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# In a Maths excellence competition, there are 47 male and

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In a Maths excellence competition, there are 47 male and [#permalink]

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10 Feb 2007, 04:14
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In a Maths excellence competition, there are 47 male and female students. Among the female students:
+ 1st female student knows 16 male students.
+ 2nd female student knows 17 male students.
+ 3rd female student knows 18 male students.
...................................................................
+Last female student knows all of the male students.

How many male students are there in the competition?

A. 30
B. 31
C. 32
D .33
E. 34
Senior Manager
Joined: 04 Jan 2006
Posts: 279
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Re: PS Maths excellence competition [#permalink]

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10 Feb 2007, 06:41
laxieqv wrote:
In a Maths excellence competition, there are 47 male and female students. Among the female students:
+ 1st female student knows 16 male students.
+ 2nd female student knows 17 male students.
+ 3rd female student knows 18 male students.
...................................................................
+Last female student knows all of the male students.

How many male students are there in the competition?

A. 30
B. 31
C. 32
D .33
E. 34

1st female student knows 16 male: Total 17 students
2nd female student knows 17 male: Total 19 students
3rd female student knows 18 male: Total 21 students

Sequence: 17, 19, 21, ... And assuming f = female student
OR
17 + 2(1-0), 17 + 2(2-1), 17 + 2(3-1), ..., 17 + 2(f-1)

47 = 17 + 2(f-1)
30 = 2(f-1)
f = 16

Male students = 47 - 16 = 31

Last edited by devilmirror on 10 Feb 2007, 09:20, edited 1 time in total.
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10 Feb 2007, 07:40
+ 1st female student knows 16 male students.
+ 2nd female student knows 17 male students.
+ 3rd female student knows 18 male students.
...................................................................
+Last female student knows all of the male students

So nth female student knows (n+15) male students

So 2n + 15 =47

n = 16

Number of male students = 31
Manager
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Re: PS Maths excellence competition [#permalink]

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10 Feb 2007, 11:53
laxieqv wrote:
In a Maths excellence competition, there are 47 male and female students. Among the female students:
+ 1st female student knows 16 male students.
+ 2nd female student knows 17 male students.
+ 3rd female student knows 18 male students.
...................................................................
+Last female student knows all of the male students.

How many male students are there in the competition?

A. 30
B. 31
C. 32
D .33
E. 34

f(1) = 16
f(2) = 17
f(3) = 18
...
f(15) = 30
f(30)= 45
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11 Feb 2007, 00:49
With each female we increase by two. 1 female 1 male.

With 3 females and 18 males we have 21 and 47 - 21 = 26 or 26 more place/students. 26/2 = 13 males.

18 + 13 = 31
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