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

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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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Joined: 02 Sep 2009
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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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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.

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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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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!

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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.

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 $$\sqrt{x}$$, 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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

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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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 $$\sqrt{x}$$, 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, $$\sqrt{125} =5$$ and $$\sqrt{-64} =-4$$.

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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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 .
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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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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.
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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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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
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GMAT 1: 530 Q39 V23 Re: If n and k are positive integers, is (n + k)^(1/2) > 2n^(1/2)?  [#permalink]

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

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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.

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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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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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.

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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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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.
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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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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.
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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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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
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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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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".
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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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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!
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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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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]
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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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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

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