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

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Math Expert
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Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jul 2012, 01:18
Expert's post
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Difficulty:

55% (hard)

Question Stats:

68% (03:24) correct 32% (02:52) wrong based on 370 sessions
Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring 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 of the parents volunteered to bring refreshments?

(A) 25
(B) 36
(C) 38
(D) 42
(E) 45

Diagnostic Test
Question: 14
Page: 22
Difficulty: 650
[Reveal] Spoiler: OA

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Kudos [?]: 40298 [1] , given: 5420

Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jul 2012, 01:19
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SOLUTION

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring 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 of the parents volunteered to bring refreshments?

(A) 25
(B) 36
(C) 38
(D) 42
(E) 45

Look at the matrix below:

Notice that numbers in black are given and in red are calculated. We need the value of yellow box: $$1.5x+(24+x)=84$$ --> $$x=24$$ --> $$1.5x=36$$.

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Kudos [?]: 33 [0], given: 11

Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jul 2012, 02:11
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Total = 84
who volunteered for picnic = 35
who volunteered for picnic & refr = 11
then -who opt picnic but not refreshmnt = 24
the no. of parents who didnt volunteer for picnic and refesh = x
the no. who volunteer for refreshmnt = 1.5 x

1.5x + 24 = 35
x= 24
1.5x = 36

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jul 2012, 02:37
1
KUDOS
Quote:
Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring 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 of the parents volunteered to bring refreshments?

(A) 25
(B) 36
(C) 38
(D) 42
(E) 45

Hi,

Difficulty level: 600

let, number of parents who neither bring refreshment nor supervise = x
Attachment:

venn2.jpg [ 11.03 KiB | Viewed 4453 times ]

then,
35-11+1.5x+x=84
x = 24
or Parents who bring refreshment = 1.5x = 36

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Last edited by cyberjadugar on 09 Jul 2012, 00:00, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 27053
Followers: 4183

Kudos [?]: 40298 [0], given: 5420

Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  06 Jul 2012, 02:05
Expert's post
SOLUTION

Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered both to supervise children during the picnic and to bring refreshments to the picnic. If the number of parents who volunteered to bring 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 of the parents volunteered to bring refreshments?

(A) 25
(B) 36
(C) 38
(D) 42
(E) 45

Look at the matrix below:
Attachment:

OG.PNG [ 5.62 KiB | Viewed 4426 times ]
Notice that numbers in black are given and in red are calculated. We need the value of yellow box: $$1.5x+(24+x)=84$$ --> $$x=24$$ --> $$1.5x=36$$.

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  22 Jun 2014, 06:16
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Of the 84 parents who attended a meeting at a school, 35 [#permalink]  23 Jun 2014, 00:00
Refer diagram below

We require to find x (Red shaded region)

$$35 + x - 11 + \frac{10x}{15} = 84$$

x = 36

Attachments

venn2.jpg [ 27.56 KiB | Viewed 1778 times ]

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  09 Jul 2014, 08:33
kashishh wrote:
Total = 84
who volunteered for picnic = 35
who volunteered for picnic & refr = 11
then -who opt picnic but not refreshmnt = 24
the no. of parents who didnt volunteer for picnic and refesh = x
the no. who volunteer for refreshmnt = 1.5 x

1.5x + 24 = 35
x= 24
1.5x = 36

Hi
the no. who volunteer for refreshmnt = 1.5 x
but no. who did refreshment but not picnic = 1.5x- 11????? why we don't apply this step just like we did for picnic numbers???

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Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
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Kudos [?]: 866 [0], given: 193

Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  09 Jul 2014, 17:33
GGMAT760 wrote:
kashishh wrote:
Total = 84
who volunteered for picnic = 35
who volunteered for picnic & refr = 11
then -who opt picnic but not refreshmnt = 24
the no. of parents who didnt volunteer for picnic and refesh = x
the no. who volunteer for refreshmnt = 1.5 x

1.5x + 24 = 35
x= 24
1.5x = 36

Hi
the no. who volunteer for refreshmnt = 1.5 x
but no. who did refreshment but not picnic = 1.5x- 11????? why we don't apply this step just like we did for picnic numbers???

Hope I got the question right

11 (who volunteered for picnic & refr) is common in both. So it has to be subtracted from ANY ONE
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Re: Of the 84 parents who attended a meeting at a school, 35   [#permalink] 09 Jul 2014, 17:33
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