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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 volunteered [#permalink]

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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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Last edited by Bunuel on 15 Nov 2017, 05:09, edited 2 times in total.
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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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GMATD11 wrote:
14) 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

when to use double set matrix and when to use venn diagram for two type of information


Most GMAT questions can be easily and quickly solved using Venn Diagrams. (Different people prefer different strategies but I have found that no matter how tricky the question wording is, once you draw the Venn diagram, it all seems very clear)

Check out the Venn diagram for this question:
Attachment:
Ques2.jpg
Ques2.jpg [ 13.38 KiB | Viewed 26348 times ]

Now, since it is given that
x+11 = 1.5 (84-(24+11+x))
x = 25
So number of parents who volunteered to bring refreshments = x+11 = 25+11 = 36
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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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This can be solved by using Double Matrix too, depends on what you're comfortable with. Please see the attached image.

So 2.5x + 24 = 84

=> 2.5x = 60

=> x = 600/25 = 24

=> 1.5x = 36

Answer - B
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Parents_Meeting.png
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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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neither volunteered to supervise children during the picnic nor volunteered to bring refreshments = x
number of parents volunteered to bring refreshments = 1.5x
so, 84 = 35 + 1.5x - 11 + x
2.5x = 60
x = 24
Thus, number of parents volunteered to bring refreshments = 24*1.5=36
Ans. B
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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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New post 25 Feb 2012, 21:13
Baten80 wrote:
neither volunteered to supervise children during the picnic nor volunteered to bring refreshments = x
number of parents volunteered to bring refreshments = 1.5x
so, 84 = 35 + 1.5x - 11 + x
2.5x = 60
x = 24
Thus, number of parents volunteered to bring refreshments = 24*1.5=36
Ans. B
Why isn't the overlap substracted also from the parents who bring refreshments?

When we are given 35 who volunteered to supervise, we substract the overlap (11), so total = 24; why isn't the final number of parents who voluntereed to refreshments = 1.5x - 11 ?

84 = (35-11) + (1.5x - 11) + x


???

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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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ElDiablo wrote:
Baten80 wrote:
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

neither volunteered to supervise children during the picnic nor volunteered to bring refreshments = x
number of parents volunteered to bring refreshments = 1.5x
so, 84 = 35 + 1.5x - 11 + x
2.5x = 60
x = 24
Thus, number of parents volunteered to bring refreshments = 24*1.5=36
Ans. B
Why isn't the overlap substracted also from the parents who bring refreshments?

When we are given 35 who volunteered to supervise, we substract the overlap (11), so total = 24; why isn't the final number of parents who voluntereed to refreshments = 1.5x - 11 ?

84 = (35-11) + (1.5x - 11) + x

???


Because parents who supervise (1.5x) consist of the parent who supervise AND bring refreshments (11) and of the parents who supervise but DO NOT bring refreshments (1.5x-11). So if we subtract 11 (the parent who supervise AND bring refreshments) we'll get the parents who supervise but DO NOT bring refreshments and no the total parents who supervise.

Generally: {Total}={Supervise}+{Refreshments}-{Both}+{Neither} (notice that we subtract {Both} since it's already included twice: once in {Supervise} and once in {Refreshments});

Given: 84=35+1.5x-11+x --> x=24 --> 1.5x=36.

Answer: B.

Below matrix might help to understand the question better:
Attachment:
Parents.PNG
Parents.PNG [ 5.62 KiB | Viewed 25085 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.

Answer: B.

Hope it's clear.
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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:

Image

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

Answer: B.

[Reveal] Spoiler:
Attachment:
Parents.PNG
Parents.PNG [ 5.62 KiB | Viewed 698 times ]

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]

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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

Answer B

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]

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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
venn2.jpg [ 11.03 KiB | Viewed 13931 times ]

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

Answer is (B)

Regards,

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 volunteered [#permalink]

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You can use a chart to help you solve this problem as taught in the MGMAT.

= S stands for Supervise and ~S means not Supervise
= R stands for Bring Refreshments and ~R means not Bring Refreshments

So how to use the chart?
= Place in the rightmost corner the total of parents which is 84.
= We know that there are 35 who volunteered to Supervise but since we do not know whether they are R or ~R, we put 35 at the bottom of column S.
= We know that there are 11 who are both S and R. So we placed 11 accordingly.
= We know those who are R is 1.5 times of those who are ~R and ~S. So we use a variable x to denote that relationship.

From the chart we can construct our equation clearly.

24 + x + 1.5X = 84

Solve for X.
X = 24

We know R = 1.5X = 1.5(24) = 36

AnsweR: B
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Re: Of the 84 parents who attended a meeting at a school, 35 volunteered [#permalink]

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summer101 wrote:
The language used in these problems confuses me!!
Example : 35 volunteered to supervise children during the school picnic ---> Only supervise + supervise & bring refreshments
However, how many of the parents volunteered to bring refreshments --> This ideally should mean: supervise & bring refreshments + Only bring refreshment.
But sadly the answer choice has value which = only bring refreshment
Any suggestions on how to go about?


You need to actively look for the word 'only' in these questions.

35 volunteered to supervise children: Overall, 35 people volunteered to supervise. This includes people who volunteered to do both - supervise and bring refreshments

35 volunteered to only supervise children: Does not include people who volunteered to do both.

How many of the parents volunteered to bring refreshments? Overall, how many volunteered to bring refreshments - it will include people who volunteered to do both. There is no ambiguity here.

How many of the parents volunteered to only bring refreshments? Now this is only refreshments.

Re-consider the calculations done above.
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Of the 84 parents who attended a meeting at a school, 35 [#permalink]

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Refer diagram below

We require to find x (Red shaded region)

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

x = 36

Answer = B
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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]

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New post 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

Answer B


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???
Please explain...

Thanks in advance

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Re: Of the 84 parents who attended a meeting at a school, 35 [#permalink]

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New post 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

Answer B


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???
Please explain...

Thanks in advance


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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New post 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]

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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).

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New post 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]

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New post 07 May 2015, 01:44
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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?!?!


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]

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New post 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.

Image

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] 07 May 2015, 09:32

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