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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 ## To furnish a room in model home, an interior decorator is to tagged by: BTGmoderatorLU ##### This topic has 4 expert replies and 0 member replies ### Top Member ## To furnish a room in model home, an interior decorator is to ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: GMAT Prep To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 The OA is A ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15023 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: GMAT Prep To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 Since 150 combinations are possible, we get: (number of ways to choose 2 chairs)(number of ways to choose 2 tables) = 150. From 5 chairs, the number of ways to choose 2 = 5C2 = (5*4)/(2*1) = 10. Thus: (10)(number of ways to choose 2 tables) = 150 number of ways to choose 2 tables = 150/10 = 15. We can PLUG IN THE ANSWERS -- which represent the number of tables -- to see which yields 15 ways to choose 2 tables. B: 8 From 8 tables, the number of ways to choose 2 = 8C2 = (8*7)/(2*1) = 28. Too big. A smaller answer choice is needed. The correct answer is A. A: 6 From 6 tables, the number of ways to choose 2 = 6C2 = (6*5)/(2*1) = 15. Success! _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12540 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: GMAT Prep To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 The OA is A Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables) So, 150 = (# of ways to select 2 chairs)(# of ways to select 2 tables) # of ways to select 2 chairs 5 tables, choose 2 of them. Since the order of the selected chairs does not matter, we can use combinations. This can be accomplished in 5C2 ways (10 ways) Total # of combinations = (# of ways to select 2 chairs)(# of ways to select 2 tables) 150 = (10)(# of ways to select 2 tables) (# of ways to select 2 tables) = 15 # of ways to select 2 tables Let N = # of tables. We have N tables, choose 2. This can be accomplished in NC2 ways So, NC2 = 15 Our goal is to find the value of N. From here, we can just start checking answer choices. We get 6C2 = 15, so N = 6, which means there are 6 tables. Answer = A 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 09 Oct 2010 Posted: 1114 messages Followed by: 29 members Upvotes: 59 BTGmoderatorLU wrote: Source: GMAT Prep To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 $$? = T$$ $$C\left( {T,2} \right) \cdot \underbrace {C\left( {5,2} \right)}_{ = \,\,10} = 150\,\,\,\,\, \Rightarrow \,\,\,\,\,C\left( {T,2} \right) = 15$$ $${{T\left( {T - 1} \right)} \over 2} = 15\,\,\,\,\,\,\mathop \Rightarrow \limits^{T\, > \,0} \,\,\,\,\,\,? = T = 6$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1793 messages Followed by: 14 members Upvotes: 43 BTGmoderatorLU wrote: Source: GMAT Prep To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are in the warehouse? A. 6 B. 8 C. 10 D. 15 E. 30 We are given that an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables. We are also given that there are 5 chairs in the warehouse and 150 different possible combinations. We must determine the number of tables. We can let n = the number of tables and create the following equation: 5C2 x nC2 = 150 [(5 x 4)/2!] x [(n x (n - 1))/2!] = 150 20/2 x (n^2 - n)/2 = 150 10 x (n^2 - n)/2 = 150 (n^2 - n)/2 = 15 n^2 - n = 30 n^2 - n - 30 = 0 (n - 6)(n + 5) = 0 n = 6 or n = -5. Since n must be positive, the number of tables is 6. 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