• PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep

Venn Diagram vs. Formula [Grp 1 + Grp 2 - Both + Neither ]

This topic has 6 expert replies and 10 member replies
Goto page
  • 1,
  • 2
Next
tar32 Newbie | Next Rank: 10 Posts Default Avatar
Joined
06 Aug 2009
Posted:
1 messages
Target GMAT Score:
720

Venn Diagram vs. Formula [Grp 1 + Grp 2 - Both + Neither ]

Post Sat Dec 18, 2010 2:40 pm
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sat Jan 11, 2014 6:49 am
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45
We can also solve this question using 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.
Here, we have a population of 200 households , and the two characteristics are:
- using or not using Brand A soap
- using or not using Brand B soap

So, we can set up our matrix as follows (where "~" represents "not"):
ttp://postimg.org/image/tp60ss1k9/" target="_blank">

80 used neither Brand A nor Brand B soap
We can add this to our diagram as follows:
ttp://postimg.org/image/qjlf2kiy1/" target="_blank">

60 used only Brand A soap
We get...
ttp://postimg.org/image/se2uy1vc9/" target="_blank">

At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.
ttp://postimg.org/image/ogazuwj55/" target="_blank">

Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.
ttp://postimg.org/image/ovqv1nug9/" target="_blank">

For every household that used BOTH brands of soap...
Let's let x = # of households that use BOTH brands....
ttp://postimg.org/image/n57u06cx5/" target="_blank">

...3 used only Brand B soap.
So, 3x = # of households that use ONLY brand B soap
ttp://postimg.org/image/o8ryc4xk9/" target="_blank">

At this point, when we examine the left-hand column, we can see that x + 3x = 60
Simplify to get 4x = 60
Solve to get x = 15

How many of the 200 households surveyed used BOTH brands of soap?
Since x = # of households that use BOTH brands of soap, the correct answer here is A

------------------------------------
To learn more about the Double Matrix Method, watch our free video: http://www.gmatprepnow.com/module/gmat-word-problems?id=919

Then try these additional practice questions that can be solved using the Double Matrix Method:
- http://www.beatthegmat.com/mba/2011/05/05/random-double-matrix-question-1
- http://www.beatthegmat.com/mba/2011/05/09/random-double-matrix-question-2
- http://www.beatthegmat.com/mba/2011/05/16/random-double-matrix-question-3
- http://www.beatthegmat.com/ds-quest-t187706.html
- http://www.beatthegmat.com/overlapping-sets-questions-t183320.html
- http://www.beatthegmat.com/finance-majors-non-finance-majors-overlapping-set-question-t167425.html
- http://www.beatthegmat.com/ds-french-japanese-t222297.html
- http://www.beatthegmat.com/sets-t269449.html#692540
- http://www.beatthegmat.com/in-costume-for-halloween-t269355.html#692116

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
KristenH88 Junior | Next Rank: 30 Posts Default Avatar
Joined
20 Feb 2013
Posted:
18 messages
Upvotes:
1
Post Fri Jan 10, 2014 4:11 pm
Nevermind, "showbiz" below gave the PERFECT link, those with my question should read it asap. Smile Thank you showbiz.

GMATGuruNY wrote:
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Sep 08, 2014 2:48 pm
That's perfect, smkhan.

However, as you can see, there's quite a bit of extra reasoning beyond just plugging numbers into the formula. That's why Mitch suggested that the "Group 1 + Group 2 - Both + Neither = Total" formula might not be the easiest route.

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
smkhan Junior | Next Rank: 30 Posts Default Avatar
Joined
24 Apr 2013
Posted:
17 messages
Post Mon Sep 08, 2014 2:44 pm
Hi,

Sorry should have written the solution but it was the same as anshumishra's at the top that's why I didnt write it. But here's how I solved it first using the group formula and than with Venn diagram.

A' alone - 60
A&B both - x
B' alone - 3x
N - Neither A nor B - 80
A - Total Brand A, 60+x
B - Total Brand B, 3x+x

Using the group formula, A+B-A&B+N=200

(60+x)+(3x+x)-x+80=200
60+4x+80=200
4x=200-140=60
x=15

Using Venn diagarm, Total = Only Brand A + Only Brand B + Both + Neither
200= 60+3x+x+80
200=60+4x+80

Thanks

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Mon Sep 08, 2014 7:40 am
smkhan wrote:
Hi,

Why is the group formula (Group 1 + Group 2 - Both + Neither = Total )not suitable for this problem as pointed out by Mitch. It reduces the equation to the same equation as you would get if you use Venn diagram. 60+4x+80=200. Just trying to clarify the concept.
It might help us if you explain how 60+4x+80=200 is related to Group 1 + Group 2 - Both + Neither = Total
In your equation there are only 3 terms (60+4x+80) on the left side, yet there are 4 terms (Group 1 + Group 2 - Both + Neither) on the left side of the group formula.

The transition from 4 terms to 3 terms is what makes it tricky to apply the formula here.

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with Beat The GMAT's free 60-Day Study Guide

Check out the online reviews of our course
Come see all of our free resources

  • +1 Upvote Post
  • Quote
  • Flag
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
smkhan Junior | Next Rank: 30 Posts Default Avatar
Joined
24 Apr 2013
Posted:
17 messages
Post Mon Sep 08, 2014 7:32 am
Hi,

Why is the group formula (Group 1 + Group 2 - Both + Neither = Total )not suitable for this problem as pointed out by Mitch. It reduces the equation to the same equation as you would get if you use Venn diagram. 60+4x+80=200. Just trying to clarify the concept.

  • +1 Upvote Post
  • Quote
  • Flag
KristenH88 Junior | Next Rank: 30 Posts Default Avatar
Joined
20 Feb 2013
Posted:
18 messages
Upvotes:
1
Post Fri Jan 10, 2014 4:01 pm
Why is neither not subtracted in this case, and when do you know to use the original a+b-both+neither=total instead of adding them all? In this Diag I got it wrong using the formula I learned and tried yours and got it right. When to use? Thank you.

GMATGuruNY wrote:
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.

  • +1 Upvote Post
  • Quote
  • Flag
ankur.agrawal Master | Next Rank: 500 Posts
Joined
31 Mar 2010
Posted:
261 messages
Followed by:
3 members
Upvotes:
11
Test Date:
23rd April, 2011
Target GMAT Score:
700
GMAT Score:
NA
Post Mon Jan 17, 2011 1:04 am
I am facing a hard time analyzing Questions based on SET theory, Venn Diagrams.

Sumbody pls suggest the way out. Concepts, Practice question anythg that can help.

Thanx in advance.

  • +1 Upvote Post
  • Quote
  • Flag
showbiz Senior | Next Rank: 100 Posts
Joined
22 Jun 2010
Posted:
44 messages
Upvotes:
3
Test Date:
13 August
Target GMAT Score:
720+
Post Mon Dec 20, 2010 7:21 pm
The key to this question are the words "Only Brand A"

The Venn diagram drawn above puts 60 and x in one circle, which doesn't apply in this case. In essence, you would have to take the middle slice (x) separately from 60 and 3x.

http://www.manhattangmat.com/forums/post4973.html

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sun Dec 19, 2010 9:01 pm
diebeatsthegmat wrote:
GMATGuruNY wrote:
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.
hi, can you please explain me why the brand B is 3x??? it says that only 3 household in both used brand B. does it mean that B=3?
As mentioned above, for every household that used both brands, 3 used only Brand B means that the ratio of both:only B = 1:3. Thus, if x used both brands, 3x used only Brand B.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
anshumishra Legendary Member
Joined
15 Jun 2010
Posted:
543 messages
Followed by:
3 members
Upvotes:
147
Post Sun Dec 19, 2010 6:34 pm
diebeatsthegmat wrote:
GMATGuruNY wrote:
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.
hi, can you please explain me why the brand B is 3x??? it says that only 3 household in both used brand B. does it mean that B=3?
That is because the question says :
For every household that used both brands of soap, 3 used only Brand B soap

That means if x households used both the brands, then 3x used brand B.

Thanks

  • +1 Upvote Post
  • Quote
  • Flag
diebeatsthegmat Legendary Member Default Avatar
Joined
07 May 2010
Posted:
1119 messages
Followed by:
2 members
Upvotes:
29
Post Sun Dec 19, 2010 6:30 pm
GMATGuruNY wrote:
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.
hi, can you please explain me why the brand B is 3x??? it says that only 3 household in both used brand B. does it mean that B=3?

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post Sat Dec 18, 2010 4:50 pm
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
The formula above is not the best approach for this problem. In the formula above, Group 1 = (households that used only Brand A + households that used both Brand A and Brand B). The problem gives us the number of households that used only Brand A (60). There is no easy way to plug this value into the formula.

Here is a formula that would work for this problem:

Total = Only Brand A + Only Brand B + Both + Neither

Total = 200
Only Brand A = 60
Neither = 80
Both = x
Only Brand B = 3x

Plugging these values into the formula, we get:

200 = 60 + 3x + x + 80
60 = 4x
x = 15.

The correct answer is A.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.
Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.

  • +1 Upvote Post
  • Quote
  • Flag
Thanked by: bajwa2307
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.
anshumishra Legendary Member
Joined
15 Jun 2010
Posted:
543 messages
Followed by:
3 members
Upvotes:
147
Post Sat Dec 18, 2010 4:11 pm
tar32 wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

A: 15
B: 20
C: 30
D: 40
E: 45


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]
Both are good, as long as you are comfortable with them .
I have used Venn diagram to solve this question :

So, 200 = 60 + x+ 3x + 80 => x = 15

Without Venn diagram :

Total = Group 1 + Group2 - Both + Neither
=> 200 = (60+x) + (3x+x) - x + 80 = 60 + 4x + 80 => x = 15.

Thanks
Attachments

This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user.

  • +1 Upvote Post
  • Quote
  • Flag

Best Conversation Starters

1 Roland2rule 170 topics
2 lheiannie07 110 topics
3 ardz24 56 topics
4 LUANDATO 50 topics
5 swerve 48 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

155 posts
2 image description Scott@TargetTestPrep

Target Test Prep

122 posts
3 image description GMATGuruNY

The Princeton Review Teacher

121 posts
4 image description Rich.C@EMPOWERgma...

EMPOWERgmat

110 posts
5 image description DavidG@VeritasPrep

Veritas Prep

81 posts
See More Top Beat The GMAT Experts