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

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

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Question Stats:

69% (03:25) correct 31% (02:51) wrong based on 467 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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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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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jul 2012, 02:37
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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 5589 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.
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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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Kudos [?]: 47516 [0], given: 7123

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 5588 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 2912 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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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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Of the 84 parents who attended a meeting at a school, 35 volunte [#permalink]  26 Jan 2015, 04:05
I find the best way to do these types of problems is to create a table and fill in the information

Refreshments No Refreshments Total
Supervise 11 24 35
No supervise x
Total 1.5x 84

I figured out the 24, by the fact that the number who volunteered to do both was 11 and the total number who volunteered to supervise children was 35, so the number who volunteered to only supervise children was 24.

from this chart, we know that 84-1.5x=24+x
Therefore, 60=2.5x and x equals 24

However, we are looking for the total number of parents who volunteered to bring refreshments, which is 1.5x or 36 (B)
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  26 Jan 2015, 11:49
Expert's post
Hi All,

This is an example of a modified Overlapping Sets question. While it's wordy, it's based on simple Arithmetic and little bit of Algebra, so it's not inherently a high-level question. You can see from the thread that there are several different ways to approach it and none are really all that complicated (it's more a matter of how you organize the information than anything else). There was a comment about how it couldn't be a 750-level question and that's true. It's not.

While just about everyone sees at least one Overlapping Sets question on Test Day, the adaptive nature of GMAC's scoring algorithm means that the version that YOU see might come with a "quirk" or a "twist" (depending on when it shows up and how well you're performing). The basic organizational approaches are the same though (and the Tic-Tac-Toe Board tends to best handle all of the variations, so it's worth practicing).

GMAT assassins aren't born, they're made,
Rich
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  06 May 2015, 18:28
This question is confusing me so if anyone could explain in detail I would really appreciate it. I don't understand why it isn't solved the same way as practice question 6... in that question you had Brand A + Brand B + both brands + neither brands = 200 and the answer was 15... on this question though, it is leaving out AND part (11) out of the results. Why isn't it 24 + 1.5x + 11 + × = 84?!?!
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  07 May 2015, 00:38
danepenell wrote:
This question is confusing me so if anyone could explain in detail I would really appreciate it. I don't understand why it isn't solved the same way as practice question 6... in that question you had Brand A + Brand B + both brands + neither brands = 200 and the answer was 15... on this question though, it is leaving out AND part (11) out of the results. Why isn't it 24 + 1.5x + 11 + × = 84?!?!

Hi danepenell

Please post practice question 6 (or the link for it) here and I'll be happy to help with your doubt.
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  07 May 2015, 01:44
Expert's post
danepenell wrote:
This question is confusing me so if anyone could explain in detail I would really appreciate it. I don't understand why it isn't solved the same way as practice question 6... in that question you had Brand A + Brand B + both brands + neither brands = 200 and the answer was 15... on this question though, it is leaving out AND part (11) out of the results. Why isn't it 24 + 1.5x + 11 + × = 84?!?!

It's {Group 1} + {Group 1} - {Both} + {Neither} = {Total}

You CAN solve this problem with this formula:
{refreshments} + {supervise} - {both} + {Neither} = {Total}

35 + 1.5x - 11 + x = 84
x = 24.
1.5x = 36.

Hope it helps.

P.S. Practice question 6 is here: of-the-84-parents-who-attended-a-meeting-at-a-school-135191.html
All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  07 May 2015, 09:32
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danepenell wrote:
This question is confusing me so if anyone could explain in detail I would really appreciate it. I don't understand why it isn't solved the same way as practice question 6... in that question you had Brand A + Brand B + both brands + neither brands = 200 and the answer was 15... on this question though, it is leaving out AND part (11) out of the results. Why isn't it 24 + 1.5x + 11 + × = 84?!?!

Hi danepenell,

The underlying concept behind both the questions is the same. However, there is slight change in the way the information has been provided. Let me explain with a venn diagram.

In the questions with two overlapping sets a + b + c + d = Total no. of objects. In both the questions, the same concept has been used.

However there is a difference between the way information has been provided. Let's see how.

In this question let's assume group 1 = parents who volunteer to supervise children and group 2 =parents who bring refreshements

The question gives us the value of no. of parents who volunteer to supervise children = 35. Please note that this includes parents who only supervise children as well as parents who supervise children and bring refreshments both. So, a + b = 35. Also, parents who volunteer to supervise children as well as bring refreshment = b = 11. So, we can write the value of a = 24.

Since we are also told that no. of parents who volunteered to bring refreshment is 1.5 times the no. of parents who neither volunteered to supervise children nor bring refreshment, we can write b + c = 1.5d. Note here that parents who volunteered to bring refreshments include parents who only bring refreshments as well as parents who bring refreshments and supervise children both.

Since a + b + c + d = Total number of parents = 84, we can write 24 + (b + c) + d = 84. Since b + c = 1.5d, 24 + 2.5d = 84 which gives us the value of d = 24 and hence b + c = 1.5*24 = 36.

For every set question, please keep an eye on the use of word "Only". In this case the question asked the number of parents who volunteered to bring refreshments which also included parents who volunteered to supervise the children as well as bring refreshments.

In practice question no. 6, note the use of word "Only". The question there uses the term extensively to segregate the users of the brands. For your reference, in Q6 we can write the value of a = 60, b = x, c = 3x and d = 80 assuming group 1 as users of brand A and group 2 as users of brand B.

Hope its clear! Let me know if you still have trouble at any point of the explanation.

Regards
Harsh
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]  31 May 2015, 14:18
Given:

{Total} = {Supervise} + {Refreshments} - {Both} + {Neither}

Given:

{Refreshments} = 1.5 {Neither}

Calculations:

84 = 35 + 1.5 {Neither} - 11 + {Neither}

84 + 11 - 35 = 2.5 {Neither}

60 = 2.5 {Neither}

{Neither} = 24

{Refreshments} = 1.5 {Neither} = 1.5 {24} = 36
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Of the 84 parents who attended a meeting at a school, 35 [#permalink]  02 Jun 2015, 08:26
Expert's post
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?

Let's say that a = supervise group, b = supervise and refreshment group c = neither
a + b + c = 84
b = ?

a is 35 - 11 = 24 (We subtract so as not to double count those who volunteered for both)
24 + b + c = 84 => b + c = 60
=> c = 60 - b

We're told that b = 1.5c. You can substitute for c.
b = 1.5 (60-b) => 90 - 1.5b
2.5b = 90
b = 36

A) 25
B) 36
C) 38
D) 42
E) 45
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Of the 84 parents who attended a meeting at a school, 35   [#permalink] 02 Jun 2015, 08:26
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