GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 04 Aug 2020, 04:13

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 172
If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

26 Dec 2012, 04:31
7
1
70
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:18) correct 25% (01:38) wrong based on 2700 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
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

26 Dec 2012, 04:36
9
13
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.

_________________
##### General Discussion
Manager
Joined: 24 Mar 2010
Posts: 71
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

27 Jun 2014, 01:36
1
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.

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!

_________________
Start to fall in love with GMAT <3
Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

27 Jun 2014, 01:53
7
6
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.

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!

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 non-negative 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.
_________________
Manager
Joined: 24 Mar 2010
Posts: 71
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.

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!

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 non-negative 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.

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: 65785
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

19 Aug 2014, 07:06
1
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.

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.
_________________
Manager
Joined: 18 Feb 2015
Posts: 76
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.

Regards,
H
Intern
Joined: 05 Dec 2016
Posts: 5
Location: India
Concentration: Strategy, General Management
Schools: ISB'21
GMAT 1: 530 Q39 V23
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.

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{100-36}
\sqrt{64} = 8
Manager
Joined: 01 Dec 2016
Posts: 99
Concentration: Finance, Entrepreneurship
GMAT 1: 650 Q47 V34
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
1
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: 65785
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

23 Mar 2017, 22:44
5
7
guialain wrote:
Careless mistake!
Can someone share a link on how to reduce careless mistake please?
Frustrating to miss this kind of easy questions

Check below topics:

Careless Mistakes on GMAT Math BY MIKE MCGARRY, MAGOOSH;
3 Deadly Mistakes you must avoid in LCM-GCD Questions BY EGMAT;
Do you make these 3 mistakes in GMAT Even-Odd Questions? BY EGMAT;
Common Quant Mistakes That You Must Avoid by VERITAS PREP.

Hope it helps.
_________________
Manager
Joined: 01 Dec 2016
Posts: 99
Concentration: Finance, Entrepreneurship
GMAT 1: 650 Q47 V34
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.

Math Expert
Joined: 02 Sep 2009
Posts: 65785
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

19 Jul 2017, 20:59
1
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.

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.
_________________
Intern
Joined: 20 Apr 2015
Posts: 20
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.

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.
Intern
Joined: 11 Jul 2012
Posts: 47
GMAT 1: 650 Q49 V29
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.

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: 65785
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.

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

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".
_________________
Intern
Joined: 26 May 2016
Posts: 14
Location: India
Concentration: Strategy, Healthcare
GRE 1: Q303 V304
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
1
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!
Intern
Joined: 31 Jan 2019
Posts: 1
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

21 Feb 2019, 13:03
Marshy wrote:
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

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![/quote]
Intern
Joined: 20 Jan 2017
Posts: 38
Location: United Arab Emirates
Schools: Owen '22
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

### Show Tags

31 Jul 2019, 13:56
Is √(n+k)>2√n , yes/no?

Condition n>0 (I) k>0 (I) [n and k are positive integers]

Simplify:
(√(n+k) / √n)^2 > 2
n+k/n>4

n+k>4n

Therefore is k>3n... yes/no?
or
Is k>3 where the least possible value of n is 1
:. Possible values of k = 4,5,6....

St 1: k>3n ...Sufficient

Possible values of k= 4, 5, 6...

St 2: K>2n

possible values of k = 3,4,5....

Because K can be equal to 3 or greater than 3 it is not sufficient.
Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?   [#permalink] 31 Jul 2019, 13:56

Go to page    1   2    Next  [ 27 posts ]