Help me understand GMATprep PS#24

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,

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.

answer is 6

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