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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 ## If N is a positive integer... tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 1 member reply ### Top Member ## If N is a positive integer... If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors? A)30 B)60 C)180 D)210 E)cannot be determined The OA is D. Why D is the correct answer? Can any expert explain this PS question please?. Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello. If you see carefully the options on the list you can determine which is the correct answer. Let's see option by option. - Option A: 30 30=2*3*5, so 30 has 3 different prime factors. OUT - Option B: 60 60=2*2*3*5, so 60 has 3 different prime factors. OUT. - Option C: 180 180=2*2*3*3*5, so 180 has 3 different prime factors, OUT. - Option D: 210 210=2*3*5*7, so 210 has exactly 4 different prime factors. In addition, 14*210/60=49, so 14N/60 is an integer. CORRECT. We don't need to analyze the last option. So, the answer is D. I hope this answer could help you. I'm available if youd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 LUANDATO wrote: If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors? A)30 B)60 C)180 D)210 E)cannot be determined 14N/60 = 7N/30. The smallest prime numbers are 2, 3, 5 and 7. Thus, the smallest integer with 4 different prime factors = 2*3*5*7 = 210. Test whether N=210 yields an integer value for 7N/30: (7*210)/30= 7*7 = 49. Success! Thus, the least possible value for N = 210. The correct answer is D. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### Top Member Moderator Joined 15 Oct 2017 Posted: 1108 messages Followed by: 5 members Hello, Excellent, your explanations was helpful to me a lot! Thank you so much! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 LUANDATO wrote: If N is a positive integer and 14N/60 is an integer. What is the smallest value of N for which N has exactly four different prime factors? A)30 B)60 C)180 D)210 E)cannot be determined . We are given that 14N/60 is an integer, and we need to determine the smallest value of N for which N has exactly four different prime factors. 14N/60 = 7N/30 In order for 7N/30 to be an integer, N must be divisible by 30. In other words, N must be a multiple of 30. However, since 30 = 2 x 3 x 5, which are 3 different primes, the smallest value of n with 4 different primes is 2 x 3 x 5 x 7 = 210. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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