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A marketing firm determined that, of 200 households [#permalink]
07 Jun 2008, 00:35

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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?

Re: A marketing firm determined that, of 200 households [#permalink]
10 Jun 2008, 04:12

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I use a completely different system for these kinds of questions. It works every single time, as long as there are two groups (if there are three, I use the venn diagram).

Draw a 3 by 3 box, as in the diagram. All rows add down to the bottom row, and all columns add across to the right column. The bottom right box is the total of the whole system.

Fill in what is given, and then infer what is not.

Then answer the question.

In my attached example, the black numbers are given, the red ones are what is inferred.

Once finished, in this question, see that the right column adds all the way down and has one variable:

4x + 140 = 200 x = 15

In this case, the boxes with the question marks are irrelevant, so I leave them alone. In other types of questions, you may fill them in.

Try it on other ones. It will never be confusing again.

Re: A marketing firm determined that, of 200 households [#permalink]
14 Jun 2010, 09:26

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Expert's post

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. 50

Given:

Attachment:

Brands.JPG [ 12.11 KiB | Viewed 13864 times ]

The bold part 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 [#permalink]
13 Jan 2010, 22:33

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You should think of these question in a graphical way. So the best way to represent this question is to quickly draw a set. Look below for the picture. Inside the set we have quantity of ONLY Brand A, ONLY Brand B, BOTH Brands A&B, and NEITHER Brands A&B. The outside number (200 in this case) represents the TOTAL amount.

From your question (and my graph) you can create the following equation:

200 = 60 + x + 3x + 80; 200 = 4x + 140; 60 = 4x 15 = x

As you can see "x" represents the quantity of both A and B brands being used. So the answer is B.

Now, I think that you are having problem because of the English since the statement "for every household that used both brands of soap, 3 used only Brand B soap" means that Brand B was used 3 times more than both A and B by the same household [and not in total].

Re: A marketing firm determined that, of 200 households [#permalink]
14 Oct 2010, 10:44

1

This post received KUDOS

Expert's post

sivai87 wrote:

Hi, Please help on the below question.

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 one of the problems in diagnostic test in OG12.

Total # of Soap (A+B) = Total of brand A + Total of Brand B + Neither Brand A nor Brand B - Both.

From the question we have, (A+B) = 200 Neither Brand A nor Brand B = 80 Only Brand A = 60 Let household # using both the brands be "B" and so the no of house holds using Brand B is 3B.

From the eqn above we have,

200 = 80+60+3B-B

2B = 60, and finally B = 30.

But 30 is wrong... Where am I doing the mistake. Plz help.... ( I understand the steps explained in OG. But why this methodology is not working out here. Believe there is no problem with the formula though)

If we do the way you are doing then:

Total=A+B-Both+Neither. Let the # of housholds that use both A and B be \(x\), then # of households that use only B will be \(3x\).

Total=200; A=60+x; B=x+3x Both=x; Neither=80;

\(200=(60+x)+(x+3x)-x+80\) --> \(x=15\)

Answer: A.

Also merging with earlier discussion to see different approaches.

Re: A marketing firm determined that, of 200 households [#permalink]
07 Jun 2008, 00:58

redbeanaddict 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 My answer was different from the answer given by OG. Help!

Let me take a shot ->

out of 200 80 are not using either A or B, so total household of concern = 200-80 = 120 Only Brand A = 60 Only Brand B = 3x Both A and B = x

Re: A marketing firm determined that, of 200 households [#permalink]
07 Jun 2008, 05:53

redbeanaddict 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 My answer was different from the answer given by OG. Help!

total surveyed=200 households neither Brand A nor Brand B soap = 80 households that use one of the 2 brands atleast=200-80=120 Out of these 120, 60 use only brand A, therefore rest 60 consist of households that use only brand B+households that use both the brands. ratio of both to only B is 1:3 this means if households that use both the brands = x, then households that use only brand B = 3x 60=x+3x therefore x=15. Ans is (A)

Re: A marketing firm determined that, of 200 households [#permalink]
08 Jun 2008, 20:16

redbeanaddict 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 My answer was different from the answer given by OG. Help!

Shouldn't the equation be Total= Brand A-both brands+Brand B+Neither? 200=60-x+3x+80 so x=30 ?( uses both brand a and B) I've always used this formula...

Re: A marketing firm determined that, of 200 households [#permalink]
09 Jun 2008, 09:06

redbeanaddict wrote:

redbeanaddict 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 My answer was different from the answer given by OG. Help!

Shouldn't the equation be Total= Brand A-both brands+Brand B+Neither? 200=60-x+3x+80 so x=30 ?( uses both brand a and B) I've always used this formula...

the formula is correct but the way its been interpreted is little incorrect - let me clarify:

Total= Brand A-both brands+Brand B+Neither here, brand A=only brand A+both brands and brand B=only brand B+both brands now use this in your formula and instead of getting a "-x" you would end up with a "+x" in your equation and that would make your answer as x=15.

Re: A marketing firm determined that, of 200 households [#permalink]
13 Apr 2012, 16:17

the formula is correct but the way its been interpreted is little incorrect - let me clarify:

Total= Brand A-both brands+Brand B+Neither here, brand A=only brand A+both brands and brand B=only brand B+both brands now use this in your formula and instead of getting a "-x" you would end up with a "+x" in your equation and that would make your answer as x=15.

Hope that helps.[/quote]

When using the formula Total= Brand A + Brand B- both brands +Neither, brand A and brand b have to be double counted. In the sense that each needs to include those that only use their brand and those that use both. Hence for this question, we are given "60 used ONLY brand A" and "for every household that used both brands, 3 used ONLY brand B" there is no double counting. Thus, we should tweak the formula to be Total= Brand A + Brand B + both brands +Neither

Re: A marketing firm determined that, of 200 households [#permalink]
13 Apr 2012, 23:33

redbeanaddict 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?

Re: A marketing firm determined that, of 200 households [#permalink]
06 Dec 2012, 13:36

aviator83 wrote:

redbeanaddict wrote:

redbeanaddict 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 My answer was different from the answer given by OG. Help!

Shouldn't the equation be Total= Brand A-both brands+Brand B+Neither? 200=60-x+3x+80 so x=30 ?( uses both brand a and B) I've always used this formula...

the formula is correct but the way its been interpreted is little incorrect - let me clarify:

Total= Brand A-both brands+Brand B+Neither here, brand A=only brand A+both brands and brand B=only brand B+both brands now use this in your formula and instead of getting a "-x" you would end up with a "+x" in your equation and that would make your answer as x=15.

Hope that helps.

I've always used this formula too, and it does work. However this problem is worded a little weird and I misinterpreted it too, the way you setup the equation is wrong, mainly because like me, you didn't understand the ""and for every household that used both brands of soap, 3 used only Brand B soap" properly, this represents B - AB = 3(AB) not B = 3(AB)

Total = A + B + N - AB can be expanded to:

Total = (A - AB) + (B - AB) + N + AB

200 = 60 + 3AB + 80 + AB

200 = 60 + 80 + 4AB

60 = 4AB

15 = AB

or the way you set it up using x

200=60 + 4x +80

I think like most problems there's more than a few ways to get it wrong. Took me a LONG time to figure out where I went wrong, hope this clarifies the one way I got it wrong based on that formula.

Re: A marketing firm determined that, of 200 households [#permalink]
05 Oct 2014, 03:51

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Re: A marketing firm determined that, of 200 households [#permalink]
15 Dec 2014, 05:30

redbeanaddict 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?

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