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 ]
Venn Diagram vs. Formula [Grp 1 + Grp 2 - Both + Neither ]
- anshumishra
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Both are good, as long as you are comfortable with them .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 ]
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
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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.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 ]
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.
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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?GMATGuruNY wrote: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.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 ]
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.
- anshumishra
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That is because the question says :diebeatsthegmat wrote: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?GMATGuruNY wrote: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.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 ]
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.
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
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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.diebeatsthegmat wrote: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?GMATGuruNY wrote: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.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 ]
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.
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As a tutor, I don't simply teach you how I would approach problems.
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For more information, please email me (Mitch Hunt) at [email protected].
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
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As a tutor, I don't simply teach you how I would approach problems.
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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.
https://www.manhattangmat.com/forums/post4973.html
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.
https://www.manhattangmat.com/forums/post4973.html
- ankur.agrawal
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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.
Sumbody pls suggest the way out. Concepts, Practice question anythg that can help.
Thanx in advance.
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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: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.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 ]
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.
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Nevermind, "showbiz" below gave the PERFECT link, those with my question should read it asap. Thank you showbiz.
GMATGuruNY wrote: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.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 ]
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.
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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.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
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"):
80 used neither Brand A nor Brand B soap
We can add this to our diagram as follows:
60 used only Brand A soap
We get...
At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.
Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.
For every household that used BOTH brands of soap...
Let's let x = # of households that use BOTH brands....
...3 used only Brand B soap.
So, 3x = # of households that use ONLY brand B soap
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: https://www.gmatprepnow.com/module/gmat- ... ems?id=919
Then try these additional practice questions that can be solved using the Double Matrix Method:
- 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
- https://www.beatthegmat.com/ds-quest-t187706.html
- https://www.beatthegmat.com/overlapping- ... 83320.html
- https://www.beatthegmat.com/finance-majo ... 67425.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/sets-t269449.html#692540
- https://www.beatthegmat.com/in-costume-f ... tml#692116
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Fri Apr 13, 2018 11:38 am, edited 1 time in total.
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.
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.
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It might help us if you explain how 60+4x+80=200 is related to Group 1 + Group 2 - Both + Neither = Totalsmkhan 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.
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
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
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
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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
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