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A marketing firm determined that, of 200 households surveyed

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

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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

Diagnostic Test
Question: 6
Page: 21
Difficulty: 650
[Reveal] Spoiler: OA

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SOLUTION

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

Given:

Image

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Answer: A.

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New post 25 Jun 2012, 05:04
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60(number of brand A) + X(number of households that use both brans)+ 3x(number of households that use only brand B) + 80 = 200

X = 15

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

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New post 26 Jun 2012, 09:52
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Shouldn't the answer be [C]

60(Brand A) +3x(Brand B)-x(Both Brands) = 200-80(total is 120 since 80 use neither)

60+2x = 120 => x =30

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

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New post 28 Jun 2012, 02:26
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I think a (poorly drawn) diagram really helps.

Image

60 + x + 3x + 80 = 200

4x = 60
x = 15

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

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pallavisatsangi wrote:
Shouldn't the answer be [C]

60(Brand A) +3x(Brand B)-x(Both Brands) = 200-80(total is 120 since 80 use neither)

60+2x = 120 => x =30

No pallavisatsangi
The answer is A (15) you can not subtract x (both using A and B) Because in the question it is mentioned that 60 people is only brand A and accordingly 3x people use only Brand B.... if the term 'ONLY' had not been used in the question then you would have subtracted x .. but since in both cases term 'only' has been used, you can not subtract x
So eq. becomes
60 +x+3x+80=200
x=15
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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Nice question, i took around 1 minute to comprehend this line "for every household that used both brands of soap, 3 used only Brand B soap" and still over looked the word "only" Brand B. I chose (C)30 , but it should be 15. Nice explanation every one.

One important thing i observed in these questions, in which we have to deal with Only A/ Only B type issues that it is better to go with Venn-Dia. rather than table as it adds to complexity (only A-->not B)and consumes more time than former.
On the other hand, the table is easier to work with when the questions deal with "both/neither-nor" elements, range of elements.
Just my opinion.
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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New post 04 Sep 2012, 18:11
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

If someone could tell me how to solve the problem using the manhattan method (with grids), that would be awesome. For such a simple problem, I can't figure out how I'm messing up setting up the grid.
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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New post 05 Sep 2012, 00:24
egiles 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

If someone could tell me how to solve the problem using the manhattan method (with grids), that would be awesome. For such a simple problem, I can't figure out how I'm messing up setting up the grid.


The data in your table should be as follow:

x 3x 60
60 80 140
60+x 80+3x 200

From the first line, x + 3x = 60 (the same equation can be obtained using the last line - 60 + x + 80 + 3x = 200).

Your mistake was misplacing 60 - it is the number of households using only brand A (meaning A but not B).
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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New post 06 Sep 2012, 05:50
Answer is 15...I have sticky memory (I don't know if its good or bad). I am afraid, but unknowingly I have memorized lot of solutions and I tend to use that memory on mocks (As most of the problems in the post come from prep and Manhattan tests). The bad thing is when I am posed with a problem, perhaps testing the same concept, I just take too much of a time..should I keep doing problems from the posts or should I practice from some other source? Guys need your advice on this...

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New post 10 Dec 2012, 16:23
fun question!

these always remind me of sudoku.

in any case, the twist here is that the relationship defining the square's occupant is a bit different than just concrete numbers, it's a tiny little ratio problem stuck inside of an overlapping set problem.

1:3 = 60

unknown multiplier of x...and: 1x+3x= 60 ... 4x= 60 ... x=15.

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

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New post 09 Jan 2014, 09:49
Thanks a lot to everybody for your explainations... I still have issues with understanding the exercise.
Indeed, when we just said that "for every household that used both brands of soap, 3 used only Brand B soap" what did we mean exactly? It is a bit confusing for me... First we say that they use both brands, but then we say that 3 (3 from what?) use only B... And all the 4x and 1x thing is also confusing me :(

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New post 10 Jan 2014, 03:49
LucianoC wrote:
Thanks a lot to everybody for your explainations... I still have issues with understanding the exercise.
Indeed, when we just said that "for every household that used both brands of soap, 3 used only Brand B soap" what did we mean exactly? It is a bit confusing for me... First we say that they use both brands, but then we say that 3 (3 from what?) use only B... And all the 4x and 1x thing is also confusing me :(


Explained here: a-marketing-firm-determined-that-of-200-households-surveyed-134890.html#p1099109

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A).
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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New post 10 Jan 2014, 09:14
Bunuel wrote:
LucianoC wrote:
Thanks a lot to everybody for your explainations... I still have issues with understanding the exercise.
Indeed, when we just said that "for every household that used both brands of soap, 3 used only Brand B soap" what did we mean exactly? It is a bit confusing for me... First we say that they use both brands, but then we say that 3 (3 from what?) use only B... And all the 4x and 1x thing is also confusing me :(


Explained here:

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A).


Thanks for your help, but I am still confused. The sentence states that for every household using BOTH soaps, there are 3 using only B... But how is it possible if we just said that those people use both soaps?

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

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Hi Luciano,

Look at it this way:

Some use only A + some use both + some use only B + 80 use none = 200(Total people) ---(1)

It is given that those who use only A is 60 ---(2)
Let those who use both be x. ---(3)
Now the question says for every person using both soaps there are 3 people using soap B only. Meaning if 1 person uses both soaps then 3 other people use soap B only. hope its clear till now.

now for 1 person using both, 3*1 =3 use only B.
for 2 people using both, 3*2 = 6 use only B.
for 3 people using both, 3*3 = 9 use only B.

So for some x number of people using both, there are 3*x number of other people who use soap B only.

That is, if x use both soaps, 3x use only B. ---(4)

Now using (2),(3) & (4) in (1) we get


60+x+3x+80 = 200

140+4x = 200

4x = 60
x = 15.

Hope this helps.



LucianoC wrote:
Thanks a lot to everybody for your explainations... I still have issues with understanding the exercise.
Indeed, when we just said that "for every household that used both brands of soap, 3 used only Brand B soap" what did we mean exactly? It is a bit confusing for me... First we say that they use both brands, but then we say that 3 (3 from what?) use only B... And all the 4x and 1x thing is also confusing me :(

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

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Bunuel 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"):
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:
[Reveal] Spoiler:
A


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

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New post 02 Feb 2017, 02:05
Hi experts,

I am confused about the understanding of the following sentence

and for every household that used both brand of soap, 3 use only Brand B soap.

at first I got that 3 households use only Brand B soap,
given AB as abbreviate both use A and B,
then 60+3+AB=120,
AB = 57
WOW, out of the choice.

later, I read the explanation, then I got here is 3 times as many as used B.

Appreciate if help how should I distinguish the difference between 3 household use Brand B and 3 times as many as use Brand B.

have a nice day
>_~

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New post 08 Feb 2017, 11:33
Bunuel 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. A great way to solve this problem is to set up a table with two main categories: Brand A and Brand B. More specifically, our table will be labeled as follows:

1) Brand A

2) No Brand A

3) Brand B

4) No Brand B

We are given that of 200 households surveyed, 80 did not use either brand and 60 used only Brand A. We are also given that for every household that used both brands, 3 used only Brand B. Thus, we can let x = the number of households that used both brands and 3x = the number of households that only used Brand B. We need to determine how many households used both brands.

Let’s fill all of this into our table.

Image

We can create the following equation with the “Total” column and determine x:

4x + 140 = 200

4x = 60

x = 15

Thus, 15 households used both brands of soap.

Alternative solution:

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

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New post 16 Nov 2017, 01:47
Bunuel wrote:
SOLUTION

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

Given:

Image

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Answer: A.


Can you please explain "if x used both A and B, then 3x used only B (but not A).So, \(4x+140=200\) --> \(x=15\)"
I can't comprehend this part. it is specifically mentioned in the question that 3 used 'only' brand B soap. So, why it is dependable on "both brands of soap" part. if so, why isn't 60 written as "60x".
help.

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

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abhishek94 wrote:
Bunuel wrote:
SOLUTION

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

Given:

Image

"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A). So, \(4x+140=200\) --> \(x=15\).

Answer: A.


Can you please explain "if x used both A and B, then 3x used only B (but not A).So, \(4x+140=200\) --> \(x=15\)"
I can't comprehend this part. it is specifically mentioned in the question that 3 used 'only' brand B soap. So, why it is dependable on "both brands of soap" part. if so, why isn't 60 written as "60x".
help.


"For every household that used both brands of soap, 3 used only Brand B soap" means that if x used both A and B, then 3x used only B (but not A).

So, for example:
If 10 people used both brands of soap, 3*10 = 30 used only Brand B soap.
If 12 people used both brands of soap, 3*12 = 36 used only Brand B soap.
If x people used both brands of soap, 3x used only Brand B soap.
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Re: A marketing firm determined that, of 200 households surveyed   [#permalink] 16 Nov 2017, 02:05

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A marketing firm determined that, of 200 households surveyed

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