It is currently 16 Dec 2017, 01:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 28 May 2009
Posts: 155

Kudos [?]: 277 [0], given: 91

Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
A research study found that, of 500 people surveyed, 220 [#permalink]

### Show Tags

06 Mar 2013, 18:37
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:14) correct 29% (01:07) wrong based on 145 sessions

### HideShow timer Statistics

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

_________________

Kudos [?]: 277 [0], given: 91

VP
Joined: 24 Jul 2011
Posts: 1354

Kudos [?]: 663 [1], given: 20

GMAT 1: 780 Q51 V48
GRE 1: 1540 Q800 V740
Re: A research study found that, of 500 people surveyed, 220 [#permalink]

### Show Tags

06 Mar 2013, 19:53
1
KUDOS
1
This post was
BOOKMARKED
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.
Attachments

figure.jpg [ 28.56 KiB | Viewed 2520 times ]

_________________

GyanOne | Top MBA Rankings and MBA Admissions Blog

Premium MBA Essay Review|Best MBA Interview Preparation|Exclusive GMAT coaching

Get a FREE Detailed MBA Profile Evaluation | Call us now +91 98998 31738

Kudos [?]: 663 [1], given: 20

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7799

Kudos [?]: 18138 [2], given: 236

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

### Show Tags

06 Mar 2013, 20:51
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 18138 [2], given: 236

Math Expert
Joined: 02 Sep 2009
Posts: 42630

Kudos [?]: 135779 [1], given: 12714

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

### Show Tags

07 Mar 2013, 00:52
1
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

_________________

Kudos [?]: 135779 [1], given: 12714

Manager
Joined: 28 May 2009
Posts: 155

Kudos [?]: 277 [0], given: 91

Location: United States
Concentration: Strategy, General Management
GMAT Date: 03-22-2013
GPA: 3.57
WE: Information Technology (Consulting)
Re: A research study found that, of 500 people surveyed, 220 [#permalink]

### Show Tags

07 Mar 2013, 08:08
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.
_________________

Kudos [?]: 277 [0], given: 91

Intern
Joined: 28 Nov 2012
Posts: 44

Kudos [?]: 62 [0], given: 3

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

### Show Tags

08 Mar 2013, 14:38
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....

Kudos [?]: 62 [0], given: 3

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7799

Kudos [?]: 18138 [0], given: 236

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

### Show Tags

08 Mar 2013, 23:32
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

Veritas Prep Reviews

Kudos [?]: 18138 [0], given: 236

Intern
Joined: 16 Dec 2012
Posts: 1

Kudos [?]: [0], given: 3

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

### Show Tags

29 May 2013, 09:34
Can anyone solve the same problem using 2 way matrix

Kudos [?]: [0], given: 3

Math Expert
Joined: 02 Sep 2009
Posts: 42630

Kudos [?]: 135779 [1], given: 12714

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

### Show Tags

29 May 2013, 14:09
1
KUDOS
Expert's post
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 1969 times ]
From above 4x+340=500 --> x=40.

Hope it helps.
_________________

Kudos [?]: 135779 [1], given: 12714

Intern
Joined: 02 May 2013
Posts: 24

Kudos [?]: 58 [0], given: 16

WE: Engineering (Aerospace and Defense)
Re: A research study found that, of 500 people surveyed, 220 [#permalink]

### Show Tags

29 May 2013, 17:57
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
Attachments

venn_1.JPG [ 7.66 KiB | Viewed 1922 times ]

Kudos [?]: 58 [0], given: 16

Non-Human User
Joined: 09 Sep 2013
Posts: 14816

Kudos [?]: 288 [0], given: 0

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

### Show Tags

19 Jun 2014, 07:07
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 288 [0], given: 0

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1849

Kudos [?]: 2792 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: A research study found that, of 500 people surveyed, 220 [#permalink]

### Show Tags

25 Jul 2014, 01:26
Refer diagram below

We require to find the shaded region

Equation setup would be:

120 + x + 3x + 220 = 500

4x = 160

x = 40

Attachments

shad.png [ 4.15 KiB | Viewed 1322 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2792 [0], given: 193

Re: A research study found that, of 500 people surveyed, 220   [#permalink] 25 Jul 2014, 01:26
Display posts from previous: Sort by