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# If x is a positive integer, is sqrt(x) < 2.5*x - 5 ? 1) x

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Senior Manager
Joined: 21 Jul 2009
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Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.
If x is a positive integer, is sqrt(x) < 2.5*x - 5 ? 1) x [#permalink]

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14 Mar 2010, 13:09
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If x is a positive integer, is sqrt(x) < 2.5*x - 5 ?

1) x < 3
2) x is a prime number

How can OA be?
[Reveal] Spoiler:
A
X is positive integer, sqrt(x) can still be negative.
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Joined: 26 May 2005
Posts: 207
Re: Gmatclub test M 05, question 15/37 [#permalink]

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14 Mar 2010, 22:01
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BarneyStinson wrote:
If x is a positive integer, is sqrt(x) < 2.5*x - 5 ?

1) x < 3
2) x is a prime number

st 1) x< 3 ==> x can be 1 or 2
x = 1 --> -2.5 > 1 .. NO
x = 2 --> 0>1.414 .. NO
sufficient
st 2 ) x is prime ..
x = 2, NO
x=3 or above YES
not sufficient

A
BarneyStinson wrote:
X is positive integer, sqrt(x) can still be negative.

the square roots of x are +sqrt(x) and -sqrt(x)
sqrt(x) is ALWAYS POSITIVE
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Re: Gmatclub test M 05, question 15/37 [#permalink]

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14 Mar 2010, 22:40
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BarneyStinson wrote:
If x is a positive integer, is sqrt(x) < 2.5*x - 5 ?
1) x < 3
2) x is a prime number
How can OA be?
[Reveal] Spoiler:
A
X is positive integer, sqrt(x) can still be negative.

1: if x>0 and x<3 then possible values 1,2 (0 is neither positive nor negative)
with both values sqrt(x) < 2.5*x - 5. hence sufficient.
2: x can be 2,3,5,7,11 .....
any value of x greater than 4 will result in sqrt(x) > 2.5*x - 5 hence insufficient.
Hence A.

Also sqrt of positive number is always +ve it can't be negative.
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Re: Gmatclub test M 05, question 15/37 [#permalink]

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15 Mar 2010, 00:35
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sidhu4u wrote:
bangalorian2000 wrote:

Also sqrt of positive number is always +ve it can't be negative.

Sqrt of any positive number can be negative, its not necessarily to be positive.
for example, if we have 9 as number, than its sqrt can be 3 or -3 since 9 = 3*3 or (-3)*(-3)

Mate just need to clarify that on Gmat Land , root of any number is +ve

i.e. root of 4 has to be taken as 2 only and not -2....

however if you are given x^2 = 4 then that would give x = +2 and -2

You can confirm this from various sources !!!

Hope this helps !!!
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Re: Gmatclub test M 05, question 15/37 [#permalink]

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14 Mar 2010, 23:52
bangalorian2000 wrote:

Also sqrt of positive number is always +ve it can't be negative.

Sqrt of any positive number can be negative, its not necessarily to be positive.
for example, if we have 9 as number, than its sqrt can be 3 or -3 since 9 = 3*3 or (-3)*(-3)
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Re: Gmatclub test M 05, question 15/37   [#permalink] 14 Mar 2010, 23:52
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# If x is a positive integer, is sqrt(x) < 2.5*x - 5 ? 1) x

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