Combinotronics GMAT PRep

[adwaitkasbekar]

Hi,

Please help me in understand this problem

Thanks

[anshumishra]

Hi,

Please help me in understand this problem

Thanks

5 - chairs
n - tables

Number of ways to select 2 chairs and 2 tables = 5C2 * nC2 = 150
=> nC2 = 150/5C2 = 150*2/(4*5) = 15
=> n(n-1)/2 = 15
=> n(n-1) = 30
=> n*(n-1) = 6*5

So, n = 6

Hence, A

[GMATGuruNY]

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 at the warehouse?

a. 6
b. 8
c. 10
d. 15
e. 30

a

150 = (total possible chair combinations) * (total possible table combinations)

Thus, number of table combinations = 150/(total possible chair combinations)

Total possible chair combinations = number of ways to choose 2 chairs from 5 choices = 5C2 = 10.
Number of table combinations = Total combinations/Chair combinations = 150/10 = 15.

Now we can plug in the answer choices, which represent the number of tables, to see which yields 15 possible combinations.

Only answer choice A works:
6C2 = 15.

The correct answer is A.