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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 the smallest of three consecutive positive integers tagged by: VJesus12 ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If n is the smallest of three consecutive positive integers ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If n is the smallest of three consecutive positive integers, which of the following must be true? (A) n is divisible by 3 (B) n is even (C) n is odd (D) (n)(n + 2) is even (E) n(n + 1)(n + 2) is divisible by 3 OA=E Source: Manhattan GMAT ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12985 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply VJesus12 wrote: If n is the smallest of three consecutive positive integers, which of the following must be true? (A) n is divisible by 3 (B) n is even (C) n is odd (D) (n)(n + 2) is even (E) n(n + 1)(n + 2) is divisible by 3 There's a nice rule says: The product of k consecutive integers is divisible by k, k-1, k-2,...,2, and 1 So, for example, the product of any 5 consecutive integers will be divisible by 5, 4, 3, 2 and 1 Likewise, the product of any 11 consecutive integers will be divisible by 11, 10, 9, . . . 3, 2 and 1 By the above rule, the product of 3 consecutive integers will be divisible by 3, 2 and 1 If we recognize that n, n+1 and n+2 represent 3 consecutive integers So, n(n + 1)(n + 2) must be divisible by 3 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! ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 965 messages Followed by: 4 members The product of 3 consecutive positive integers is divisible by 6 $$6=3*26=3âˆ-2$$, Thus the Product of $$3$$ consecutive positive integers is divisible by both $$2$$ and $$3$$, Answer must be (E) ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2801 messages Followed by: 18 members Upvotes: 43 VJesus12 wrote: If n is the smallest of three consecutive positive integers, which of the following must be true? (A) n is divisible by 3 (B) n is even (C) n is odd (D) (n)(n + 2) is even (E) n(n + 1)(n + 2) is divisible by 3 OA=E Source: Manhattan GMAT Looking at the answer choices, we see that answer choice E represents the product of 3 consecutive integers, and that product is always divisible by 3! = 6, so it also must be divisible by 3. 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 • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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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