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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 ## Manhattan Number Prop.DS question not understood ##### This topic has 4 member replies ## Manhattan Number Prop.DS question not understood Hi, Can some one please explain the concept behind this question as I have not understood. If X>1 what is the value of X? 1) x unique factors of x. Reason for unique factors and only 1 and 2 number cosidered and not 3 or 4 for some reason in explaination.Kindly answer as I have just preparing. ANuj Master | Next Rank: 500 Posts Joined 01 May 2013 Posted: 149 messages Followed by: 9 members Upvotes: 54 1 has exactly 1 factor : 1 But it is already mentioned that X > 1 So, X cannot be equal to 1. Now, 2 has exactly 2 factors : 1 and 2 So, X can be equal to 2. Now, for any integer X greater than 2, the number of unique factors of X must be less than X. Why so? Because any X greater than 2 will not be divisible by (X - 1) Why so? Because X and (X - 1) are consecutive integers. So, one of them will be odd and the other one will be even. So, (X - 1) cannot divide X. So, only possible value of X is 2. Hope that helps. Junior | Next Rank: 30 Posts Joined 26 Aug 2010 Posted: 15 messages Not understood. Now, for any integer X greater than 2, the number of unique factors of X must be less than X. This above statement is understood by me by the fact that factors cant be greater than the number. Why so? Because any X greater than 2 will not be divisible by (X - 1)? Why this statement has come? This X-1 is if purely notation for consecutive integer then why not X+1 and as a fact any number which is consecutive can not be divisible by its immediate before number. Right? Why so? Because X and (X - 1) are consecutive integers. So, one of them will be odd and the other one will be even. So, (X - 1) cannot divide X. Why this statement? Senior | Next Rank: 100 Posts Joined 04 Jan 2013 Posted: 38 messages Upvotes: 11 For any positive integer x to have x unique factors means that it must be a multiple of every integer from 1 to x. So, x must be a factor of x-1, which can't be true for any x > 2. So, x = 2 is the only solution. Junior | Next Rank: 30 Posts Joined 26 Aug 2010 Posted: 15 messages I got your point!!!thanks for the info.!!!you must be a expert in maths...have you taken gmat, if yes kindly tell me which book to refer after manhattan gmat maths. One more thing is why not X+1 is talked about? Anuj • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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