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 GRE 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.
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:
Your score will improve and your results will be more realistic
Is there something wrong with our timer?Let us know!
A marketing firm determined that, of 200 households surveyed
[#permalink]
22 Sep 2016, 12:04
1
6
Bookmarks
00:00
Question Stats:
60% (01:34) correct
40% (02:11) wrong based on 70 sessions
HideShow
timer Statistics
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 marketing firm determined that, of 200 households surveyed
[#permalink]
22 Sep 2016, 12:05
3
GreenlightTestPrep 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's a step-by-step approach 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
Re: A marketing firm determined that, of 200 households surveyed
[#permalink]
03 Jun 2019, 07:47
This math is little confusing to me - for example, for every household that used both brands of soap, 3 used only Brand B soap. how come we find 3 households use ONLY brand B? I request for little more elucidation , if there is any. Regards
Re: A marketing firm determined that, of 200 households surveyed
[#permalink]
22 Aug 2019, 13:26
1
GreenlightTestPrep 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
Quick and dirty:
200 people must be accounted for.
so 200 = (number of people in all the categories)
we've got 80 that didn't use anything, 60 that only used A, x that used both, and 3x that used B.
so 200 = 80 + 60 + 4x
60 = 4x
x = 15.
(Helps to draw a Ven diagram as well. That's how I set up the problem and then then came up with the equation from there..)
~~~~~~ Looks like the x and 3x is the most confusing part. The ratio between both and just B is 1:3 (for every 1 that does both we have 3 that do B). "Multiply" the ratio by x so that it's general. x:3x
Re: A marketing firm determined that, of 200 households surveyed
[#permalink]
05 Mar 2024, 20:50
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.