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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 ## The "length" of a positive integer greater than 1 ##### This topic has 2 expert replies and 1 member reply ### Top Member ## The "length" of a positive integer greater than 1 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult The "length" of a positive integer greater than 1 is the number of prime numbers, including repeats, that are factors of that integer. For instance, the length of 20 is 3, because 2X2X5=202X2X5=20. What is the length of 5,950? A. 1 B. 2 C. 3 D. 4 E. 5 OA E Source: Manhattan Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2204 messages Followed by: 17 members Upvotes: 43 BTGmoderatorDC wrote: The "length" of a positive integer greater than 1 is the number of prime numbers, including repeats, that are factors of that integer. For instance, the length of 20 is 3, because 2X2X5=202X2X5=20. What is the length of 5,950? A. 1 B. 2 C. 3 D. 4 E. 5 5,950 = 595 x 10 = 119 x 5 x 2 x 5 = 7 x 17 x 5 x 2 x 5 Since 5,950 has 5 prime factors (including repeats), the length of 5,950 is 5. Answer: E ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1429 messages Followed by: 31 members Upvotes: 59 BTGmoderatorDC wrote: The "length" of a positive integer greater than 1 is the number of prime numbers, including repeats, that are factors of that integer. For instance, the length of 20 is 3, because 2X2X5=20. What is the length of 5,950? A. 1 B. 2 C. 3 D. 4 E. 5 Source: Manhattan Prep $$?\,\,\, = \,\,\,\# \,\,{\rm{prime}}\,\,{\rm{factors}}\,\,\,\left( {{\rm{not}}\,\,{\rm{necessarily}}\,\,{\rm{distincts}}} \right)$$ $$5,950 = 10 \cdot 595\,\,\mathop = \limits^{\left( * \right)} \,\,10 \cdot 5 \cdot \underline {119} \,\,\mathop = \limits^{\left( {**} \right)} \,\,2 \cdot {5^2} \cdot \underline {7 \cdot 17}$$ $$\left( * \right)\,\,{{550 + 45} \over 5} = 110 + 9\,\,\,\,\, \Rightarrow \,\,\,\,595 = 5 \cdot 119$$ $$\left( {**} \right)\,{{70 + 49} \over 7} = 10 + 7\,\,\,\,\, \Rightarrow \,\,\,\,119 = 7 \cdot 17$$ $$?\,\,:\,\,\,2,5,5,7,17\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 5$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Junior | Next Rank: 30 Posts Joined 03 Oct 2018 Posted: 10 messages The prime factorization of the given number is 5950 = 5*5*2*17*7 Since there are 5 prime factors( including the repeating ones) , the length of the number is 5. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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