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A research study found that, of 500 people surveyed, 220 [#permalink]

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06 Mar 2013, 19:37

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A research study found that, of 500 people surveyed, 220 watched neither Network A nor Network B, 120 watched only Network A, and for every person who watched both networks, 3 watched only Network B. How many of the 500 people surveyed watched both networks?

(A) 40 (B) 60 (C) 80 (D) 100 (E) 120

I always screw up with the correct usage of this relationship: [Total = Group1 + Group2 - Both + Neither] vs [Total = Group1 + Group2 + Both + Neither], i.e. when to subtract Both and when to add Both

Re: A research study found that, of 500 people surveyed, 220 [#permalink]

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06 Mar 2013, 20:53

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megafan, see the attached figure.

the portion in green corresponds to neither A nor B. The one in brown corresponds to only A. The one in blue to only B. The one in red to both A and B.

n(Total) = n(Neither A nor B) + n(only A) + n(only B) + n(both A and B) => 500 = 220 + 120 + 3x + x => x = 160/4 = 40

Used when Group1 includes Both. e.g. given 160 people watch network A. This means 160 watch network A and it includes those people who watch both the networks. Similarly, Group2 includes people who watch both the networks e.g. given 160 watch network B - 160 includes the number of people who watch both networks. Since no of people who watch both networks is included twice, you subtract it out once.

500 = 160 + 160 - 40 + 220

2. [Total = Group1 + Group2 + Both + Neither]

Used when Group1 is the number of people who watch ONLY network A e.g. given 120 people watch ONLY network A (compare this with above where the word ONLY is missing). Group2 includes people who watch ONLY network B. Since you haven't accounted for the people who watch both, you add Both once.

500 = 120 + 120 + 40 + 220

Hope both the formulas make sense now.

Here, you are given that 120 watched only network A so you use the second formula. Also, it might be a good idea to get comfortable with venn diagrams. Such confusions do not occur if you always use the venn diagram.
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A research study found that, of 500 people surveyed, 220 watched neither Network A nor Network B, 120 watched only Network A, and for every person who watched both networks, 3 watched only Network B. How many of the 500 people surveyed watched both networks?

(A) 40 (B) 60 (C) 80 (D) 100 (E) 120

I always screw up with the correct usage of this relationship: [Total = Group1 + Group2 - Both + Neither] vs [Total = Group1 + Group2 + Both + Neither], i.e. when to subtract Both and when to add Both

Re: A research study found that, of 500 people surveyed, 220 [#permalink]

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07 Mar 2013, 09:08

VeritasPrepKarishma wrote:

Here are the two formulas

1. [Total = Group1 + Group2 - Both + Neither]

Used when Group1 includes Both. e.g. given 160 people watch network A. This means 160 watch network A and it includes those people who watch both the networks. Similarly, Group2 includes people who watch both the networks e.g. given 160 watch network B - 160 includes the number of people who watch both networks. Since no of people who watch both networks is included twice, you subtract it out once.

500 = 160 + 160 - 40 + 220

2. [Total = Group1 + Group2 + Both + Neither]

Used when Group1 is the number of people who watch ONLY network A e.g. given 120 people watch ONLY network A (compare this with above where the word ONLY is missing). Group2 includes people who watch ONLY network B. Since you haven't accounted for the people who watch both, you add Both once.

500 = 120 + 120 + 40 + 220

Hope both the formulas make sense now.

Here, you are given that 120 watched only network A so you use the second formula. Also, it might be a good idea to get comfortable with venn diagrams. Such confusions do not occur if you always use the venn diagram.

Wow, thanks a lot! This makes the problem seem like a 300-level question. I think I usually don't pay attention to the elements in the set -- i.e. whether there is an overlap or not. Note to self: watch out for only.
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and for every person who watched both networks, 3 watched only Network B. How many of the 500 people surveyed watched both networks?

Can someone clarify this wording? I understood what they were testing but I couldn't figure out what that meant....

It just gives you the relation between the two groups:

- No of people who watched both networks - No of people who watched only network B

It means that if there is only 1 person who watches both networks, there are 3 who watch only network B. If there are 2 people who watch both networks, there are 6 who watch only network B and so on... It is just another way of telling that the ratio of no of people watching both networks and no of people who watch only network B is 1:3

So if x people watch both networks, 3x watch only network B.
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Can anyone solve the same problem using 2 way matrix

A research study found that, of 500 people surveyed, 220 watched neither Network A nor Network B, 120 watched only Network A, and for every person who watched both networks, 3 watched only Network B. How many of the 500 people surveyed watched both networks? (A) 40 (B) 60 (C) 80 (D) 100 (E) 120

Re: A research study found that, of 500 people surveyed, 220 [#permalink]

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19 Jun 2014, 08:07

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