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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 ## x is the product of all even numbers from 2 to 50, inclusive tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## x is the product of all even numbers from 2 to 50, inclusive ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Veritas Prep x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be A. Between 1 and 10 B. Between 11 and 15 C. Between 15 and 20 D. Between 20 and 25 E. Greater than 25 OA E ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that X is the product of all even numbers from 2 to 50, inclusive. We're asked to define what the smallest prime factor of (X+1) must be. This particular question is a variation on an Official question that periodically pops up in the forums. The main idea behind this prompt is: "The ONLY number that will divide into X and (X+1) is 1." In other words, NONE of the factors of X will be factors of X+1, EXCEPT for the number 1. Here are some examples: X = 2 X+1 = 3 Factors of 2: 1 and 2 Factors of 3: 1 and 3 ONLY the number 1 is a factor of both. X = 9 X+1 = 10 Factors of 9: 1, 3 and 9 Factors of 10: 1, 2, 5 and 10 ONLY the number 1 is a factor of both. Etc. Since X is (50)(48)(46)....(4)(2)....we can deduce.... 1) This product will have LOTS of different factors 2) NONE of those factors will divide into (X + 1) except for the number 1. X contains all of the primes from 2 through 23, inclusive (the 23 can be "found" in the "46"), so NONE of those primes factors will be in (X + 1). We don't have to calculate the value of the smallest prime factor though ; we know that it MUST be a prime greater than 23....and there's only one answer that fits. Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: Veritas Prep x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be A. Between 1 and 10 B. Between 11 and 15 C. Between 15 and 20 D. Between 20 and 25 E. Greater than 25 OA E x = (2)(4)(6)....(46)(48)(50) = (1)(2)(2)(2)(3)(2).....(23)(2)(24)(2)(25)(2) Notice that: x is divisible by 2. This tells us that x+1 is 1 greater than a multiple of 2. In other words, x+1 is NOT divisible by 2 x is divisible by 3. This tells us that x+1 is 1 greater than a multiple of 3. In other words, x+1 is NOT divisible by 3 x is divisible by 4. This tells us that x+1 is 1 greater than a multiple of 4. In other words, x+1 is NOT divisible by 4 x is divisible by 5. This tells us that x+1 is 1 greater than a multiple of 5. In other words, x+1 is NOT divisible by 5 . . . x is divisible by 23. This tells us that x+1 is 1 greater than a multiple of 23. In other words, x+1 is NOT divisible by 23 x is divisible by 24. This tells us that x+1 is 1 greater than a multiple of 24. In other words, x+1 is NOT divisible by 24 x is divisible by 25. This tells us that x+1 is 1 greater than a multiple of 25. In other words, x+1 is NOT divisible by 25 We see that x+1 is NOT divisible by 2 to 25 In other words, all integers from 2 to 25 are NOT factors of x+1 So, if a number IS a factor of x+1, that number must be greater than 25 Answer: E Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 members Upvotes: 43 AAPL wrote: Veritas Prep x is the product of all even numbers from 2 to 50, inclusive. The smallest prime factor of x+1 must be A. Between 1 and 10 B. Between 11 and 15 C. Between 15 and 20 D. Between 20 and 25 E. Greater than 25 OA E Two consecutive integers do not share any common prime factors. Thus, we know that x and x + 1 cannot share any of the same prime factors. We also see that x, the product of the even numbers from 2 to 50, contains prime factors of 2, 3, 5, 7, 11, 13, 17,19, and 23. Thus, since x contains the primes from 2 to 23, we see that the smallest prime factor of x + 1 must be at least 29, i.e., greater than 25. Answer: E _________________ 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 • Magoosh Study with Magoosh GMAT prep 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 Veritas GMAT Class Experience Lesson 1 Live Free 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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