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Overlapping sets - OG12

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mdavidm_531: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 07, 2010 3:12 am; Thanked: 10 times

by mdavidm_531 » Wed May 16, 2012 7:08 pm

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

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Source: Beat The GMAT — Problem Solving | Wed May 16, 2012 7:08 pm

amsm25: Junior | Next Rank: 30 Posts; Posts: 28; Joined: Thu Jul 28, 2011 11:53 am

by amsm25 » Wed May 16, 2012 7:31 pm

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

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transfer9858: Senior | Next Rank: 100 Posts; Posts: 95; Joined: Wed Aug 03, 2011 1:52 pmFollowed by: 2 members; Thanked: 16 times

by transfer9858 » Wed May 16, 2012 7:37 pm

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.

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mathbyvemuri: Master | Next Rank: 500 Posts; Posts: 142; Joined: Thu Apr 26, 2012 3:24 am; Location: India; Thanked: 28 times

by mathbyvemuri » Wed May 16, 2012 7:39 pm

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

RaviSankar Vemuri

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mdavidm_531: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 07, 2010 3:12 am; Thanked: 10 times

by mdavidm_531 » Wed May 16, 2012 7:55 pm

This is how I interpreted the problem.

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

Kindly enlighten me

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Wed May 16, 2012 9:29 pm

mdavidm_531 wrote:

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").

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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mdavidm_531: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Mon Jun 07, 2010 3:12 am; Thanked: 10 times

by mdavidm_531 » Wed May 16, 2012 10:56 pm

Stuart Kovinsky wrote:
mdavidm_531 wrote:

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?

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Thu May 17, 2012 8:25 am

Hi!

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

Stuart

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