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megafan
Joined: 28 May 2009
Last visit: 15 Oct 2017
Posts: 137
Given Kudos: 91
Location: United States
Concentration: Strategy, General Management
Schools: Stern PT Fall'18 Booth PT '18
GMAT Date: 03-22-2013
GPA: 3.57
WE:Information Technology (Consulting)
06 Mar 2013, 19:37
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
69% (01:51) correct
31%
(02:09)
wrong
based on 295
sessions
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Not Attempted Yet
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
(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
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.
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.
General Discussion
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.
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.
Attachments
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