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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 \(\sqrt[3]{-64} =-4\).

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

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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 \(\sqrt[3]{-64} =-4\).

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

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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.

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.
_________________

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

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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.

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

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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.

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

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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 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

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

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23 Mar 2017, 23:57

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

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

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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.

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.
_________________

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

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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.

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

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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

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".
_________________