Help me understand GMATprep PS#24

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satishkhatri5: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Sun Dec 16, 2007 3:34 pm

by satishkhatri5 » Sun Feb 03, 2008 12:32 pm

Q: To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a colelction 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 in the warehouse?

Ans Choices:
-6
-8
-10
-15
-30

Ans: 6

Please help me understand the question and solution.

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Source: Beat The GMAT — Problem Solving | Sun Feb 03, 2008 12:32 pm

TkNeo: Senior | Next Rank: 100 Posts; Posts: 96; Joined: Wed Dec 19, 2007 10:21 am; Thanked: 5 times

Re: Help me understand GMATprep PS#24

by TkNeo » Sun Feb 03, 2008 2:27 pm

satishkhatri5 wrote:Q: To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a colelction 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 in the warehouse?

Ans Choices:
-6
-8
-10
-15
-30

Ans: 6

Please help me understand the question and solution.

The question is asking you to find the number of tables in the warehouse, so that the total number of possible ways to select 2 chairs out of 5 chairs and 2 tables out of the #of tables is 150... Hope it makes sense.

Let there be N tables

# of ways to select 2 chairs out of 5 chairs = 5 C 2
# of ways to select 2 tables out of N tables = N C 2

Total ways = (5 C 2) * (N C 2) = 150
Solve for N to get 6

HTH,

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evansbd: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Jul 01, 2008 10:50 am

More insight

by evansbd » Thu Jul 17, 2008 11:08 am

This is a great type of question to see how you can use how the GMAT is structured to your advantage.

The answer choices are ALWAYS in chronological order least to greatest.

In this example, since you know you need to find n, it helps when you have to plug in a number to start with choice C. If this does not yield your answer, at least you know if A,B or C,D are feasible answers which can save you some valuable time.

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hakyology: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Tue Jun 05, 2007 1:39 pm; Thanked: 1 times

answer is 6

by hakyology » Thu Jul 17, 2008 11:29 am

answer is 6

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moliver: Senior | Next Rank: 100 Posts; Posts: 63; Joined: Wed Jul 16, 2008 6:43 am; Thanked: 3 times; GMAT Score:680

by moliver » Thu Jul 17, 2008 12:11 pm

You have 5 chairs and n tables:

5*4*n*(n-1)/(2!*2!) = 150

n*(n-1) = 150/5 = 30

look at the answer and we try with 6
6*(6-1) = 30

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