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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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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

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

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

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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:
Attachment:

A marketing firm determined.JPG [ 12.11 KiB | Viewed 15588 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, $$4x+140=200$$ --> $$x=15$$.

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

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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 [#permalink]

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26 Jun 2012, 08:52
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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26 Jun 2012, 13:17
answer - 15 (A)
did with table for overlapping set.
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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26 Jun 2012, 15:50
Ans: A (15)

Using given information, 60 people used Brand B. x used both A & B, 3x used only B. Solve for x.
x+3x = 60
x=15
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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28 Jun 2012, 01:26
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I think a (poorly drawn) diagram really helps.

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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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 [#permalink]

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28 Jun 2012, 11:22
Bunuel.. plz disclose the ASAP ..because sometimes we cant remember where we have replied..

I think its answer is 30..

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

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29 Jun 2012, 01:13
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:
Attachment:

A marketing firm determined.JPG [ 12.11 KiB | Viewed 15541 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, $$4x+140=200$$ --> $$x=15$$.

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

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30 Jun 2012, 20:00
Thank q so much Manimani & Bunnel for clarifying my doubt
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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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 [#permalink]

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

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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 [#permalink]

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04 Sep 2012, 23:29
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.

Merging similar topics.

Please search the forum before posting a question.
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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06 Sep 2012, 04:50
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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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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10 Dec 2012, 15:23
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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30 Jan 2013, 10:11
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?

[Reveal] Spoiler:
60+x+3x=120
x=15

I don't understand from where does the 3x come from...

Thanks a lot

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

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30 Jan 2013, 10:16
sokoma wrote:
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?

[Reveal] Spoiler:
60+x+3x=120
x=15

I don't understand from where does the 3x come from...

Thanks a lot

Best regard

Merging similar topics. Please refer to the solutions above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rules #1, 3, 5, 7, and 8!
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Re: A marketing firm determined that, of 200 households surveyed [#permalink]

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09 Jan 2014, 08:49
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
Re: A marketing firm determined that, of 200 households surveyed   [#permalink] 09 Jan 2014, 08:49

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