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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

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 [#permalink]

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28 Jun 2012, 02:41

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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 [#permalink]

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13 Aug 2012, 07:02

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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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Whatever one does in life is a repetition of what one has done several times in one's life! If my post was worth it, then i deserve kudos

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

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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.

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

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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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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...

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

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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.

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

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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

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

"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).
_________________

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

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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?

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

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23 Jan 2014, 02:52

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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

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 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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GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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

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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:

"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.

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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