BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Help needed to use overlapping sets grid method in solve

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Thu Apr 15, 2010 1:05 am

Help needed to use overlapping sets grid method in solve

by focusgmat » Thu Dec 02, 2010 9:37 am
Resource : GMATclub test question
Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

* 20
* 25
* 30
* 35
* 40

[spoiler]
OA : 40[/spoiler]
How to use the Double-Set Matrix (the MGMAT grid method) to solve the problem?
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Dec 02, 2010 10:37 am
focusgmat wrote:Resource : GMATclub test question
Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

* 20
* 25
* 30
* 35
* 40

[spoiler]
OA : 40[/spoiler]
How to use the Double-Set Matrix (the MGMAT grid method) to solve the problem?
I wouldn't use a matrix to solve this problem.

Here's the big idea with overlapping groups: subtract the overlap.

In the problem above, there is an overlap between the two groups (those who read A and those who read B). When we count the total number who read A and the total number who read B, the overlap -- the students who read both A and B -- gets counted twice. So we need to subtract the students who read both books (the overlap) so that they don't get double-counted.

Thus we get the following equation:

Total students = A + B - both

both = .2A (since 20% who read A also read B)
both = .25B (since 25% who read B also read A)
Thus, .2A = .25B
A = 1.25B

So the equation Total students = A + B - both can be rewritten in terms of B:

200 = 1.25B + B - .25B
B = 100
Thus:
A = 1.25B = 125
both = .25B = .25*100 = 25

Subtracting the overlap (25) from the total who read B (100), we get that the number who read only B = 100-25 = 75.
Subtracting the overlap (25) from the total who read A (125), we get that the number who read only A = 125-25 = 100.
Only A - Only B = 100-75 = 25.

The correct answer is B. Are you certain the OA is D?
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Thu Apr 15, 2010 1:05 am

by focusgmat » Thu Dec 02, 2010 10:12 pm
Thank you, GMATGURUNY for giving a fabulous explanation.

I have been using the MGMAT grid method all the time for overlapping sets and it has worked always until I encountered this problem.

Will you be able to explain the same in grid method as well? Or is there a way to tell whether using venn diagram or using grid method is better.
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Dec 03, 2010 7:05 am
focusgmat wrote:Thank you, GMATGURUNY for giving a fabulous explanation.

I have been using the MGMAT grid method all the time for overlapping sets and it has worked always until I encountered this problem.

Will you be able to explain the same in grid method as well? Or is there a way to tell whether using venn diagram or using grid method is better.
For problems with overlapping groups, I use the approach described above or a Venn diagram. Here's another example:

https://www.beatthegmat.com/overlapping- ... 70045.html

For problems in which two groups are further divided into smaller groups, I use a group grid (or matrix). Here are some problems that I solved using the group grid:

https://www.beatthegmat.com/probability- ... 66390.html
https://www.beatthegmat.com/650-800-question-t68610.html
https://www.beatthegmat.com/interns-at-h ... 62065.html

Hope this helps!
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Junior | Next Rank: 30 Posts
Posts: 28
Joined: Thu Apr 15, 2010 1:05 am

by focusgmat » Tue Dec 21, 2010 8:39 am
GMATGURUNY,

I really want to thank you very much again for the links you have provided and the explanation you have given. I practiced them and I really feel confident in answering Overlapping set questions.


Focusgmat
Top
Senior | Next Rank: 100 Posts
Posts: 38
Joined: Mon Jun 21, 2010 12:37 pm

by subhakam » Wed Jan 02, 2013 7:21 pm
Based on this problem can some one please help me understand - when to use Venn Diagram versus double set matrix? Still not very clear unless i actually start doing the problem. On test day do not want to waste time using the wrong method and then switching to another method. Is there a way - specific key words that trigger the use of one method (e.g. double set matrix over the other- venn diagram?)
All help is greatly appreciated!
Thanks
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Wed Jan 02, 2013 7:26 pm
subhakam wrote:Based on this problem can some one please help me understand - when to use Venn Diagram versus double set matrix? Still not very clear unless i actually start doing the problem. On test day do not want to waste time using the wrong method and then switching to another method. Is there a way - specific key words that trigger the use of one method (e.g. double set matrix over the other- venn diagram?)
All help is greatly appreciated!
Thanks
I prefer the Double Matrix method for all questions of this nature. This method can be used for most questions featuring a population in which each member has two criteria associated with it.

For more information about this technique and some additional practice questions, check out these 3 BTG articles:

- https://www.beatthegmat.com/mba/2011/05/ ... question-1
- https://www.beatthegmat.com/mba/2011/05/ ... question-2
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Newbie | Next Rank: 10 Posts
Posts: 2
Joined: Wed Jan 02, 2013 9:58 pm
Location: Hyderabad

by srinivas2357 » Wed Jan 02, 2013 10:14 pm
Of 200 surveyed students, 20% of those who read book A also read book B and 25% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?

* 20
* 25
* 30
* 35
* 40
Given, 0.2A = 0.25B implies those who read book A plus those who read only book B = 200 which implies A + 0.75B = A + 0.6A = 200. Therefore A = 125 and B = 100. Hence the best answer is 25.
Top
Post new topic Post Reply
• Page 1 of 1