Source: Gmat Prep, mba.com, Test II
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its desert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
a. 8
b. 12
c. 15
d. 21
e. 27
I will post the answer later. Thanks!
GMAT Forum
3 postsPage 1 of 1
- dbernst
- ManhattanGMAT Staff
- Posts: 300
- Joined: Mon May 09, 2005 9:03 am
There are several manners to approach combinatorics problems, and the above approach is perfectly correct. However, because we strongly encourage consistency, I will also explain this problem in terms of the Manhattan GMAT "Anagram Grid" strategy. This will help our current and future MGMAT students (which we hope includes you!).
For this problem there are two scenarios:
1. two cheese and two fruit
2. one cheese and one fruit
In each senario, the "cheese grid" will have six spaces and the "fruit grid" will have two spaces.
Scenario 1: "cheese grid" = YYNNNN; "fruit grid" = YY
Thus, the solution for the cheese is 6!/2!4! = 15 and the fruit is 2!/2! =1. Therefore, there are (15)(1) = 15 options
Scenario 2: "cheese grid" = YNNNNN; "fruit grid" = YN
Thus, the solution for the cheese is 6!/1!5! = 6 and the fruit is 2!/1!1! =2. Therefore, there are (6)(2) = 12 options
Scenario 1 + Scenario 2 = 27 Options. The correct answer is E.
For this problem there are two scenarios:
1. two cheese and two fruit
2. one cheese and one fruit
In each senario, the "cheese grid" will have six spaces and the "fruit grid" will have two spaces.
Scenario 1: "cheese grid" = YYNNNN; "fruit grid" = YY
Thus, the solution for the cheese is 6!/2!4! = 15 and the fruit is 2!/2! =1. Therefore, there are (15)(1) = 15 options
Scenario 2: "cheese grid" = YNNNNN; "fruit grid" = YN
Thus, the solution for the cheese is 6!/1!5! = 6 and the fruit is 2!/1!1! =2. Therefore, there are (6)(2) = 12 options
Scenario 1 + Scenario 2 = 27 Options. The correct answer is E.
Source: Gmat Prep, mba.com, Test II
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its desert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer?
a. 8
b. 12
c. 15
d. 21
e. 27
3 posts Page 1 of 1