Sets problem

Let the number of parents who volunteered to bring refreshments only be x.
Let the number of parents who neither volunteered to supervise children nor volunteered to bring refreshments be y.
It is given that 11 parents volunteered to both supervise children and bring refreshments.
So 11+x parents volunteered to bring refreshments.
So 11+x = 1.5y.
Also 35+x+y = 84.
From this we have y = 24.
So 1.5y = 36.
Or 11+x = 36.
Or numbrer of parents who volunteered to bring refreshments is 36.

The correct answer is (B).

kvcpk wrote: ↑

Sat Jun 05, 2010 2:47 am

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

Can someone please explain me the soluton. I think that the OG's solution is wrong. this is review problem from OG12.

OA is B

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).
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

kvcpk wrote: ↑

Sat Jun 05, 2010 2:47 am

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

Can someone please explain me the soluton. I think that the OG's solution is wrong. this is review problem from OG12.

OA is B

Solution:

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