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555-605 (Medium)|   Overlapping Sets|                        
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A marketing firm determined that, of 200 households surveyed, 80 used 30 Sep 2018, 13:38
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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.
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A marketing firm determined that, of 200 households surveyed, 80 used 12 Feb 2019, 11:49
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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.
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A marketing firm determined that, of 200 households surveyed, 80 used 04 May 2020, 22:12
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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
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A marketing firm determined that, of 200 households surveyed, 80 used 05 May 2020, 05:38
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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 14165 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!
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A marketing firm determined that, of 200 households surveyed, 80 used 05 May 2020, 15:34
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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.

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A marketing firm determined that, of 200 households surveyed, 80 used 13 May 2020, 14:35
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~ 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.
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A marketing firm determined that, of 200 households surveyed, 80 used 25 Jan 2021, 19:09
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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.
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A marketing firm determined that, of 200 households surveyed, 80 used 14 Feb 2021, 02:11
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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
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A marketing firm determined that, of 200 households surveyed, 80 used 17 Apr 2021, 01:37
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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

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A marketing firm determined that, of 200 households surveyed, 80 used 04 Aug 2022, 07:06
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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?
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A marketing firm determined that, of 200 households surveyed, 80 used 04 Aug 2022, 16:01
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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).

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A marketing firm determined that, of 200 households surveyed, 80 used 29 May 2024, 20:34
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­Straightforward overlapping sets:

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A marketing firm determined that, of 200 households surveyed, 80 used 03 Mar 2026, 13:06
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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
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Show Spoiler
A




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

[email protected]
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A marketing firm determined that, of 200 households surveyed, 80 used 23 Jul 2026, 07:31
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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
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