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

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Of the 84 parents who attended a meeting at a school, 35 vol [#permalink] New post 29 Jun 2020, 05:29
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Question Stats:

66% (03:00) correct 33% (00:00) wrong based on 3 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
[Reveal] Spoiler: OA

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Re: Of the 84 parents who attended a meeting at a school, 35 vol [#permalink] New post 29 Jun 2020, 05:29
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Re: Of the 84 parents who attended a meeting at a school, 35 vol [#permalink] New post 29 Jun 2020, 06:40
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Carcass 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


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

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

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Re: Of the 84 parents who attended a meeting at a school, 35 vol   [#permalink] 29 Jun 2020, 06:40
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Of the 84 parents who attended a meeting at a school, 35 vol

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