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neerajkumar1_1: Master | Next Rank: 500 Posts; Posts: 270; Joined: Wed Apr 07, 2010 9:00 amFollowed by: 2 members; Thanked: 24 times

by neerajkumar1_1 » Wed Jun 23, 2010 8:50 am

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

OA:E

Help.. .thanks..

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Source: Beat The GMAT — Problem Solving | Wed Jun 23, 2010 8:50 am

sk818020: Master | Next Rank: 500 Posts; Posts: 214; Joined: Mon Mar 29, 2010 1:46 pm; Location: Houston, TX; Thanked: 37 times; GMAT Score:700

by sk818020 » Wed Jun 23, 2010 9:24 am

There are two possibilities with this problem. You either have one cheese and one fruit, or you have 2 fruits and 2 cheese. You can not have any other combinations because there must be equal amounts of both and there are only 2 different kinds of fruit.

If you use one of each then, you multiply the number of options for each group by each other. There are 6 cheeses and 2 fruits so the number of combinations for one of each would be;

6*2=12

If you have to chose 2 of each, then you need to figure out how many combinations of 2 cheese you can come up with. You don't need to worry about the fruit because no matter what the combinations of cheeses you will be using all the avaiable fruit. To figure out how many different combinations of cheese to use, you would calculate it as follows;

6!/(2!*4!)=(6*5)/2=3*5=15

To solve the problem you add the sets of options together;

12+15=27

Hope this helps.

Jared

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singhpreet1: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Tue Jun 08, 2010 11:27 am; Thanked: 7 times

by singhpreet1 » Wed Jun 23, 2010 9:26 am

neerajkumar1_1 wrote: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

OA:E

Help.. .thanks..

the only logical reasoning i can pick from this question is 6C2, that equals 15 + 6 cheeses can be selected along with 2 kinda of fruit in 12 different ways, which equals 27 therefore E.
Preet

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neerajkumar1_1: Master | Next Rank: 500 Posts; Posts: 270; Joined: Wed Apr 07, 2010 9:00 amFollowed by: 2 members; Thanked: 24 times

by neerajkumar1_1 » Wed Jun 23, 2010 9:28 am

it surely did... i was doing a calculation mistake.. for some reason i dont know why... i was calculating 6x2=8...

... my mistake... simple problem...

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