A marketing firm determined that, of 200 households surveyed, 80 used

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!

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

~ 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.

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

Answer: Option A

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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?

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: Rich.C@empowergmat.com

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