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A marketing firm determined that, of 200 households surveyed, 80 used
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25 Jun 2012, 01:28

7

59

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A

B

C

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E

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45% (medium)

Question Stats:

66% (01:43) correct 34% (02:14) wrong based on 1879 sessions

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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

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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25 Jun 2012, 01:28

10

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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:

"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, \(4x+140=200\) --> \(x=15\).

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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28 Jun 2012, 01:41

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1

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
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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
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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.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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04 Sep 2012, 23:24

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, 80 used
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Updated on: 02 Jan 2019, 12:16

Top Contributor

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"):

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

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

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Originally posted by GMATPrepNow on 22 Sep 2016, 12:03.
Last edited by GMATPrepNow on 02 Jan 2019, 12:16, edited 3 times in total.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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08 Feb 2017, 10:33

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

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.

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
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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:

"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.

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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16 Nov 2017, 01:05

1

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:

"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
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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")!

\(? = x\)

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

Regards, Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net

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

gmatclubot

Re: A marketing firm determined that, of 200 households surveyed, 80 used
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12 Feb 2019, 10:49