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Problem Solving on Set Theory

This topic has 2 expert replies and 1 member reply
mohaprasad Newbie | Next Rank: 10 Posts Default Avatar
Joined
02 Feb 2014
Posted:
2 messages

Problem Solving on Set Theory

Post Wed Feb 19, 2014 4:53 pm
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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GMAT/MBA Expert

Post 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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GMAT/MBA Expert

Patrick_GMATFix GMAT Instructor
Joined
21 May 2010
Posted:
1053 messages
Followed by:
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Upvotes:
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Post Thu Feb 20, 2014 12:51 am
This is a great question; the full solution below is taken from the GMATFix App (QID 8412).



-Patrick

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tomada Master | Next Rank: 500 Posts
Joined
25 Jan 2010
Posted:
406 messages
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Upvotes:
23
Test Date:
March 14, 2014
GMAT Score:
740
Post 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.

http://gmatclub.com/forum/of-the-84-parents-who-attended-a-meeting-at-a-school-35-volunteered-111450.html

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