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Problem Solving on Set Theory

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by mohaprasad » Wed Feb 19, 2014 4:53 pm

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Hello,

Could you please assist me with the below question.
The below question is from OG13 diagnostic test Q14.

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 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
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by tomada » Wed Feb 19, 2014 6:13 pm
mohaprasad wrote:Hello,

Could you please assist me with the below question.
The below question is from OG13 diagnostic test Q14.

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 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
Looks like this question has been floating around the internet for a while. The following page contains a good explanation for how to solve this problem.

https://gmatclub.com/forum/of-the-84-par ... 11450.html
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Problem Solving on Set Theory

by Patrick_GMATFix » Thu Feb 20, 2014 12:51 am
This is a great question; the full solution below is taken from the GMATFix App (QID 8412).

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by GMATGuruNY » Thu Feb 20, 2014 3:55 am
mohaprasad wrote:Hello,

Could you please assist me with the below question.
The below question is from OG13 diagnostic test Q14.

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 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
Total = Group 1 + Group 2 - Both + Neither.

The big idea with overlapping groups is the SUBTRACT THE OVERLAP.
When we count everyone in Group 1 (those who volunteer to supervise) and everyone in Group 2 (those who volunteer to bring refreshments), those in BOTH groups (those who volunteer to do both) are counted TWICE.
Thus, we SUBTRACT THE OVERLAP -- the number in both groups -- so that these people are not double-counted.

In the problem above:
Total = 84.
Group 1 = Supervise = 35.
Both = 11.
Neither = x.
Since the number of parents who volunteered to bring refreshments was 1.5 times the number of parents who neither volunteered to supervise during the picnic nor volunteered to bring refreshments:
Group 2 = Refreshments = 1.5x.

Plugging these values into the formula, we get:

84 = 35 + 1.5x - 11 + x
84 = 24 + 2.5x
x = 60/(2.5) = 600/25 = 24.

Thus:
Refreshments = (1.5)x = (1.5)(24) = 36.

The correct answer is B.
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by Scott@TargetTestPrep » Thu Apr 12, 2018 3:56 pm
mohaprasad wrote:Hello,

Could you please assist me with the below question.
The below question is from OG13 diagnostic test Q14.

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 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
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, then Refreshment = 1.5 x 24 = 36.

Answer: B

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Problem Solving on Set Theory

by Brent@GMATPrepNow » Thu Aug 09, 2018 6:15 am
mohaprasad 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 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
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:
Image

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
Image


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.
Image

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




NOTE: 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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/finance-maj ... 67425.html

Medium Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/920
- https://www.beatthegmat.com/posted-spee ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appl ... 70255.html
- https://www.beatthegmat.com/opening-nig ... 64869.html
- https://www.beatthegmat.com/at-least-10 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.gmatprepnow.com/module/gmat- ... /video/946
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping ... 64092.html
- https://www.beatthegmat.com/mba/2011/05 ... question-2

Easy Data Sufficiency questions
- https://www.gmatprepnow.com/module/gmat- ... /video/943
- https://www.beatthegmat.com/for-what-pe ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peo ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume- ... 69355.html
- https://www.beatthegmat.com/mba/2011/05 ... question-1

Difficult Data Sufficiency questions
- https://youtu.be/dsCeqF9Kbk8
- https://www.beatthegmat.com/double-set- ... 71423.html
- https://youtu.be/dOZ9KM1m5Hs
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05 ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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