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

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

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

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

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

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New post 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 :).

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

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

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New post 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.

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

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New post 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
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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.

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

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New post 23 Mar 2017, 23:57
Thanks a lot Bunnuel.
Very useful
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Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]

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New post 19 Jul 2017, 19:58
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.

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

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New post 19 Jul 2017, 21:59
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.
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Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink]

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New post 08 Aug 2017, 23:38
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.

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

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New post 11 Oct 2017, 11:46
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

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

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New post 11 Oct 2017, 21:03
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 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".
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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.


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Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2?   [#permalink] 11 Oct 2017, 21:03
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