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.

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:



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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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
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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.

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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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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