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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 ## In a group of 24 musicians, some are pianists and the rest a ##### This topic has 4 expert replies and 0 member replies ### Top Member ## In a group of 24 musicians, some are pianists and the rest a ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In a group of 24 musicians, some are pianists and the rest are violinists. Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. What is the least possible number of union members in the group? A. 12 B. 13 C. 14 D. 15 E. 16 OA B Source: Princeton Review ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: In a group of 24 musicians, some are pianists and the rest are violinists. Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. What is the least possible number of union members in the group? A. 12 B. 13 C. 14 D. 15 E. 16 OA B Source: Princeton Review We can let p = the number of pianists, v = the number of violinists, and u = the number of union members. We see that p is a multiple of 2, and v is a multiple of 3. Also, the number of violinists canâ€™t be odd; otherwise, the number of pianists would be odd. Thus, v can only be 6, 12, or 18. If v = 6, then p = 18 and u = Â½(18) + â…"(6) = 9 + 4 = 13. If v = 12, then p = 12 and u = Â½(12) + â…"(12) = 6 + 8 = 14. If v = 18, then p = 6 and u = Â½(6) + â…"(18) = 3 + 12 = 15. Of the 3 possible values of u that we have calculated (13, 14, 15), the least possible number of union members in the group is 13. Alternate Solution: We see that the number of violinists must be a multiple of 3, and the number of pianists must be an even number. We want to minimize the number of violinists, since a greater percentage of violinists are in the union. We could start with 3 violinists and 21 pianists, but this wonâ€™t work. But with 6 violinists, we have 18 pianists. Thus, we would have (2/3)(6) = 4 violinists and 18/2 = 9 pianists in the union, for a total of 13 musicians in the union. Answer: B. _________________ 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 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Top Reply BTGmoderatorDC wrote: In a group of 24 musicians, some are pianists and the rest are violinists. Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. What is the least possible number of union members in the group? A. 12 B. 13 C. 14 D. 15 E. 16 OA B Source: Princeton Review We can let p = the number of pianists, v = the number of violinists, and u = the number of union members. We see that p is a multiple of 2, and v is a multiple of 3. Also, the number of violinists canâ€™t be odd; otherwise, the number of pianists would be odd. Thus, v can only be 6, 12, or 18. If v = 6, then p = 18 and u = Â½(18) + â…"(6) = 9 + 4 = 13. If v = 12, then p = 12 and u = Â½(12) + â…"(12) = 6 + 8 = 14. If v = 18, then p = 6 and u = Â½(6) + â…"(18) = 3 + 12 = 15. Of the 3 possible values of u that we have calculated (13, 14, 15), the least possible number of union members in the group is 13. Alternate Solution: We see that the number of violinists must be a multiple of 3, and the number of pianists must be an even number. We want to minimize the number of violinists, since a greater percentage of violinists are in the union. We could start with 3 violinists and 21 pianists, but this wonâ€™t work. But with 6 violinists, we have 18 pianists. Thus, we would have (2/3)(6) = 4 violinists and 18/2 = 9 pianists in the union, for a total of 13 musicians in the union. Answer: B. _________________ 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: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: In a group of 24 musicians, some are pianists and the rest are violinists. Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. What is the least possible number of union members in the group? A. 12 B. 13 C. 14 D. 15 E. 16 In a group of 24 musicians, some are pianists and the rest are violinists. Let x = number of pianists So, 24-x = number of violinists Exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. So, the number of pianists in the union = x/2 And the number of violinists in the union = (2/3)(24-x) = 16 - 2x/3 What is the least possible number of union members in the group? Number of union members = x/2 + (16 - 2x/3) Rewrite with common denominators to get: 3x/6 + 16 - 4x/6 Simplify to get: 16 - x/6 Our goal is to MINIMIZE the value of 16 - x/6 To do so, we must MAXIMIZE the value of x/6 Since x must be divisible by 6 and since x must be less than 24, the greatest possible value of x is 18 When x = 18, we get 16 - x/6 = 16 - 18/6 = 16 - 3 = 13 Answer: B 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 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 in a group of 24 musicians, some are pianists and the rest are violinists and exactly 1/2 of the pianists and exactly 2/3 of the violinists belong to a union. We're asked for the LEAST possible number of union members in the group. This question can be approached in a couple of different ways, including the use of some Number Properties and some simple 'brute force' Arithmetic. To start, since we can't have a 'fraction' of a musician, we know a couple of things about the number of pianists and the number of violinists: -The number of pianists MUST be a multiple of 2 (since 1/2 of them are in a union) -The number of violinists MUST be a multiple of 3 (since 2/3 of them are in a union). To MINIMIZE the total number of union members, we need there to be MORE pianists (since only 1/2 of pianists are in a union vs. 2/3 of violinists). Thus, we need to add a multiple of 2 to a multiple of 3 and get a total of 24.... with the multiple of 2 being as big as possible. We can list out the first few options until we find a match: 24 total people could be: 3 violinists and 21 pianists --> NOT possible (number of pianists here is NOT a multiple of 2). 6 violinists and 18 pianists --> This matches both of the 'restrictions' in the prompt and gives us the maximum number of pianists This option gives us 6(2/3) + 18(1/2) = 4 + 9 = 13 union members. Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • 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 • Award-winning private GMAT tutoring Register now and save up to$200

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