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Data Sufficiency Question

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Data Sufficiency Question [#permalink] New post 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

The correct answer is "A"
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Is it the New paper test for June? [#permalink] New post 12 Jul 2003, 15:03
:o

Don't spoil the answer.
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 [#permalink] New post 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

A is the answer.
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 [#permalink] New post 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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AkamaiBrah
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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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 [#permalink] New post 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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 [#permalink] New post 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!
  [#permalink] 14 Jul 2003, 21:19
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