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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 (n+k)^1/2>2n^1/2? [#permalink] New post 26 Dec 2012, 04:31
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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
[Reveal] Spoiler: OA
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Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink] New post 26 Dec 2012, 04:36
Expert's post
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.

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

_________________

whatever happens, live with smiles

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Re: If n and k are positive integers, is (n+k)^1/2>2n^1/2? [#permalink] New post 27 Jun 2014, 01:53
Expert's post
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.

_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

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Kudos [?]: 6 [0], given: 45

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

_________________

whatever happens, live with smiles

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