GMAT Changed on April 16th - Read about the latest changes here

It is currently 24 May 2018, 18:35

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Among 250 viewers interviewed who watch at least one of the three TV

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

1 KUDOS received
Intern
Intern
avatar
Joined: 31 Aug 2015
Posts: 31
Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post Updated on: 30 Mar 2016, 11:54
1
This post received
KUDOS
12
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

82% (13:39) correct 18% (03:29) wrong based on 144 sessions

HideShow timer Statistics

Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

(A) 185
(B) 180
(C) 175
(D) 190
(E) 195

source - pearson

Originally posted by excelingmat on 11 Oct 2015, 22:31.
Last edited by Bunuel on 30 Mar 2016, 11:54, edited 1 time in total.
Renamed the topic and edited the question.
Expert Post
4 KUDOS received
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8077
Location: Pune, India
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 12 Oct 2015, 00:47
4
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

a) 185
b) 180
c) 175
d)190
e) 195

source - pearson


250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let's find the value of n(Exactly 3 channels) = x

250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 50 - 2x
x = 25

250 = n(Exactly 1 channel) + 50 + 25
n(Exactly 1 channel) = 175

Answer (C)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 19 Mar 2015
Posts: 13
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 17 Oct 2015, 07:41
VeritasPrepKarishma wrote:
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

a) 185
b) 180
c) 175
d)190
e) 195

source - pearson


250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let's find the value of n(Exactly 3 channels) = x

250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 50 - 2x
x = 25

250 = n(Exactly 1 channel) + 50 + 25
n(Exactly 1 channel) = 175

Answer (C)

Hi Veritasprep,
Thanks for this great explanation. But I m little confused about this statement: 250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
I drew the venn diagram and I wasnt able to come up to this formulae. Please help!
Thanks again!
Retired Moderator
User avatar
B
Joined: 05 Jul 2006
Posts: 1734
GMAT ToolKit User Premium Member
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 17 Dec 2016, 03:45
1
This post was
BOOKMARKED
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

(A) 185
(B) 180
(C) 175
(D) 190
(E) 195

source - pearson


Since none = 0 , therefore at least 1 = total = 250 .

and since A+B+C = 350 thus (A and B)+ (B and C)+(C and A) - (A and B and C) = 100

but (A and B)+ (B and C)+(C and A) = Exactly 2 sets + 3 (A and B and C)

Thus(A and B)+ (B and C)+(C and A) - (A and B and C) = 100 =Exactly 2 sets + 2(A and B and C) and since Exactly 2 sets = 50 thus all three (A and B and C) = 25

Exactly 1 = Total - Exactly 2 - All 3 = 250-50-25 = 175
Intern
Intern
avatar
S
Joined: 30 Jan 2016
Posts: 7
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 18 Dec 2016, 09:12
VeritasPrepKarishma wrote:
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

a) 185
b) 180
c) 175
d)190
e) 195

source - pearson


250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let's find the value of n(Exactly 3 channels) = x

250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 50 - 2x
x = 25

250 = n(Exactly 1 channel) + 50 + 25
n(Exactly 1 channel) = 175

Answer (C)





Could someone please clarify the 3x+x part at the end of the equation as a substitute for what should be "neither" - n(A and B and C) in the equation ? Or am I looking at this from the wrong perspective ?
Intern
Intern
avatar
S
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
Schools: HBS '18, ISB '17, IIMA
GMAT 1: 710 Q49 V38
GPA: 3.95
WE: Design (Manufacturing)
GMAT ToolKit User
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 05 Feb 2017, 14:18
stanoevskas wrote:
VeritasPrepKarishma wrote:
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

a) 185
b) 180
c) 175
d)190
e) 195

source - pearson


250 = n(Exactly 1 channel) + n(Exactly 2 channels) + n(Exactly 3 channels)
250 = n(Exactly 1 channel) + 50 + n(Exactly 3 channels)

Let's find the value of n(Exactly 3 channels) = x

250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)
Note that each of n(A and B) is the sum of 'number of people watching exactly two channels A and B' and 'number of people watching all three channels'.
250 = 116 + 127 + 107 - n(Exactly 2 channels) - 3x + x
250 = 116 + 127 + 107 - 50 - 2x
x = 25

250 = n(Exactly 1 channel) + 50 + 25
n(Exactly 1 channel) = 175

Answer (C)





Could someone please clarify the 3x+x part at the end of the equation as a substitute for what should be "neither" - n(A and B and C) in the equation ? Or am I looking at this from the wrong perspective ?


For a 3 set overlapping venn diagram,
n(A and B) = n (people who exactly watch A and B but not C) + n(A and B and C)
Similarly
n(B and C) = n (people who exactly watch B and C but not A) + n(A and B and C)
n(C and A) = n (people who exactly watch C and A but not B) + n(A and B and C)

n(A and B)+n(B and C)+n(C and A) = n(people who watch exactly 2 channels) + 3x .. equation 1

250 = n(A) + n(B) + n(C) - n(A and B) - n(B and C) - n(C and A) + n(A and B and C)

Substituting equation 1 in the above equation we get

250 = 116 + 127 + 107 - n(people who watch Exactly 2 channels) - 3x + x

Hope it is clear
Manager
Manager
User avatar
S
Joined: 01 Dec 2016
Posts: 119
Concentration: Finance, Entrepreneurship
GMAT 1: 650 Q47 V34
WE: Investment Banking (Investment Banking)
GMAT ToolKit User
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 01 Mar 2017, 09:23
Tough most GMAT takers must be familiar to the concept of 3 overlapping sets , I think the difficulty of this question's diffculty is average.
I would say Level 600-650 question.
_________________

What was previously considered impossible is now obvious reality.
In the past, people used to open doors with their hands. Today, doors open "by magic" when people approach them

Manager
Manager
avatar
G
Joined: 14 Oct 2012
Posts: 176
Premium Member Reviews Badge CAT Tests
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 22 Apr 2017, 14:15
My 2 cents:
I solved this question as follows:

Personally, i would to say that the only formulas i remember are
T = A + B + C - [exactly 2 sets] - 2*[all 3 sets] + None &
T = A + B + C - [among 2 sets] + [all 3 sets] + None.
If you can't solve with these 2 formulas than the best option will be dividing 3 overlapping sets into various sections as a, b, c, d, e, f and g as you might already have seen in various examples solved here.
(If not refer - https://gmatclub.com/forum/three-table- ... 05637.html)
Honestly, after 2 tries i have understood one thing that GMAT does NOT give time to anaylse question and see which formula to use. So remembering lot of formulas isn't a way to prepare for GMAT. Also, question where you can apply it directly will hardly be ever asked.
Attachments

a+b+c.jpg
a+b+c.jpg [ 600.44 KiB | Viewed 1006 times ]

Expert Post
2 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2638
Location: United States (CA)
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 13 May 2018, 17:52
2
This post received
KUDOS
Expert's post
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

(A) 185
(B) 180
(C) 175
(D) 190
(E) 195


We can use the equation:

Total = watched A + watched B + watched C - watched exactly two - 2(watched all 3) + watched none

250 = 116 + 107 + 127 - 50 - 2T + 0

250 = 300 - 2T

2T = 50

T = 25

So we have:

250 = watched exactly 1 + watched exactly 2 + watched all 3 + watched none

250 = n + 50 + 25 + 0

175 = n

Answer: C
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

1 KUDOS received
Director
Director
User avatar
P
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 960
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge
Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]

Show Tags

New post 24 May 2018, 00:58
1
This post received
KUDOS
ScottTargetTestPrep wrote:
excelingmat wrote:
Among 250 viewers interviewed who watch at least one of the three TV channels namely A, B &C. 116 watch A, 127 watch C, while 107 watch B. If 50 watch exactly two channels. How many watch exactly one channel?

(A) 185
(B) 180
(C) 175
(D) 190
(E) 195


We can use the equation:

Total = watched A + watched B + watched C - watched exactly two - 2(watched all 3) + watched none

250 = 116 + 107 + 127 - 50 - 2T + 0

250 = 300 - 2T

2T = 50

T = 25

So we have:

250 = watched exactly 1 + watched exactly 2 + watched all 3 + watched none

250 = n + 50 + 25 + 0

175 = n

Answer: C


Easiest and the best way from all above. Kudos as I was about to giving up on this question.

Thanks


QZ
_________________

"Success is not as glamorous as people tell you. It's a lot of hours spent in the darkness."

Re: Among 250 viewers interviewed who watch at least one of the three TV   [#permalink] 24 May 2018, 00:58
Display posts from previous: Sort by

Among 250 viewers interviewed who watch at least one of the three TV

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.