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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 home library consisting of 108 books, some hardcover ##### This topic has 3 expert replies and 1 member reply ### Top Member ## In a home library consisting of 108 books, some hardcover ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library? A) 18 B) 40 C) 67 D) 72 E) 96 OA C Source: Veritas Prep ### GMAT/MBA Expert GMAT Instructor Joined 09 Apr 2015 Posted: 1461 messages Followed by: 17 members Upvotes: 39 Top Reply BTGmoderatorDC wrote: In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library? A) 18 B) 40 C) 67 D) 72 E) 96 Since 2/3 of the hardcover are nonfiction as opposed to only 1/4 of the softcover, we want as many hardcover books as possible in the library if we want to determine the greatest possible number of nonfiction books. However, we can we canâ€™t have all 108 books as hardcover books since itâ€™s stated that there is a least one softcover book. In fact, the number of softcover books must be a multiple of 4 since exactly 1/4 of them are nonfiction. Similarly, the number of hardcover books must be a multiple of 3 since exactly 2/3 of the hardcover books are nonfiction. Since we want the greatest possible number of nonfiction books in this home library and the fraction of hardcover that is nonfiction is greater than that of softcover, we want as many hardcover books as possible and as few softcover books as possible. Letâ€™s say there are 4 softcover books in the library; then there would be 104 hardcover books. However, 104 is not a multiple of 3. Now letâ€™s try 8 softcover books; then there would be 100 hardcover books. However, 100 is not a multiple of 3, either. Finally, letâ€™s try 12 softcover books; then there would be 96 hardcover books, and 96 is a multiple of 3. Thus, the greatest possible number of nonfiction books in the library is: â…"(96) + Â¼(12) = 64 + 3 = 67 Answer: C _________________ Jeffrey Miller Head of GMAT Instruction ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12563 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 Top Reply The concept tested here is the same as is tested in this official GMAT question: https://www.beatthegmat.com/og-help-problem-t286349.html Give it a try. Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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 May 2010 Posted: 15029 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: In a home library consisting of 108 books, some hardcover and some softcover, exactly 2/3 of the hard cover and exactly 1/4 of the softcover books are nonfiction. What is the greatest possible number of nonfiction books in this home library? A) 18 B) 40 C) 67 D) 72 E) 96 Goal: To MAXIMIZE the number of nonfiction books. Since the fraction of hardcover books that are nonfiction (2/3) is greater than the fraction of softcover books that are nonfiction (1/4), the number of nonfiction books will be maximized if we must MAXIMIZE THE NUMBER OF HARDCOVER BOOKS. Since 2/3 of the hardcover books are nonfiction, the total number of hardcover books must be a MULTIPLE OF 3. Since 1/4 of the softcover books are nonfiction, the total number of softcover books must be a MULTIPLE OF 4. Some some of the books must be softcover, not all 108 books may be hardcover. The greatest possible multiple of 3 that is less than 108 is 105. Starting with 105, test decreasing multiples of 3 for the hardcover books until a multiple of 4 is yielded for the number of softcover books. Options: Hard = 105, soft = 108-105 = 3. Hard = 102, soft = 108-102 = 6. Hard = 99, soft = 108-99 = 9. Hard = 96, soft = 108-96 = 12. The option in blue yields a multiple of 4 for the number of softcover books. Implication: Greatest number of hardcover books that could be nonfiction = (2/3)(96) = 64. Resulting number of softcover books that are nonfiction = (1/4)(12) = 3. Thus: Greater number of books that could be nonfiction = 64+3 = 67. The correct answer is C. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 737 messages Followed by: 4 members To get the greatest number of non-fiction books, hardcover needs to be maximized while softcover minimized. S = 12 H = 96 1/4*S = 3 2/3*H = 64 3 + 64 = 67. Hence, C is the correct answer. Regards! • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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 • Magoosh Study with Magoosh GMAT prep 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 GMAT Exam Know how you'd score today for$0

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