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# Two members of a club are to be selected to represent the

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Manager
Joined: 17 Jul 2006
Posts: 50
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Two members of a club are to be selected to represent the [#permalink]  24 Oct 2006, 16:16
Two members of a club are to be selected to represent the club at a national meeting. If the re are 190 different possible selection of 2 members, How many members does the club have?

A)20
B)40
C)57
D)95
E)170

In a class of 30 student, 2 student did not borrowed any books from the library. 12 student each borrowed 1 book, 10 students ach borrowed 2 books and the rest of the students each borrowed at least 3 books. If the average (mean) number of books borrowed per students was 2. What is the maximum number of books that any student could have borrowed?

A)3
B)5
C)8
D)13
E)15
Senior Manager
Joined: 01 Sep 2006
Posts: 302
Location: Phoenix, AZ, USA
Followers: 1

Kudos [?]: 15 [0], given: 0

(1) Number of combinations of 2 for P things

PC2= P!/2!*(P-2)!=190==> P(P-1)=380===> 20*19 So P = 20

(2)

2 Students no books 2*0=0
12 students 1 book = 12*1
10 students 2 book = 10*2=20
of remianing 6
asuume 5 borroed 3 = 15
6th students n books = 6*n

(12+20+ 15+n)/30= 2 ==> 47+n=60 ==> n = 13

Director
Joined: 23 Jun 2005
Posts: 847
GMAT 1: 740 Q48 V42
Followers: 5

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Re: Two Math questions [#permalink]  24 Oct 2006, 19:57
Two members of a club are to be selected to represent the club at a national meeting. If the re are 190 different possible selection of 2 members, How many members does the club have?

A)20
B)40
C)57
D)95
E)170

C(n,2) = 190
n!/2(n-2)! = 190

n(n-1) = 380.
n=20

In a class of 30 student, 2 student did not borrowed any books from the library. 12 student each borrowed 1 book, 10 students ach borrowed 2 books and the rest of the students each borrowed at least 3 books. If the average (mean) number of books borrowed per students was 2. What is the maximum number of books that any student could have borrowed?

A)3
B)5
C)8
D)13
E)15

Total number of books borrowed = 60.
24 students already account for 32 books.
No. of students left = 6; books left = 28.
Each student borrowed at least 3 books. So 5 students borrowed 15 books. The remaining student borrowed the remaining 13 books.
Re: Two Math questions   [#permalink] 24 Oct 2006, 19:57
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# Two members of a club are to be selected to represent the

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