Last visit was: 17 Jul 2025, 11:52 It is currently 17 Jul 2025, 11:52
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
555-605 Level|   Overlapping Sets|                        
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,700
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
new2on
Joined: 05 Jan 2019
Last visit: 25 Feb 2020
Posts: 7
Own Kudos:
Given Kudos: 61
Posts: 7
Kudos: 7
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 17 Jul 2025
Posts: 4,847
Own Kudos:
8,645
 [3]
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,847
Kudos: 8,645
 [3]
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

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 13663 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: 21,788
Own Kudos:
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: 21,788
Kudos: 12,499
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

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
Joined: 17 Apr 2020
Last visit: 13 Sep 2020
Posts: 2
Own Kudos:
Given Kudos: 31
Posts: 2
Kudos: 1
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
Joined: 11 Aug 2020
Last visit: 14 Apr 2022
Posts: 1,212
Own Kudos:
Given Kudos: 332
Posts: 1,212
Kudos: 247
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
Joined: 14 Jul 2010
Last visit: 24 May 2021
Posts: 945
Own Kudos:
Given Kudos: 690
Status:No dream is too large, no dreamer is too small
Concentration: Accounting
Posts: 945
Kudos: 5,468
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


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: 17 Jul 2025
Posts: 6,377
Own Kudos:
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:
Expert
Expert reply
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,377
Kudos: 15,602
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

Answer: Option A

Video solution by GMATinsight

User avatar
peaarrr
Joined: 03 Jul 2022
Last visit: 22 Feb 2023
Posts: 4
Given Kudos: 127
Posts: 4
Kudos: 0
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: 21,788
Own Kudos:
12,499
 [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: 21,788
Kudos: 12,499
 [1]
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
Joined: 02 Oct 2015
Last visit: 17 Jul 2025
Posts: 354
Own Kudos:
Given Kudos: 9
Expert
Expert reply
Posts: 354
Kudos: 172
Kudos
Add Kudos
Bookmarks
Bookmark this Post
­Straightforward overlapping sets:

User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,437
Own Kudos:
Posts: 37,437
Kudos: 1,013
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
   1   2 
Moderators:
Math Expert
102603 posts
PS Forum Moderator
697 posts