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
Answer: B
Source: Official Guide
Of the 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and
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One 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).Gmat_mission wrote: ↑Sun Sep 12, 2021 8:27 amOf 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
Answer: B
Source: Official Guide
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 righthand 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: 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/financemajo ... 67425.html
Medium Problem Solving questions
 https://www.gmatprepnow.com/module/gmat ... /video/920
 https://www.beatthegmat.com/postedspeed ... 72374.html
 https://www.beatthegmat.com/motelt271938.html
 https://www.beatthegmat.com/oftheappli ... 70255.html
 https://www.beatthegmat.com/openingnigh ... 64869.html
 https://www.beatthegmat.com/atleast100 ... 74669.html
 https://www.beatthegmat.com/prblemsolvingt279424.html
Difficult Problem Solving questions
 https://www.gmatprepnow.com/module/gmat ... /video/946
 https://www.beatthegmat.com/ratioproblemt268339.html
 https://www.beatthegmat.com/overlapping ... 65223.html
 https://www.beatthegmat.com/fractionst264254.html
 https://www.beatthegmat.com/overlapping ... 64092.html
 https://www.beatthegmat.com/mba/2011/05/ ... question2
Easy Data Sufficiency questions
 https://www.gmatprepnow.com/module/gmat ... /video/943
 https://www.beatthegmat.com/forwhatper ... 70596.html
 https://www.beatthegmat.com/dsquestt187706.html
Medium Data Sufficiency questions
 https://www.beatthegmat.com/setsmatrixdst271914.html
 https://www.beatthegmat.com/eachofpeop ... 71375.html
 https://www.beatthegmat.com/amanufacturert270331.html
 https://www.beatthegmat.com/incostumef ... 69355.html
 https://www.beatthegmat.com/mba/2011/05/ ... question1
Difficult Data Sufficiency questions
 https://youtu.be/dsCeqF9Kbk8
 https://www.beatthegmat.com/doublesetm ... 71423.html
 https://youtu.be/dOZ9KM1m5Hs
 https://www.beatthegmat.com/setst269449.html
 https://www.beatthegmat.com/mba/2011/05/ ... question3
Cheers,
Brent