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Venn Diagram Vs. Group Box Method ?

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Venn Diagram Vs. Group Box Method ?

by famber4 » Mon Mar 30, 2009 1:54 pm
This questions is in diagnostic test of OG 11th edition Q14.

I assume it is a "group problem". I try to solve it by drawing the group box, a method taught in the princeton math workbook. But I cannot solve it using that method. The OG is using Venn Diagram to solve this question.
I understand their explanation but can anyone solve it by just using the group box?
Moreover, when to use Venn diagram? What kind of questions will demand the use of Venn Diagram? Since I there is no mention of Venn Diagram in the workbook I am studying.

For those who dont have OG, 11th edition, I am typing the whole question below:
Q14: Of 84 parents who attended a meeting at a school, 35 volunteered to supervise children during the school picnic and 11 volunteered to both supervise the children and to bring refreshments to the picnic. If the number of parents who volunteered to bring refreshmens was 1.5times the number of parents who neither volunteered to supervise children nor volunteered to bring refreshments, how many of the parents volunteered to bring refreshments?

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by Ian Stewart » Mon Mar 30, 2009 3:43 pm
I don't know what content is in the Princeton math workbook, and have no idea what a 'group box' is, but the book really ought to have something on Venn diagrams - they certainly are useful quite often on the GMAT. If it doesn't, you may want to get another book.

In any case, we use Venn diagrams when we have two or three groups or sets, and when people (or things, or whatever) can belong to more than one of the groups. Some examples of setups where you might want to use a Venn diagram:

In Town X, 50 people play golf and 40 people play tennis. Since it is, of course, possible to play both golf and tennis, this is a Venn diagram question.

In Town X, 50 people own dogs, and 40 people own cats. Again, since it's possible to own both a cat and a dog, this is a Venn diagram question.

At University X, 60 people take a math course, 50 people take a chemistry course, and 40 people take a physics course. Since you can take several courses at university, this is a Venn question.

Those examples aren't full questions, of course - you can't solve anything. I'm just giving examples of the first sentence of a question in which you could use a Venn diagram approach.

There are other questions where groups can't overlap - you might know that 60 employees at a company are men, and 70 are women, and since someone can't be both a man and a woman, these groups cannot overlap. Typically these questions have a second division of the group as well (perhaps some are seniors, others are juniors). While it's actually possible to use Venn diagrams for these questions as well, most books teach a different approach - some, for example, describe using a table for these problems, which can be effective. There are a couple of diagrammatic approaches you can use as well, but it would be too difficult to explain them here, since I can't draw those diagrams easily.

Ron and I each discussed working with Venn diagrams (and the usefulness of the formulas you can learn for these types of problems) in this thread:

www.beatthegmat.com/set-theory-request- ... 28362.html
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by VP_Jim » Mon Mar 30, 2009 4:36 pm
I think that a "group box" is used when we have two groups (e.g., males and females) with two possible characteristics in each group (e.g., seniors and juniors).

I've never been a huge Venn diagram fan. Instead, I use the handy equation:

Group 1 + Group 2 + Neither - Both = Total

(which is really just a Venn diagram in equation form, but for some reason, it makes more sense to me, at least on the relatively simple questions!)

We can use this equation with the question you posted:

35 + 1.5y + y - 11 = 84

Then just solve for y (24), which will give you the "neither", so multiply that by 1.5 (=36) to find "Group 2".
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by sanju09 » Tue Mar 31, 2009 6:22 am
A 'group box' method of solving such problems is still not a general approach because it uses matrix methods (otherwise) that are out of scope for GMAT aspirants as it is more oftenly time consuming. The above posts are worth noting, we should rely on Venn Diagrams for such questions on GMAT, to get quicker and accurate results. It's unbelievable to me that a recognised book on GMAT doesn't discuss Venn approaches; if really so, one should of course have another. I am ready to solve the same problem using 'group box' on some special individual proposal, but on this forum, that won't be worthwhile simply because it consumes more time than a Venn approach.
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by mkbigmoz » Tue Mar 31, 2009 9:17 pm
I had the same question regarding this particular problem. I don't care for Venn diagrams, so I opted for the group box method. I've attached a jpg. which includes the first bit of information needed to solve the problem.

The question states that there are 1.5 times as many people who brought refreshments as there are people who neither brought refreshments or volunteered to supervise children. Notice the placement of 1.5X and X in the box. There is a total of 84 people.


1.5X + (24 + X) = 84

2.5X = 60

x= 24

The total number of parents who brought refreshments is

1.5X

1.5(24) = 36


After we solve for X, we can complete the rest of the diagram. Hope this helps.
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