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Restaurant

by gmatblood » Wed Nov 02, 2011 12:35 pm
A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert 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

Need the easiest/Quickest method to solve :)
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by rijul007 » Wed Nov 02, 2011 12:40 pm
No of desert platter with 1 kind of cheeese and 1 kind fruit = 6*2 = 12
No of desert platter with 2 kinds of cheeese and 2 kind fruit = 6C2 * 1 = 15

Total no of platters = 27

Option E
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by GmatMathPro » Wed Nov 02, 2011 12:42 pm
Any given dessert platter could have exactly one kind of cheese and one kind of fruit, or it can have exactly 2 kinds of cheese and exactly 2 kinds of fruit.

If we have one of each there are 6 ways to choose the cheese and 2 ways to choose the fruit, for a total of 6*2=12 dessert platters.

OR

If we have two of each, there are 6C2=15 ways to choose the two kinds of cheese, and only one way to choose the two fruits for a total of 15 dessert platters.

[spoiler]12+15=27[/spoiler] possible dessert platters
Pete Ackley
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