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# Of the 84 parents who attended a meeting at a school, 35

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Intern
Joined: 16 Jun 2004
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Of the 84 parents who attended a meeting at a school, 35 [#permalink]  16 Apr 2007, 06:05
Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the scholl picnic and 11 volunteered both to supervise children during the picnic and bring refreshments to the picnic. If the number of parents who volunteered to bring the refreshments was 1.5 times the number of parents who neither volunteered to supervise children during the picnic nor volunteered to bring refreshments, how many parents volunteered to bring the refreshments?
A. 25
B. 36
C. 38
D. 42
E. 45
VP
Joined: 08 Jun 2005
Posts: 1147
Followers: 6

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Its a simple Vann Diagram:

total parents = 84

supervise = 35

supervise & refreshment = 11

refreshment= 1.5x

neither= x

hence:

35+1.5x+x-11 = 84 (you have to remember not to take 11 twice !!!)

x=24

1.5x = refreshment= 36

Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait
Followers: 12

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Break down the problem into variables as following:

T: total parents
R: parents who brought refreshments
S: parents who suprvised children
B: parents who did both S and R
N: parents who neither did S nor R

T = R + S - B + N
84 = R + 35 - 11 + N -----> R + N = 60
R = 1.5 N
1.5 N + N = 60 ---> 2.5 N = 60 --> N = 60/2.5 = 120/5 = 24 = N
So, R = 1.5 N = 1.5 x 24 = 36 = R

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