2017, 22:38
Bunuel wrote: IWilWin wrote: Hi Bunuel,
I couldn't understand the 2nd part.
The objective is the check if k>3n (after simplification). From option 2 we find K>2n , so it's also sufficient to answer that K is not greater than 3n.
Please explain. Say a question asks: is x > 3? We got that x > 2. Is this sufficient to answer the question? No, because if x= 2.5, then the answer is NO but if x = 4, then the answer is YES. Perfect Explanation, This is what I was looking for.



Manager
Joined: 11 Jul 2012
Posts: 50

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
11 Oct 2017, 10:46
Bunuel wrote: IWilWin wrote: Hi Bunuel,
I couldn't understand the 2nd part.
The objective is the check if k>3n (after simplification). From option 2 we find K>2n , so it's also sufficient to answer that K is not greater than 3n.
Please explain. Say a question asks: is x > 3? We got that x > 2. Is this sufficient to answer the question? No, because if x= 2.5, then the answer is NO but if x = 4, then the answer is YES. Bunuel : I always have a confusion in questions such as these... We know that on simplifying the question stem we get k>3n The second premise is reduced to k>2n Now my understanding is that the second premise is sufficient for us to say that k is not greater than 3n, hence answer choice D. When it itself deduces to k>2n isn't it enough for us to answer the original question stem whether k>3n? In this case No k is not greater than 3n



Math Expert
Joined: 02 Sep 2009
Posts: 50625

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
11 Oct 2017, 20:03
avaneeshvyas wrote: Bunuel wrote: IWilWin wrote: Hi Bunuel,
I couldn't understand the 2nd part.
The objective is the check if k>3n (after simplification). From option 2 we find K>2n , so it's also sufficient to answer that K is not greater than 3n.
Please explain. Say a question asks: is x > 3? We got that x > 2. Is this sufficient to answer the question? No, because if x= 2.5, then the answer is NO but if x = 4, then the answer is YES. Bunuel : I always have a confusion in questions such as these... We know that on simplifying the question stem we get k>3n The second premise is reduced to k>2n Now my understanding is that the second premise is sufficient for us to say that k is not greater than 3n, hence answer choice D. When it itself deduces to k>2n isn't it enough for us to answer the original question stem whether k>3n? In this case No k is not greater than 3nNo. Say a question asks is x > 3? (1) x > 2. Is this sufficient to answer the question whether x is greater than 3? No. If x = 100, then we'd have an YES answer to the question but if x = 2.5 (so if x is any number from 2 to 3), then we'd have a NO answer to the question. In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  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



Intern
Joined: 26 May 2016
Posts: 14
Location: India
Concentration: Strategy, Healthcare
GPA: 4
WE: Medicine and Health (Consulting)

Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?
[#permalink]
Show Tags
25 Nov 2017, 23:17
We know that on simplifying the question stem we get k>3n The second premise is reduced to k>2n Now my understanding is that the second premise is sufficient for us to say that k is not greater than 3n, hence answer choice D. When it itself deduces to k>2n isn't it enough for us to answer the original question stem whether k>3n? In this case No k is not greater than 3n[/quote]
No. Say a question asks is x > 3?
(1) x > 2. Is this sufficient to answer the question whether x is greater than 3? No. If x = 100, then we'd have an YES answer to the question but if x = 2.5 (so if x is any number from 2 to 3), then we'd have a NO answer to the question.
In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".[/quote]
This explanation..... this is going to save lots of lives on the GMAT. Thank you Bunuel!




Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)? &nbs
[#permalink]
25 Nov 2017, 23:17






