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# Data Sufficiency Question

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Intern
Joined: 23 Jun 2003
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12 Jul 2003, 15:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Can someone please explain the answer to this question (in the official paper test)

SQRT = Square root

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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Eternal Intern
Joined: 07 Jun 2003
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Is it the New paper test for June? [#permalink]

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12 Jul 2003, 15:03

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SVP
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13 Jul 2003, 05:13
My rationale:

(1) k>3n; since both k and n are positive integers, the smallest k, satisfying (1) is 3n+1. Check it. sqrt(4n+1)>2sqrt(n) -- correct

Any other k (3n+2, 3n+3, and so on) will be larger, making the original stuff correct as well.

(2) n+k>3n
k>2n

Pick k=3n, then sqrt(4n)=2sqrt(n)
Pick k=10n, then sqrt(11n)>2 sqrt (n)

Different answers; thus, it is wrong

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GMAT Instructor
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Schools: Haas, MFE; Anderson, MBA; USC, MSEE

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14 Jul 2003, 00:20
An alternative method might be to restate the question by squaring both sides of the inequality. (raising 2 positive numbers to positive powers maintains the inequality).

"Is sqrt(n + k) > 2 sqrt(n)?" is equivalent to asking "Is n + k > 4 n? " or "is k > 3n?"

1) answers the question directly so A or D.
2) restated say k > 2n. if k > 2n we still don't know k's relationship to 3n so not sufficient, and not D, but A.
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Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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Manager
Joined: 03 Jun 2003
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14 Jul 2003, 07:27
2SQRT (n) = SQRT (4n)

WIth 1) K>3n, so SQRT (n+K) > than SQRT (4n)

With this you can definetely answer the question

With 2) n+K > 3n, here it can be > or < than 4n

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SVP
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14 Jul 2003, 21:19
MBA04 wrote:
2SQRT (n) = SQRT (4n)

WIth 1) K>3n, so SQRT (n+K) > than SQRT (4n)

With this you can definetely answer the question

With 2) n+K > 3n, here it can be > or < than 4n

the best approach!

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14 Jul 2003, 21:19
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# Data Sufficiency Question

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