To furnish a room in model home, an interior decorator is to

Question

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

GMATGuruNY · Answer

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!

Brent@GMATPrepNow · Answer

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

fskilnik@GMATH · Answer

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.

Scott@TargetTestPrep · Answer

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

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