Problem Solving

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"):


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

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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:

Easy Problem Solving questions
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Medium Problem Solving questions
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- https://www.beatthegmat.com/of-the-appli ... 70255.html
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- https://www.beatthegmat.com/at-least-100 ... 74669.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

neha shekhawat 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 soap,3 used only brand B soap. How many of the 200 household surveyed used both brands soap?

A) 15
B) 20
c) 30
D) 40
E) 45

We know that 200 - 80 = 120 use ONLY A, ONLY B, and BOTH A & B.

Thus, 120 = ONLY A + ONLY B + BOTH A & B

=> 120 = 60 + ONLY B + BOTH A & B

Say x households use BOTH A & B, thus, ONLY B households = 3*x = 3x

=> 60 = 3x + x

=> [spoiler]x = 15[/spoiler]

Relevant book: Manhattan Review GMAT Word Problems

Answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangalore | Guangzhou | Buenos Aires | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

neha shekhawat 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 soap,3 used only brand B soap. How many of the 200 household surveyed used both brands soap?

A) 15
B) 20
c) 30
D) 40
E) 45

We know that 200 - 80 = 120 use ONLY A, ONLY B, and BOTH A & B.

Thus, 120 = ONLY A + ONLY B + BOTH A & B

=> 120 = 60 + ONLY B + BOTH A & B

Say x households use BOTH A & B, thus, ONLY B households = 3*x = 3x

=> 60 = 3x + x

=> [spoiler]x = 15[/spoiler]

Relevant book: Manhattan Review GMAT Word Problems

Answer: A

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Bangalore | Guangzhou | Buenos Aires | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.