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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## DS - Is n an integer ? ##### This topic has 8 member replies ## DS - Is n an integer ? Is n an integer ? (1) n² is an integer (2) √n is an integer I am interested in learning different approaches in solving this particular question. Thanks. Legendary Member Joined 16 Apr 2008 Posted: 1159 messages Upvotes: 56 Target GMAT Score: 750+ can it be done other then pluggin numbers? N^2=2 , then N is not an integer. N^2=4 , N is an integer. 1- insuff Sq root N is an integer. Then N definately will be an integer. 2-suff Hence,B Legendary Member Joined 08 Jul 2008 Posted: 661 messages Upvotes: 48 1) is insufficient it's ok 2) sqrt(n) is an integer The possible values of n so as sqrt(n) is an integer are 1 4 9 16 25 36 ... n has to be the square of a number so n has to ba an integer Hope it helps Master | Next Rank: 500 Posts Joined 10 Dec 2007 Posted: 400 messages Upvotes: 19 Target GMAT Score: 700 GMAT Score: 680 Guys ... I suppose I am looking for a more thoery based answer to this, rather than just plugging in numbers ... Legendary Member Joined 08 Jul 2008 Posted: 661 messages Upvotes: 48 Between plugging in and theory, I would opt for plugging in most of the time... For the 1) n^2 is an integer --> counter-example with n=sqrt(2) For the 2) sqrt(n) is an integer --> The form of "n" is: n=a^2 with "a" an integer --> The square of an integer is an integer --> n is an integer Master | Next Rank: 500 Posts Joined 10 Dec 2007 Posted: 400 messages Upvotes: 19 Target GMAT Score: 700 GMAT Score: 680 pepeprepa wrote: Between plugging in and theory, I would opt for plugging in most of the time... For the 1) n^2 is an integer --> counter-example with n=sqrt(2) For the 2) sqrt(n) is an integer --> The form of "n" is: n=a^2 with "a" an integer --> The square of an integer is an integer --> n is an integer Thanks pepeprepa ... I agree that in a lot of the cases plugging numbers is more efficient, but I want to make sure I understand the theory behind these things ! Junior | Next Rank: 30 Posts Joined 30 Mar 2009 Posted: 13 messages Upvotes: 1 I seem to be missing something. What number can you square to get two? Wouldn't that just be an approximation? Master | Next Rank: 500 Posts Joined 18 Mar 2009 Posted: 345 messages Upvotes: 12 Test Date: July XX Target GMAT Score: 680+ GMAT Score: 660 cholloway wrote: I seem to be missing something. What number can you square to get two? Wouldn't that just be an approximation? 1,4142135623731 Junior | Next Rank: 30 Posts Joined 30 Mar 2009 Posted: 13 messages Upvotes: 1 From Wikipideia - The square root of 2, also known as Pythagoras' constant, is the positive real number that, when multiplied by itself, gives the number 2. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. Its numerical value truncated to 65 decimal places[1] is: 1.41421 35623 73095 04880 16887 24209 69807 85696 71875 37694 80731 76679 73799.... I thought gmat only deals with rational numbers? • Award-winning private GMAT tutoring Register now and save up to$200

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