Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A marketing firm determined that, of 200 households [#permalink]

Show Tags

29 Dec 2007, 18:40

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200 x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

200 total
80 use niether
120 use either A or B or Both
60 use only A
so 60 use B or bothAB

For every AB there are three B
3AB=B
AB+B=60
AB+3AB=60
4AB=60
AB=15

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

200 total 80 use niether 120 use either A or B or Both 60 use only A so 60 use B or bothAB

For every AB there are three B 3AB=B AB+B=60 AB+3AB=60 4AB=60 AB=15

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.

Attachments

Venn Diagram.PNG [ 15.54 KiB | Viewed 1281 times ]

Could you please post the correct formula because, the link does not open after trying hard!

In the formula A + B + neither - both, A represents all those who use brand A, not just those who use only brand A, and B represents all those who use brand B, not just those who use only brand B. So A = the number who use only brand A (60) plus the number who use both brands (x), and B = the number who use only brand B (3x) plus the number who use both brands (x):

A + B + neither - both
(60 + x) + (3x + x) + 80 - x = 200
140 + 4x = 200
x = 15

Ian, I really like this method. I got 30 on this two and like a idiot knew this was going to be wrong. I've seen this type of only A/only B questions in the OG and should have been looking out for it.

Your system seems pretty good! I'm going to start using it. Similar to the Manhattan quad system.

ian7777 wrote:

I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200 x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.

A marketing firm determined that, of 200 households surveyed, 80 use neither Brand A nor 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 households surveyed used both brands of soap.