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# A marketing firm determined that, of 200 households surveyed

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Intern
Joined: 25 Sep 2017
Posts: 18
Re: A marketing firm determined that, of 200 households surveyed  [#permalink]

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16 Nov 2017, 01:36
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

Diagnostic Test
Question: 6
Page: 21
Difficulty: 650

15
x->Both then
3x for only B

60+x+3x = 120
x = 15
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Joined: 05 Mar 2018
Posts: 1
A marketing firm determined that, of 200 households surveyed  [#permalink]

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05 Mar 2018, 10:13
I tried this question using:
Total = Group 1 + Group 2 - Both + Neither.
200 = 60 + 3Both - Both + 80
200 = 140 + 2Both
60 = 2Both
Both = 30.

Can someone give me some pointer on why my answer is wrong but when I used the same approach for question 14 on OG 2017, page 14. I was able to have it correct.

Thank you.
VP
Joined: 09 Mar 2016
Posts: 1076
Re: A marketing firm determined that, of 200 households surveyed  [#permalink]

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22 Mar 2018, 11:51
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, $$4x+140=200$$ --> $$x=15$$.

Attachment:
A marketing firm determined.JPG

Hello Bunuel i reviewed the whole thread before to ask a question

but i still dont understand

IF:

neither is 80

A soap = 60

both = x

only 3 used B only

so 200 = 60+3 -x+80

i used the formula --- > total = group1 +group 2- both +neither

so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ...
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A marketing firm determined that, of 200 households surveyed  [#permalink]

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22 Mar 2018, 17:36
1
dave13 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, $$4x+140=200$$ --> $$x=15$$.

Attachment:
A marketing firm determined.JPG

Hello Bunuel i reviewed the whole thread before to ask a question

but i still dont understand

IF:

neither is 80

A soap = 60

both = x

only 3 used B only

so 200 = 60+3 -x+80

i used the formula --- > total = group1 +group 2- both +neither

so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ...

hi

I am not Bunuel the great, but I will try to help you understand the concept

Yes, I agree with you, the formula you have applied to the problem is okay, but to get this formula help you, you have to put the values with great care

okay, let me explain to you, where you went wrong

Total = group1 + grpup2 - both + neither

here, in this formula, group1 or grpup2 doesn't exclude the possibilities where people can use both brands. You can see this arrangement as inclusive OR. When you select gorup1 (brand A) chances are still there that, some customers using brand B are also counted. When you select brand B, as before, chances are still there that, some customers using Brand A, are counted.

thus, to avoid the double counting, "both" is subtracted once. As I mentioned earlier, since it is inclusive OR, "both" is counted once. So, when you say "A + B", it means A, and B, or both.

now if you want to use this formula, you have do so as under

200 = (60 + x) + (3x + x) - x + 80

=) x = 15

so, as you can see, the formula doesn't intend to mean, group1 = only A
and group2 = only B, but rather, it means group1 = only A + those who are using A and B both

OR

you can simply solve the problem as follows

120 = 60 + 3x + x

=) x =15

since, 80 uses neither,
total is 120,
60 uses only A,
3x uses only B, and x uses both

hope this helps and is clear!
thanks and cheers!
VP
Joined: 09 Mar 2016
Posts: 1076
A marketing firm determined that, of 200 households surveyed  [#permalink]

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23 Mar 2018, 02:17
gmatcracker2018 wrote:
dave13 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, $$4x+140=200$$ --> $$x=15$$.

Attachment:
A marketing firm determined.JPG

Hello Bunuel i reviewed the whole thread before to ask a question

but i still dont understand

IF:

neither is 80

A soap = 60

both = x

only 3 used B only

so 200 = 60+3 -x+80

i used the formula --- > total = group1 +group 2- both +neither

so what am i doing wrong ? and which method do you reccomend to solve overlapping sets ? i you seem to use either matrix, formula that i mentioned , or venn diagram ...

hi

I am not Bunuel the great, but I will try to help you understand the concept

Yes, I agree with you, the formula you have applied to the problem is okay, but to get this formula help you, you have to put the values with great care

okay, let me explain to you, where you went wrong

Total = group1 + grpup2 - both + neither

here, in this formula, group1 or grpup2 doesn't exclude the possibilities where people can use both brands. You can see this arrangement as inclusive OR. When you select gorup1 (brand A) chances are still there that, some customers using brand B are also counted. When you select brand B, as before, chances are still there that, some customers using Brand A, are counted.

thus, to avoid the double counting, "both" is subtracted once. As I mentioned earlier, since it is inclusive OR, "both" is counted once. So, when you say "A + B", it means A, and B, or both.

now if you want to use this formula, you have do so as under

200 = (60 + x) + (3x + x) - x + 80

=) x = 15

so, as you can see, the formula doesn't intend to mean, group1 = only A
and group2 = only B, but rather, it means group1 = only A + those who are using A and B both

OR

you can simply solve the problem as follows

120 = 60 + 3x + x

=) x =15

since, 80 uses neither,
total is 120,
60 uses only A,
3x uses only B, and x uses both

hope this helps and is clear!
thanks and cheers!

Hi gmatcracker2018,

many thanks for taking time to explain:) did you finally crack GMAT ?

I have one question regarding this expression:

and for every household that used both brands of soap, 3 used only Brand B soap.

why are you writing as 3x instead of just 3. it says 3 used only Brand B soap

so if those who use both A and B both is denoted as X

hence if i break down the wording of question shouldnt we get this-- >

$$60+x = A$$ means households that used only soap A only as well as+ those who use both soaps A with B
$$3+x= B$$ means households that used only soap B as well as+ those who use both soaps B with A
$$X= both$$ means households that used both A and B soaps
$$80 = neither$$ households that used neither A nor B
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A marketing firm determined that, of 200 households surveyed  [#permalink]

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23 Mar 2018, 02:24
1
dave13 wrote:
Hi gmatcracker2018,

many thanks for taking time to explain:) did you finally crack GMAT ?

I have one question regarding this expression:

and for every household that used both brands of soap, 3 used only Brand B soap.

why are you writing as 3x instead of just 3. it says 3 used only Brand B soap

so if those who use both A and B both is denoted as X

hence if i break down the wording of question shouldnt we get this-- >

$$60+x = A$$
$$3+x= B$$
$$X= both$$
$$80 = neither$$

Hey dave13 ,

You didn't understand the meaning of the sentence "for every household that used both brands of soap, 3 used only Brand B soap. " correctly.

This means if they were X households who used both the brands, there were 3X households that used only Brand B. Thus, the calculation you did is incorrect because of the wrong meaning you took. It's a 1 to 3 relationship.

Does that make sense?
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Status: love the club...
Joined: 24 Mar 2015
Posts: 267
Re: A marketing firm determined that, of 200 households surveyed  [#permalink]

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23 Mar 2018, 16:36
1
abhimahna wrote:
dave13 wrote:
Hi gmatcracker2018,

many thanks for taking time to explain:) did you finally crack GMAT ?

I have one question regarding this expression:

and for every household that used both brands of soap, 3 used only Brand B soap.

why are you writing as 3x instead of just 3. it says 3 used only Brand B soap

so if those who use both A and B both is denoted as X

hence if i break down the wording of question shouldnt we get this-- >

$$60+x = A$$
$$3+x= B$$
$$X= both$$
$$80 = neither$$

Hey dave13 ,

You didn't understand the meaning of the sentence "for every household that used both brands of soap, 3 used only Brand B soap. " correctly.

This means if they were X households who used both the brands, there were 3X households that used only Brand B. Thus, the calculation you did is incorrect because of the wrong meaning you took. It's a 1 to 3 relationship.

Does that make sense?

hi dave13

as you can see abhimahna the boss has already replied to your question very elegantly

anyway, please note that, we have got a relationship between "both" and "only B". Thus, if you don't attach a variable to the ratio, given, you won't get any hard number

thanks
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Joined: 04 Jan 2015
Posts: 2203
Re: A marketing firm determined that, of 200 households surveyed  [#permalink]

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26 Mar 2018, 10:05
1

Solution:

Given:

• Number of households surveyed = 200

• Households who used only Brand A soaps = 60

• Households who used only Brand B soaps = 3* Households who used both soaps.

• Households who used neither Brand A nor Brand B soaps = 80

Working out:

We need to find out the number of households which used soaps of both the brands.

To understand the solution, let us draw a 2-set Venn diagram

Since the total households surveyed were 200 and 80 of them used no soaps, (200-80) households used at least one of Brand A or Brand B soaps.

• Thus, $$3x +x +60 = 120$$

• Or, $$x =15$$.

Thus, 15 households used both the brands of the soaps.

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

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23 Jun 2018, 02:22
I agree with the Venn Diagram part. Makes life easier.
conty911 wrote:
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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29 Jun 2018, 02:34
The best way to answer this question is to visualize using a Venn diagram.

total: 200 households
80 don't use A or B.
only 120 households use either soap A or B.
60 use only soap A, so 60 use either only B or both soap A & B in the ratio of 3:1

therefore, 45 households use only soap B and 15 use both.
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Re: A marketing firm determined that, of 200 households surveyed  [#permalink]

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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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Re: A marketing firm determined that, of 200 households surveyed &nbs [#permalink] 30 Sep 2018, 12:38

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