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# if n and k are positive integers, is sqrt. of

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Manager
Joined: 05 Jul 2006
Posts: 197
if n and k are positive integers, is sqrt. of [#permalink]

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10 Sep 2006, 12:03
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if n and k are positive integers, is sqrt. of (n+k)>2sqrt.of n?

k>3n
n+k>3n
Senior Manager
Joined: 14 Jul 2005
Posts: 402
Re: DS- n & k [#permalink]

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10 Sep 2006, 12:46
lan583 wrote:
if n and k are positive integers, is sqrt. of (n+k)>2sqrt.of n?

k>3n
n+k>3n

A should be it...

From 1, k > 3n, adding n to both sides
k+n > 3n+n
k+n>4n

Taking sqrt, sqrt(k+n) > 2sqrt(n)
SUFF

From 2, n+k>3n, taking sqrt, sqrt(n+k) > sqrt(3n) which is INSUFF since
sqrt(3n) < sqrt(n+k) < 2*sqrt(n)
SVP
Joined: 05 Jul 2006
Posts: 1747

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11 Sep 2006, 01:31
if n and k are positive integers, is sqrt. of (n+k)>2sqrt.of n?

1)k>3n
2) n+k>3n

square both sides

n+k>4n.....ie k>3n

from one ...needless to say anything......suff

from two

k>2n we can never deduct that k>3n....insuff

11 Sep 2006, 01:31
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