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# Data Sufficiency Question

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Intern
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Data Sufficiency Question [#permalink]  12 Jul 2003, 15:02
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

Eternal Intern
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Is it the New paper test for June? [#permalink]  12 Jul 2003, 15:03

SVP
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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

GMAT Instructor
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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.
_________________

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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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
SVP
Joined: 03 Feb 2003
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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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