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A marketing firm determined that, of 200 households surveyed

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by swerve » Sat Sep 29, 2018 9:36 am

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Answers

A

B

C

D

E

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Difficulty—

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

The OA is A.

Source: Economist GMAT
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by deloitte247 » Sun Sep 30, 2018 10:04 am
Given that ;
Those who used neither brand A nor B =80
Those who used brand A only = 60
Let those who used both brands of soap = x
For every household that uses both brands,
3 households used only brand B soap
I.e if 1 household uses both soap 3 other household uses brand B soap = 3x
Total house hold surveyed = 200

Therefore, 80 + 80 + x + 3x = 200
140 + 4x = 200
4x = 200 - 140
4x = 60
Divide both sides by co-efficient of x,
$$\frac{4x}{4}=\ \frac{60}{4}$$
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A marketing firm determined that, of 200 households surveyed

by Brent@GMATPrepNow » Sun Sep 30, 2018 10:36 am
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.

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"):
Image

80 used neither Brand A nor Brand B soap
We can add this to our diagram as follows:
Image

60 used only Brand A soap
We get...
Image

At this point, we can see that the right-hand column adds to 140, which means 140 households do NOT use brand B soap.
Image

Since there are 200 households altogether, we can conclude that 60 households DO use brand B soap.
Image

For every household that used BOTH brands of soap...
Let's let x = # of households that use BOTH brands....
Image

...3 used only Brand B soap.
So, 3x = # of households that use ONLY brand B soap
Image

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

------------------------------------
Overlapping sets questions are VERY COMMON on the GMAT, so be sure to master the technique.

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

Once you're familiar with this technique, you can attempt these additional practice questions:

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Easy Data Sufficiency questions
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Medium Data Sufficiency questions
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Difficult Data Sufficiency questions
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- https://www.beatthegmat.com/mba/2011/05 ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by fskilnik@GMATH » Sun Sep 30, 2018 12:31 pm
swerve 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

Source: Economist GMAT
Excellent opportunity to use Venn diagrams (a.k.a. "overlapping sets")!
$$? = x$$
$$120 = 60 + x + 3x\,\,\,\,\, \Rightarrow \,\,\,\,? = x = 15$$

Image


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Sun Oct 07, 2018 6:35 pm
swerve 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
This is an overlapping set question. We can use the following formula:

Total = A only + B only + Both + Neither

We are given that the Total = 200, A only = 60, and Neither = 80. We are given that for every household that used both brands of soap, 3 used only Brand B. So, if we let x = Both, then 3x = B only. Thus:

200 = 60 + 3x + x + 80

200 = 140 + 4x

60 = 4x

x = 15

Thus, 15 households used both brands of soap.

Answer: A

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