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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:

Attachment:

A marketing firm determined.JPG [ 12.11 KiB | Viewed 19109 times ]

"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
_________________

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:

Attachment:

A marketing firm determined.JPG [ 12.11 KiB | Viewed 19044 times ]

"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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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.
_________________

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).
_________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

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.

Merging similar topics.

Please search the forum before posting a question. _________________

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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30 Jan 2013, 11:11

Hi,

I have a question/answer from the OG book that I don't understand, if someone could help me it could be really cool:

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 brand of soap, 3 use only Brand B soap.

How many of the 200 households surveyed used both brands of soap?

I have a question/answer from the OG book that I don't understand, if someone could help me it could be really cool:

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 brand of soap, 3 use only Brand B soap.

How many of the 200 households surveyed used both brands of soap?

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

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