Last visit was: 22 Sep 2026, 01:18 It is currently 22 Sep 2026, 01:18
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
   1   2 
555-605 (Medium)|   Overlapping Sets|                        
User avatar
fskilnik
User avatar
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 883
Own Kudos:
1,998
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 883
Kudos: 1,998
A marketing firm determined that, of 200 households surveyed, 80 used 30 Sep 2018, 13:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more
Excellent opportunity to use Venn diagrams (a.k.a. "overlapping sets")!




\(? = x\)

\(120 = 60 + x + 3x\,\,\,\,\, \Rightarrow \,\,\,\,? = x = 15\)


Regards,
Fabio.
User avatar
new2on
User avatar
Joined: 05 Jan 2019
Last visit: 25 Feb 2020
Posts: 7
Own Kudos:
23
Given Kudos: 61
Posts: 7
Kudos: 23
A marketing firm determined that, of 200 households surveyed, 80 used 12 Feb 2019, 11:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Solved this question algebraically as below:

Out of 200, 80 use none, so this leaves us with 120 using only A, only B and both.
Only A users = 60, now this leaves us with Only B and both users to be remaining 60.
Now, there's a relation given: 'for every household that used both brands of soap, 3 used only Brand B soap'
this means both:only B = 1:3, assign x to 'both' users.

So we get the below equation:
120=60+3x+x
x=15

Answer : A

Please correct me if I am wrong.
avatar
TheUltimateWinner
avatar
Schools: Harvard '24 Judge '23 LBS '24 McCombs '24 Mendoza Tepper '24 Ross '24 Cox Marshall '24 Fisher Kelley '24 Jones McDonough '24 Owen '24 Terry BU Simon '24 Katz GWU Mason Babson Gabelli Foster '24 Goizueta '24 Scheller Stern '23 CBS '23 Booth '23 Haas '25 Wharton '25 Stanford '26 Johnson'23 Fuqua '23 Kellogg '23 Kenan-Flagler'23 INSEAD Aug 22 intake Olin '23 Said '23 Sloan '23 Carey Arizona "22 Yale '23 UC Davis Madison '23 Anderson '23 Carroll Carlson '23 Darden '23
Posts: 2,464
Kudos: 2,514
 [1]
A marketing firm determined that, of 200 households surveyed, 80 used 04 May 2020, 22:12
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more
Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 18 Sep 2026
Posts: 4,849
Own Kudos:
9,375
 [3]
Given Kudos: 230
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,849
Kudos: 9,375
 [3]
A marketing firm determined that, of 200 households surveyed, 80 used 05 May 2020, 05:38
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asad
Bunuel
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
Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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
Show more

Hello Asad,

You have asked a good question and a pertinent one too. Very often, in questions on Venn diagrams, the word “ONLY” can be the difference between a correct and a wrong answer.
Let’s draw a Venn diagram to represent the situation defined in the question posed by you. It should look like this:

Attachment:
5th May 2020 - Reply 2.jpg
5th May 2020 - Reply 2.jpg [ 39.43 KiB | Viewed 14175 times ]

We see that x+y+z = 120 and x+z = 60. Therefore, y = 60 and z = 20 since \(\frac{z}{y}\) = \(\frac{1}{3}\).

The answer in this case would have been 20 i.e. option B. That should tell you that answer option B has been set up as a trap answer for students, who in their over-zealousness to get to the answer quickly may miss out the crucial keyword “only”.

Hope that helps!
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
Own Kudos:
13,283
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,775
Kudos: 13,283
A marketing firm determined that, of 200 households surveyed, 80 used 05 May 2020, 15:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Asad
Bunuel
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
Hello Experts,
EMPOWERgmatRichC, VeritasKarishma, IanStewart, Bunuel, chetan2u, ArvindCrackVerbal, GMATGuruNY, AaronPond, GMATinsight
The official answer is A. What if the word ''only'' is removed from the question prompt? It seems that the correct answer will be B (20), will it?
Thanks__
Here is the question prompt again-->

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
Show more

Hi Asad,

YES - if you edited the prompt in the way that you describe, then a change would occur in the Tic-Tac-Toe/Matrix Box that Bunuel presented. The "60" would appear in the lower-left corner of the grid, but the top row (re: X/3X/4X) would stay the same. You could then calculate the values of all of the boxes in the grid and the upper-left corner would be 20.

GMAT assassins aren't born, they're made,
Rich
avatar
rgbrao
avatar
Joined: 17 Apr 2020
Last visit: 13 Sep 2020
Posts: 2
Own Kudos:
3
Given Kudos: 31
Posts: 2
Kudos: 3
A marketing firm determined that, of 200 households surveyed, 80 used 13 May 2020, 14:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
~ I blindly applied the Two-Overlapping sets formula:

Total = Group1 + Group2 - Both + Neither

and got this wrong. Ouch.

This gives you 30 and which is likely a trap-answer. Clever.
User avatar
CEdward
User avatar
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,148
Own Kudos:
309
Given Kudos: 331
Posts: 1,148
Kudos: 309
A marketing firm determined that, of 200 households surveyed, 80 used 25 Jan 2021, 19:09
Kudos
Add Kudos
Bookmarks
Bookmark this Post
A only + Neither A/B = 60 + 80 = 140 <----Total who did not use B

200 - 140 = 60 <---- Total who did use B

x <--- Both
3x <--- B but not A

x + 3x = 60
4x = 60
x = 15

Answer is A.
User avatar
MHIKER
User avatar
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 935
Own Kudos:
5,977
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 935
Kudos: 5,977
A marketing firm determined that, of 200 households surveyed, 80 used 14 Feb 2021, 02:11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more


If both is x then it's included in B not in A as it's given that 60 used only Brand A soap;

The equation will be 200=60+3x+x+80

4x=60
x=15

So, both is 15

The answer is A
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 19 Sep 2026
Posts: 7,377
Own Kudos:
17,535
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
My Reviews
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 7,377
Kudos: 17,535
A marketing firm determined that, of 200 households surveyed, 80 used 17 Apr 2021, 01:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more

Answer: Option A

Video solution by GMATinsight

User avatar
peaarrr
User avatar
Joined: 03 Jul 2022
Last visit: 22 Feb 2023
Posts: 4
Given Kudos: 127
Posts: 4
Kudos: 0
A marketing firm determined that, of 200 households surveyed, 80 used 04 Aug 2022, 07:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Can anyone tell me why this formula does not work? For 2 overlapping sets >> total = group1 + group2 - both + neither.
Then, it suppose to be 200 = 60 + 3x - x +80 according to the venn diagram above?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,775
Own Kudos:
13,283
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,775
Kudos: 13,283
 [1]
A marketing firm determined that, of 200 households surveyed, 80 used 04 Aug 2022, 16:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi peaarrr,

The 'Overlapping Sets' formula that you are referring to refers to 5 different 'groups' - but there are actually 9 different groups that could appear in a standard Overlapping Sets question (meaning that that formula is only applicable in specific situations).

This prompt refers to two groups that are NOT represented in that formula ("60 used ONLY Brand A" and "....used ONLY Brand B"). For reference, in that formula, "Group1" actually refers to "those who use Brand A regardless of whether they also use Brand B or not" and "Group2" refers to "those who use Brand B regardless of whether they also use Brand A or not." Since these two groups almost always have some type of 'overlap', that's why the "-both" group appears in the equation (re: to eliminate the duplicate entries).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]
User avatar
DanTheGMATMan
User avatar
Joined: 02 Oct 2015
Last visit: 16 Sep 2026
Posts: 385
Own Kudos:
279
Given Kudos: 10
Expert
Expert reply
Posts: 385
Kudos: 279
A marketing firm determined that, of 200 households surveyed, 80 used 29 May 2024, 20:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Straightforward overlapping sets:

User avatar
totaltestprepNick
User avatar
Joined: 25 Aug 2014
Last visit: 16 Sep 2026
Posts: 469
Own Kudos:
9
Given Kudos: 2
GMAT 1: 750 Q49 V42
GMAT 1: 750 Q49 V42
Posts: 469
Kudos: 9
A marketing firm determined that, of 200 households surveyed, 80 used 03 Mar 2026, 13:06
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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
Show more

Show Spoiler
A




Nick Slavkovich, GMAT/GRE tutor with 20+ years of experience

[email protected]
User avatar
beebeebeebeebee
User avatar
Joined: 01 Feb 2025
Last visit: 21 Sep 2026
Posts: 2
Own Kudos:
68
Given Kudos: 1
Products:
GMAT Club Tests
Posts: 2
Kudos: 68
A marketing firm determined that, of 200 households surveyed, 80 used 23 Jul 2026, 07:31
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi, actually the question reads " and for every household that used both brands of soap, 3 used only Brand B soap" the key word being here "every". This simply means that if (say) "x" households use both the brands then 3x households use brand B.

Let me know if you're still confused :)
DonCarter
Hi :)

I have not been able to understand question 6 of the Quantitative section explanation at page 48.



Question 6 explanation: Arithmetic operations on rational numbers NOTE I copied exactly how GMAT written the question and explanation[/b]

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

[Their explanation]

Since it is given that 80 households use neither Brand A nor Brand B, then 200-80 = 120 (UNTIL HERE IT IS CORRECT) must use Brand A, Brand B, or both. It is also given that 60 households use only Brand A [b](CORRECT) and that three times as many households use both brands (WRONG? IN THE DATA GIVEN IT SAYS ONLY 3 PEOPLE USE BRAND B) [/b]. If x is the number of households that use both Brand A and Brand B, then 3x use Brand B alone. A Venn diagram can be helpful for visualizing the logic of the given information for this item:

Brand A Brand B

60 x 3x (I HAD ANSWER B. 20 60 is given 3 is given so 20 times 3 = 60 However, if we have 120 people who used Brand A (60) and B (3) than subtract 120 - 60 - 3 = 57 is left so they must use both Brand A & B. This is how I at first saw it but since non of these answers were possible it only makes sense to me the correct answer must be than 20)

All the sections in the circles can be added up and set equal to 120, and then the equation can be solved for x:

60+x+3x=120

60+4x=120 combine like terms (WHERE DOES THE 4 COMES FROM)

4x=60 subtract 60 from both sides

x=15 divided both sides by 4

Answer A


please explain to me if I am wrong. I will post more mistakes I have noticed in the book.

thanks
TD
Show more
   1   2 
Moderator:
Bunuel
Math Expert
113751 posts