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

Question

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

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

I always screw up with the correct usage of this relationship:   vs  , i.e. when to subtract Both and when to add Both

KarishmaB · Accepted Answer

Here are the two formulas

1.

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.

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.

GyanOne · Answer

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.

Bunuel · Answer

This might help: advanced-overlapping-sets-problems-144260.html (ADVANCED OVERLAPPING SETS PROBLEMS)

megafan · Answer

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 .

skiingforthewknds · Answer

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....

KarishmaB · Answer

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.

piyushdiyora · Answer

Can anyone solve the same problem using 2 way matrix

Bunuel · Answer

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

ButwhY · Answer

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

PareshGmat · Answer

Refer diagram below

We require to find the shaded region

Equation setup would be:

120 + x + 3x + 220 = 500

4x = 160

x = 40

Answer = A

generis · Answer

Focus on the target population: those who watched both

1) Eliminate the non-watchers.
500 surveyed. 220 watch neither. (500-220) = 280 watchers. From THIS total population, "both" is derived

2) A ONLY = 120

3) B? Defined in terms of Both = X. For every 1 "X" there are 3 Bs: 
  \frac{B}{X}=\frac{3}{1} 
 B = 3X

4) A only + B only + Both = 280
120 + 3X + X = 280
4X = 160
X = 40 = Both 
 
Answer A

rameshkumarm · Answer

220+120+x+3x=500
X=40

Posted from my mobile device

bumpbot · Answer

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

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