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

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Intern
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Of the 84 parents who attended a meeting at a school, 35 [#permalink] New post 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
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My answer (B) [#permalink] New post 16 Apr 2007, 06:39
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

my answer is (B)
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 [#permalink] New post 16 Apr 2007, 06:50
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

Answer: B
  [#permalink] 16 Apr 2007, 06:50
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Of the 84 parents who attended a meeting at a school, 35

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