Problem Solving

smkhan wrote: A' alone - 60
A&B both - x
B' alone - 3x
N - Neither A nor B - 80
A - Total Brand A, 60+x
B - Total Brand B, 3x+x

Using the group formula, A+B-A&B+N=200

(60+x)+(3x+x)-x+80=200
60+4x+80=200
4x=200-140=60
x=15

As Brent has mentioned, this solution is perfect.
My concern is that many test-takers will omit the values in red.
A test-taker who omits the values in red will conclude that x=30 and will choose the wrong answer (C).

I see why there is some confusion here. I know this is an old post, but I thought I'd weight in to clear things up for people who stumble upon this question.

There are actually TWO formulas being discussed here and it depends on which you use.

You SUBTRACT 'Both' when Grp 1 and 2 are the TOTAL users of 1 and 2.
You ADD 'Both' when Grp 1 and Grp 2 are ONLY users of 1 or 2.

So the two equations you could use in this question are:

200=60+3x+80+x; because 60 and 3x are the number of Grp 1 and Grp 2 who use ONLY A or B
OR
200=(60+x)+(3x+x)+80-x; because (60+x) and (3x+x) are the number of Grp 1 and Grp 2 who use BOTH A and B

Summary. Use -Both when Grp 1 and 2 are the total users of 1 and 2 (including only and both) and use +Both when Grp 1 and 2 are ONLY A or B.

I hope this clears things up.

tar32 wrote: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


*which is the better approach? Venn vs. Formula [Group 1 + Group 2 - Both + Neither = Total ]

Venn makes it much faster than using the formulae which involve too many variables