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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 ##### 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 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 Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: 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 Source: Veritas Prep We must recall the rule that two consecutive integers do not share the same prime factors. We see that x breaks into all the prime factors from 2, 3, 5, â€¦, 23 Since x + 1 wonâ€™t have any of the prime factors from 2 to 23, the smallest prime factor of x + 1 is greater than 25. Alternate Solution: Notice that x = 2 * 4 * 6 * â€¦ * 50 = (2^25)*25!. Now, x + 1 will have a remainder of 1 when divided by all the prime numbers less than 25 (because all the prime numbers less than 25 is a factor of 25!). Thus, the smallest prime factor of x + 1 must be 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 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12999 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: 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 Source: Veritas Prep Here's a very similar (official) question to practice with: https://www.beatthegmat.com/arthemetic-question-on-factors-and-prime-numbers-t275643.html 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 22 Aug 2016 Posted: 1984 messages Followed by: 30 members Upvotes: 470 BTGmoderatorDC wrote: 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 Source: Veritas Prep We have x = 2.4.6.8.....48.50 = (2.1).(2.2).(2.3).........(2.24).(2.25 ) = 2^(25)*(1.2.3........25) = 2^(25)âˆ-25! You may note that 2^(25)âˆ-25! is divisible by all the prime numbers less than 25. Again, note that two consecutive integers are co-prime to each other, i.e., they don't share any common factor except 1. For example, 14 and 15 are consecutive integers; thus, the only common factor they share is 1. We have x and (x + 1) two consecutive integers; thus, they don't share any common factor except 1. Since x has all prime numbers from 1 to 25 as its factors, (x + 1) must not have any prime factors from 1 to 25. Thus, the smallest prime factor of (x + 1) will be greater than 25. The correct answer: E Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GMAT Classes Berlin | GMAT Prep Courses Manila | LSAT Prep Courses NYC | SAT Prep Classes Orlando | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. • Free Practice Test & Review How would you score if you took the GMAT 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 • Free Trial & Practice Exam 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 • 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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