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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 ## Range Problem.,... ##### This topic has 3 expert replies and 3 member replies ## Range Problem.,... Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X? (A) 14 (B) 16 (C) 17 (D) 20 (E) 26 ### GMAT/MBA Expert GMAT Instructor Joined 28 Sep 2011 Posted: 349 messages Followed by: 54 members Upvotes: 236 Test Date: 6/14/11 GMAT Score: 770 Viren1808 wrote: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X? (A) 14 (B) 16 (C) 17 (D) 20 (E) 26 Y is the product of all of the elements and 11Y is even. 11 is odd, so for 11Y to be even, Y must be even. A product of a set of integers is even if and only if at least one of the integers is even. All of the numbers in the set thus far are odd, so if the product is even, K must be even. The only even prime number is 2, so K=2. The range is equal to the largest value minus the smallest value, so range=19-2=17 Ans: c. 17 _________________ Pete Ackley GMAT Math Pro Free Online Tutoring Trial Community Manager Joined 13 May 2011 Posted: 1060 messages Followed by: 52 members Upvotes: 318 Test Date: October 15th 2012 Viren1808 wrote: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X? (A) 14 (B) 16 (C) 17 (D) 20 (E) 26 Y = Product of all the elements in set X = 11*3*7*K*17*19 11y = 11*11*3*7*K*17*19 is an even number. For the product to be even the number K should be an even number and a prime. The only even prime in the number set is 2. So, the value of K is 2.Range of the set is equal to the difference between the highest and the least number. Range = 19-2 = 17 Answer C _________________ Anil Gandham Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch Check out GMAT Prep Nowâ€™s online course at https://www.gmatprepnow.com/ Newbie | Next Rank: 10 Posts Joined 15 Sep 2011 Posted: 9 messages Test Date: 12/6/11 Target GMAT Score: 700+ I worked backwards on this one. The question said 11 x product of the set = even. in other words, odd (11) x even = even. Thus, the product of the set must be even. The question tells us that the set consists of only prime numbers. We know that the only even and prime number is 2. So K must be 2. Greatest number in the set = 19. 19 - 2 = 17 (C) Senior | Next Rank: 100 Posts Joined 20 Dec 2018 Posted: 33 messages 11Y will be even if Y is even. Y = product of all elements in the set. There is no even no in the set X. So, â€˜kâ€™ should be even to make y even. There is only one even prime no i.e. 2. So, k = 2 The set X becomes {2, 3, 7, 11, 17, 19}. Range of the set = highest element - lowest element = 19 - 2 = 17 ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Viren1808 wrote: Set X consists of prime numbers {3, 11, 7, K, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X? (A) 14 (B) 16 (C) 17 (D) 20 (E) 26 Since 11Y is even, Y is even and hence K must be even also. Since 2 is the only even prime number, K is 2. Thus, the range of set X is 19 - 2 = 17. Answer: C _________________ 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that Set X consists of PRIME numbers {3, 11, 7, K, 17, 19}, the integer Y represents the PRODUCT of all elements in Set X and 11Y is an EVEN number. We're asked for the RANGE of Set X. This question is based on several Number Property rules - and doesn't actually require much math to solve. To start, when dealing with a RANGE, it helps to put the existing elements in order from least to greatest: {3, 7, 11, 17, 19.... and K}. It's important to note that we do NOT know what K is - we know that it's PRIME, so it could be as small as 2 or as large as whatever the largest possible prime is... Notice how the 5 numbers that we are given are ALL ODD numbers; thus, the product of those 5 ODDS would be a larger ODD number. We're told that Y is the PRODUCT of the 6 numbers.... so Y = (big-odd-number)(K). However, we're told that 11Y = EVEN; that can only happen when Y is an EVEN number. Thus, if Y = EVEN = (big-odd-number)(K) then K must also be EVEN. The only even prime number is 2, which makes Set X = {2, 3, 7, 11, 17, 19} with a range of 19 - 2 = 17 Final Answer: C GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep 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 • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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