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

Redeem

double matrix problem

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Junior | Next Rank: 30 Posts
Posts: 15
Joined: Fri Jan 20, 2017 8:11 pm

double matrix problem

by neha shekhawat » Fri Jan 27, 2017 9:47 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 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
Top
Source: — Problem Solving |

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 » Fri Jan 27, 2017 9:54 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:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- 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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Jan 30, 2017 1:30 am
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.
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

by Jay@ManhattanReview » Mon Jan 30, 2017 1:30 am
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.
Top
Post new topic Post Reply
• Page 1 of 1