Overlapping sets - OG12

[mdavidm_531]

Hi, I am having a hard time putting the question into double-matrix form.

Diagnostic Test #6 OG12

"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?"

I arranged my double matrix as:

Brand B not Brand B Total
Brand A
Not Brand A 80
Total 200

I get stuck after this. Where do I place 60?

I know I have to use ratio and proportion (unknown multiplier) to solve this. I just can't comprehend where I will place 60.

Dave

[amsm25]

T=200
Neither - 80
Only A- 60
Only B = 3(Both)

Only A +Only B + Neither - Both = Total

60 + 3*Both +80 - Both = 200
2*Both = 60
Therefore both = 30

[transfer9858]

Look at the diagram I did- Its the "3 line" method- I use it for every diagram/ven question and have yet to get one wrong... It works every time and it could be done it 20 seconds.... Practice making the chart..


In this problem just solve x+3x=60 x=15. 15 people use both brands A and B.

[mathbyvemuri]

we have four types here:
only A = 60
only B
Both A and B
Neither A Nor B = 80

assume, "Both A and B" = x => "only B" = 3x

Total = only A + only B + both + neither
200 = 60+3x+80+x
=> x = 15

Answer - 15

[mdavidm_531]

This is how I interpreted the problem.

Seems that I didn't get what "60 used only Brand A soap"

Kindly enlighten me

[Stuart@KaplanGMAT]

This is how I interpreted the problem.

Seems that I didn't get what "60 used only Brand A soap"

Kindly enlighten me

Hi!

You've put 60 in the Brand A "total" column, which includes "brand A/brand B" and "brand A/not brand B". People in the "brand A/brand B" column are NOT "brand A ONLY" - they're using both.

The 60 should go in the "brand a/not brand B" box in the grid, since those are the people who use only A (i.e. "only A" means "A but not B").

[mdavidm_531]

This is how I interpreted the problem.

Seems that I didn't get what "60 used only Brand A soap"

Kindly enlighten me

Hi!

You've put 60 in the Brand A "total" column, which includes "brand A/brand B" and "brand A/not brand B". People in the "brand A/brand B" column are NOT "brand A ONLY" - they're using both.

The 60 should go in the "brand a/not brand B" box in the grid, since those are the people who use only A (i.e. "only A" means "A but not B").

Hello,

Is this the same?

[Stuart@KaplanGMAT]

Hi!

Yes - if you want to solve with a Venn diagram, that's exactly where you'd put the 60.

Stuart