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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 a model home, an interior decorator is tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## To furnish a room in a model home, an interior decorator is ## 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 08 Dec 2008 Posted: 12663 messages Followed by: 1246 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 – 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 GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1295 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 $? = T\,\,\,\left( {\# \,\,{\text{tables}}} \right)$ $10 \cdot C\left( {T,2} \right) = C\left( {5,2} \right) \cdot C\left( {T,2} \right) = 150\,\,\,\,\,\, \Rightarrow \,\,\,\,\,C\left( {T,2} \right) = 15$ $C\left( {T,2} \right) = 15\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\left\{ \begin{gathered} T\left( {T - 1} \right) = 30 \hfill \\ 6 \cdot 5 = 30\,\,\,\,\left( {**} \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = T = 6$ $\left( * \right)\,\,\,C\left( {T,2} \right) = \underleftrightarrow {\frac{{T\left( {T - 1} \right)\left( {T - 2} \right)!}}{{2!\,\,\left( {T - 2} \right)!\,\,}}} = \frac{{T\left( {T - 1} \right)}}{2}$ $\left( {**} \right)\,\,\,\left( { - 5} \right) \cdot \left( { - 6} \right) = 30\,\,\,\,\, \Rightarrow \,\,\,\,T = - 5\,\,\,\,\left( {{\text{not}}\,\,{\text{viable}}} \right)$ (In words: we have a second-degree equation in the variable T, and we found the two real distinct roots of it: 6 and -5. From the fact that -5 is negative, our answer is really 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: 2012 messages Followed by: 15 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. Answer: A _________________ Scott Woodbury-Stewart Founder and CEO • 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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