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

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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
[Reveal] Spoiler: OA

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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

Therefore 40 people watched both networks.

Option A.
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figure.jpg [ 28.56 KiB | Viewed 2325 times ]

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

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06 Mar 2013, 21:51
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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.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 38868 Followers: 7731 Kudos [?]: 106101 [1] , given: 11607 Re: A research study found that, of 500 people surveyed, 220 [#permalink] ### Show Tags 07 Mar 2013, 01:52 1 This post received KUDOS Expert's post megafan wrote: 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 This might help: advanced-overlapping-sets-problems-144260.html (ADVANCED OVERLAPPING SETS PROBLEMS) _________________ Manager Joined: 28 May 2009 Posts: 156 Location: United States Concentration: Strategy, General Management GMAT Date: 03-22-2013 GPA: 3.57 WE: Information Technology (Consulting) Followers: 8 Kudos [?]: 232 [0], given: 91 Re: A research study found that, of 500 people surveyed, 220 [#permalink] ### Show Tags 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. _________________ Intern Joined: 28 Nov 2012 Posts: 44 Followers: 0 Kudos [?]: 41 [0], given: 3 Re: A research study found that, of 500 people surveyed, 220 [#permalink] ### Show Tags 08 Mar 2013, 15:38 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.... Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7374 Location: Pune, India Followers: 2288 Kudos [?]: 15107 [0], given: 224 Re: A research study found that, of 500 people surveyed, 220 [#permalink] ### Show Tags 09 Mar 2013, 00:32 skiingforthewknds wrote: 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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

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29 May 2013, 10:34
Can anyone solve the same problem using 2 way matrix
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Re: A research study found that, of 500 people surveyed, 220 [#permalink]

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29 May 2013, 15:09
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piyushdiyora wrote:
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
Attachment:

Matrix.png [ 5.36 KiB | Viewed 1774 times ]
From above 4x+340=500 --> x=40.

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

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29 May 2013, 18:57
let x = only A =120 given
y = both A and B
z=only B
w= neither A and B = 220 given
also given z=3*y

from below picture
x+y+z+w = 500
using above given values
y+z =160

and 4*y = 160(since z=3*y)
y=40

Sol:A
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venn_1.JPG [ 7.66 KiB | Viewed 1727 times ]

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

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25 Jul 2014, 02:26
Refer diagram below

We require to find the shaded region

Equation setup would be:

120 + x + 3x + 220 = 500

4x = 160

x = 40

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shad.png [ 4.15 KiB | Viewed 1128 times ]

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Re: A research study found that, of 500 people surveyed, 220   [#permalink] 25 Jul 2014, 02:26
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