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A marketing firm determined that, of 200 households surveyed, 80 used

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A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 25 Jun 2012, 01:28
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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

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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 25 Jun 2012, 01:28
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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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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 28 Jun 2012, 01:26
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4
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, 80 used  [#permalink]

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New post 25 Jun 2012, 04:04
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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, 80 used  [#permalink]

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New post 26 Jun 2012, 08:52
1
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, 80 used  [#permalink]

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New post 28 Jun 2012, 01:41
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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, 80 used  [#permalink]

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New post 13 Aug 2012, 06:02
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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, 80 used  [#permalink]

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New post 04 Sep 2012, 17:11
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, 80 used  [#permalink]

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New post 04 Sep 2012, 23:24
1
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, 80 used  [#permalink]

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New post Updated on: 02 Jan 2019, 12:16
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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: A

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 08 Feb 2017, 10:33
2
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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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 16 Nov 2017, 00:47
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, 80 used  [#permalink]

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New post 16 Nov 2017, 01:05
2
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, 80 used  [#permalink]

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New post 26 Mar 2018, 10:05
2

Solution:



Given:

    • Number of households surveyed = 200

    • Households who used only Brand A soaps = 60

    • Households who used only Brand B soaps = 3* Households who used both soaps.

    • Households who used neither Brand A nor Brand B soaps = 80

Working out:

We need to find out the number of households which used soaps of both the brands.

To understand the solution, let us draw a 2-set Venn diagram

Image

Since the total households surveyed were 200 and 80 of them used no soaps, (200-80) households used at least one of Brand A or Brand B soaps.

    • Thus, \(3x +x +60 = 120\)

    • Or, \(x =15\).

Thus, 15 households used both the brands of the soaps.

Answer: Option A
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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 30 Sep 2018, 12:38
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

Excellent opportunity to use Venn diagrams (a.k.a. "overlapping sets")!

Image


\(? = x\)

\(120 = 60 + x + 3x\,\,\,\,\, \Rightarrow \,\,\,\,? = x = 15\)


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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 12 Feb 2019, 10:49
Solved this question algebraically as below:

Out of 200, 80 use none, so this leaves us with 120 using only A, only B and both.
Only A users = 60, now this leaves us with Only B and both users to be remaining 60.
Now, there's a relation given: 'for every household that used both brands of soap, 3 used only Brand B soap'
this means both:only B = 1:3, assign x to 'both' users.

So we get the below equation:
120=60+3x+x
x=15

Answer : A

Please correct me if I am wrong.
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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 04 May 2020, 21:12
1
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

Diagnostic Test
Question: 6
Page: 21
Difficulty: 650

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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
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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 05 May 2020, 04:38
3
Asad wrote:
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

Diagnostic Test
Question: 6
Page: 21
Difficulty: 650

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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


Hello Asad,

You have asked a good question and a pertinent one too. Very often, in questions on Venn diagrams, the word “ONLY” can be the difference between a correct and a wrong answer.
Let’s draw a Venn diagram to represent the situation defined in the question posed by you. It should look like this:

Attachment:
5th May 2020 - Reply 2.jpg
5th May 2020 - Reply 2.jpg [ 39.43 KiB | Viewed 3381 times ]


We see that x+y+z = 120 and x+z = 60. Therefore, y = 60 and z = 20 since \(\frac{z}{y}\) = \(\frac{1}{3}\).

The answer in this case would have been 20 i.e. option B. That should tell you that answer option B has been set up as a trap answer for students, who in their over-zealousness to get to the answer quickly may miss out the crucial keyword “only”.

Hope that helps!
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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 05 May 2020, 14:34
Asad wrote:
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

Diagnostic Test
Question: 6
Page: 21
Difficulty: 650

Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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


Hi Asad,

YES - if you edited the prompt in the way that you describe, then a change would occur in the Tic-Tac-Toe/Matrix Box that Bunuel presented. The "60" would appear in the lower-left corner of the grid, but the top row (re: X/3X/4X) would stay the same. You could then calculate the values of all of the boxes in the grid and the upper-left corner would be 20.

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Re: A marketing firm determined that, of 200 households surveyed, 80 used  [#permalink]

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New post 13 May 2020, 13:35
~ I blindly applied the Two-Overlapping sets formula:

Total = Group1 + Group2 - Both + Neither

and got this wrong. Ouch.

This gives you 30 and which is likely a trap-answer. Clever.
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Re: A marketing firm determined that, of 200 households surveyed, 80 used   [#permalink] 13 May 2020, 13:35

A marketing firm determined that, of 200 households surveyed, 80 used

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