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

19. Overlapping Sets

• Theory
  Overlapping Sets Made Easy!
  How to draw a Venn Diagram for problems
  ADVANCED OVERLAPPING SETS PROBLEMS
  Formulae for 3 overlapping sets
  
  • Questions
    The E-GMAT Sets Triad: 3 Exciting Sets Questions!
    The Word “Or” in GMAT Math
    DS Questions
    PS Questions

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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:

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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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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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: \(1.5x+(24+x)=84\) --> \(x=24\) --> \(1.5x=36\).

Answer: B.


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Another approach is to use the Double Matrix Method. This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of baseball players, and the two characteristics are:
- supervised children or did not supervise children
- bring refreshments or didn't bring refreshments

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.
So, we get the following:


The number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise children during picnic nor volunteered to bring refreshments
If we let x = the number of parents who neither supervised not brought refreshments, then
1.5x = the number of parents who brought refreshments



How many of the parents volunteered to bring refreshments?
In other words, what is the value of 1.5x?
Notice that, if we add the two boxes in the right-hand column, then we see that 24+x = the total number of parents who DIDN'T bring refreshments.


At this point, we know that 1.5x = the number of parents who brought refreshments, and 24+x = the number of parents who DIDN'T bring refreshments.
We can write: 1.5x + (24 + x) = 84 (the total number of parents)
Simplify: 2.5x + 24 = 84
2.5x = 60
x = 24

We already know that 1.5x = the number of parents who brought refreshments
1.5(24) = 36
So, 36 parents brought refreshments

Answer: B

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:


EXTRA PRACTICE QUESTION


More questions to practice with:
EASY: https://gmatclub.com/forum/of-the-120-p ... 15386.html
MEDIUM: https://gmatclub.com/forum/in-a-certain ... 21716.html
HARD: https://gmatclub.com/forum/a-group-of-2 ... 24888.html
KILLER: https://gmatclub.com/forum/a-certain-hi ... 32899.html

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: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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Hi,

Difficulty level: 600

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

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

Answer is (B)

Regards,

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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Refer diagram below

We require to find x (Red shaded region)

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

x = 36

Answer = B

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

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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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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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

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

I find it easier to write the given info in the following manner:

N (Neither) -parents who will not be supervising or bringing refreshments
S (Supervising) - parents who will be only supervising
R (Refreshments) - parents who will bring refreshments only
R=1.5N

Step 1.
We know that total number of parents is 84, which is N+S+R, to find N ==>
N= 84-S-R, where S = 35-11=24
N=84-24-R
N=60-R, we already know that R=1.5N, substitute to get ==>
N=60-1.5N
2.5N=60
N=24 (24 parents will not be supervising or bringing refreshments)

Step 2.
R=1.5N, substitute to get==>
R=1.5*24
R=36 (parents will bring refreshments!!!)

We can use the following formula:

Total = Picnic + Refreshment - Both + Neither

We are given that Total = 84, Picnic = 35, Both = 11, and Refreshment = 1.5 x Neither. Thus, if we let n = Neither, we have:

84 = 35 + 1.5n - 11 + n

84 = 24 + 2.5n

60 = 2.5n

n = 60/2.5 = 600/25 = 24

Since Refreshment = 1.5 x Neither, Refreshment = 1.5 x 24 = 36.

Answer: B
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