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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

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

by BTGmoderatorLU » Fri Jan 11, 2019 2:05 pm

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

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Source: Beat The GMAT — Problem Solving | Fri Jan 11, 2019 2:05 pm

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Fri Jan 11, 2019 2:28 pm

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.
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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Fri Jan 11, 2019 3:35 pm

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

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pm; Thanked: 59 times; Followed by:33 members

by fskilnik@GMATH » Mon Jan 14, 2019 4:28 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Mon Jan 14, 2019 5:52 pm

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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