GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 19 Jun 2018, 09:06

LIVE NOW:

Tips for Your Best Possible Application - Live Chat with Tuck Admissions | Click Here to JOIN!


Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

A marketing firm determined that, of 200 households surveyed

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
User avatar
B
Joined: 25 Sep 2017
Posts: 17
GMAT ToolKit User
Re: A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 16 Nov 2017, 02:36
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
_________________

GA800

Intern
Intern
avatar
Joined: 05 Mar 2018
Posts: 1
A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 05 Mar 2018, 11:13
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.
Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 600
Re: A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 22 Mar 2018, 12:51
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:

Image


"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.

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 ...
Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 22 Mar 2018, 18:36
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:

Image


"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.

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!
:cool:
Director
Director
User avatar
G
Joined: 09 Mar 2016
Posts: 600
A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 23 Mar 2018, 03:17
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:

Image


"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.

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!
:cool:



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
1 KUDOS received
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3642
Premium Member Reviews Badge CAT Tests
A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 23 Mar 2018, 03:24
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?
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - Click here.



NEW VISA FORUM - Ask all your Visa Related Questions - Click here.



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

1 KUDOS received
Senior Manager
Senior Manager
User avatar
S
Status: love the club...
Joined: 24 Mar 2015
Posts: 275
Re: A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 23 Mar 2018, 17:36
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
Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1505
Re: A marketing firm determined that, of 200 households surveyed [#permalink]

Show Tags

New post 26 Mar 2018, 11:05

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

Image

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.

Answer: Option A
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: A marketing firm determined that, of 200 households surveyed   [#permalink] 26 Mar 2018, 11:05

Go to page   Previous    1   2   [ 28 posts ] 

Display posts from previous: Sort by

A marketing firm determined that, of 200 households surveyed

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.