subsets

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:06 pm

How many different subsets of the set 10,14,17,24 are there that contain an odd number of elements?

A) 3
B) 6
C) 8
D) 10
E) 12

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Source: Beat The GMAT — Problem Solving | Wed Feb 10, 2010 11:06 pm

harsh.champ: Legendary Member; Posts: 1132; Joined: Mon Jul 20, 2009 3:38 amFollowed by: 6 members; Location: India; Thanked: 64 times; GMAT Score:760

by harsh.champ » Wed Feb 10, 2010 11:09 pm

shashank.ism wrote:How many different subsets of the set 10,14,17,24 are there that contain an odd number of elements?

A) 3
B) 6
C) 8
D) 10
E) 12

Case 1- 1 element:-4C1 = 4
Case 2- 3 elements:-4C3 = 4
Thus,the ans. is 8.

The different subsets are
10,
14,
17,
24,
10, 14, 17
14 17 24
17 24 10
24 10 14

Hence,8.C

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Wed Feb 10, 2010 11:17 pm

harsh.champ wrote:
shashank.ism wrote:How many different subsets of the set 10,14,17,24 are there that contain an odd number of elements?

A) 3
B) 6
C) 8
D) 10
E) 12
Case 1- 1 element:-4C1 = 4
Case 2- 3 elements:-4C3 = 4
Thus,the ans. is 8.

The different subsets are
10,
14,
17,
24,
10, 14, 17
14 17 24
17 24 10
24 10 14

Hence,8.C

Harsh can we generalize something for a bigger problem or we will have to just go through the possible sets.
as you have given all the possible sets which is 8 in number here.

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komal: Legendary Member; Posts: 777; Joined: Fri Jan 01, 2010 4:02 amFollowed by: 47 members; Location: Mumbai, India; Thanked: 117 times

by komal » Tue Feb 16, 2010 11:00 am

shashank.ism wrote:How many different subsets of the set 10,14,17,24 are there that contain an odd number of elements?

A) 3
B) 6
C) 8
D) 10
E) 12

4c1.........for 1 element set
4c3 ...........for 3 elements set

adding 4c1+4c3 we get 8..

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