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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 “primeness” tagged by: rolandprowess ##### This topic has 4 expert replies and 0 member replies ### Top Member The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness? A) 10 B) 12 C) 14 D) 15 E) 18 How will i start to solve this? Can any experts help me? OA C ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness? A) 10 B) 12 C) 14 D) 15 E) 18 How will i start to solve this? Can any experts help me? Hi lheiannie07, Let's take a look at your question. The question states that the “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. To find the greatest primeness, we will find the primeness of each number given one by one by finding its factors. Primeness of 10: Factors of 10 = 1, 2, 5, 10 Smallest prime factor = 2 Largest prime factor = 5 Primeness of 10 = 5 - 2 = 3 Primeness of 12: Factors of 12 = 1, 2, 3, 4, 6, 12 Smallest prime factor = 2 Largest prime factor = 3 Primeness of 12 = 3 - 2 = 1 Primeness of 14: Factors of 14 = 1, 2, 7, 14 Smallest prime factor = 2 Largest prime factor = 7 Primeness of 14 = 7 - 2 = 5 Primeness of 15: Factors of 15 = 1, 2, 3, 5, 15 Smallest prime factor = 2 Largest prime factor = 5 Primeness of 15 = 5 - 2 = 3 Primeness of 18: Factors of 18 = 1, 2, 3, 6, 9, 18 Smallest prime factor = 2 Largest prime factor = 3 Primeness of 18 = 3 - 2 = 1 We can see that 14 has the largest primeness, i.e. 5. Therefore, Option C is correct. Hope this helps. I am available, if you'd 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 12 Sep 2012 Posted: 2635 messages Followed by: 117 members Upvotes: 625 Target GMAT Score: V51 GMAT Score: 780 Find the prime factorization, then do largest prime - smallest prime. A: 10 = 2 * 5, largest - smallest = 5 - 2 = 3 B: 12 = 2 * 2 * 3, largest - smallest = 3 - 2 = 1 C: 14 = 2 * 7, largest - smallest = 7 - 2 = 5 etc. etc. You get the idea Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 2015 messages Followed by: 31 members Upvotes: 470 lheiannie07 wrote: The “primeness” of a positive integer x is defined as the positive difference between its largest and smallest prime factors. Which of the following has the greatest primeness? A) 10 B) 12 C) 14 D) 15 E) 18 How will i start to solve this? Can any experts help me? OA C A) 10: Factors of 10 are: 1, 2, 4, 5, and 10; the largest prime factor = 5 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 5 - 2 = 3. B) 12: Factors of 12 are: 1, 2, 3, 4, 6, and 12; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 - 2 = 1. C) 14: Factors of 14 are: 1, 2, 7, and 14; the largest prime factor = 7 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 7 - 2 = 5. D) 15: Factors of 15 are: 1, 3, 5, and 15; the largest prime factor = 5 and the smallest prime factor = 3; thus, the difference between the largest and the smallest prime factors = 5 - 3 = 2. E) 18: Factors of 18 are: 1, 2, 3, 6, 9, and 18; the largest prime factor = 3 and the smallest prime factor = 2; thus, the difference between the largest and the smallest prime factors = 3 - 2 = 1. The greatest difference is 5 for number 14 (option C). The correct answer: C Hope this helps! Download free ebook: Manhattan Review GMAT Quantitative Question Bank Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Hyderabad | Mexico City | Toronto | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi lheiannie07, This question literally tells you to use prime factorization on the each of the 5 answer choices - as we're looking for the answer with the largest DIFFERENCE between its largest and smallest prime factors. Answer A: 10 = (2)(5) Answer B: 12 = (2)(2)(3) Answer C: 14 = (2)(7) Answer D: 15 = (3)(5) Answer E: 18 = (2)(3)(3) Looking at these options, the largest difference isn't hard to spot... Final Answer: C GMAT assassins aren't born, they're made, Rich • Award-winning private GMAT tutoring Register now and save up to$200

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