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# Is x an integer? 1. 4x^2 is an integer. 2. sqrt(4x)is an

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Director
Joined: 29 Aug 2005
Posts: 836
Is x an integer? 1. 4x^2 is an integer. 2. sqrt(4x)is an [#permalink]

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14 Jun 2009, 02:42
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Is x an integer?

1. 4x^2 is an integer.
2. sqrt(4x)is an integer.
Manager
Joined: 30 May 2009
Posts: 213

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14 Jun 2009, 09:37
I think the answer is C.

1. 4x^2 is an integer.
X=1 and X=1/2 both satisfy this condition. So INSUFF

2. sqrt(4x)is an integer.
X=1 and X=1/4 both satisfy this condition. So INSUFF.

Take 1 and 2 together. 2 clearly rules on the possibility that X is negative. So X can only be postive

sqrt(4x) is integer => Either X can be 1/4 or X must be some perfect square like 1,4,9,16,25,36 etc etc.
But 4x^2 cannot be an integer if X is 1/4.
So the only possible values for X are perfect suqares like 1,4,9,16,25 etc which are all integers..

What is the OA?
Re: DS: number prop1   [#permalink] 14 Jun 2009, 09:37
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