Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 31 Aug 2015
Posts: 31

Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
Updated on: 30 Mar 2016, 11:54
1
This post received KUDOS
12
This post was BOOKMARKED
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
Official Answer and Stats are available only to registered users. Register/ Login.
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.



Veritas Prep GMAT Instructor
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
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
Joined: 19 Mar 2015
Posts: 13

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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
Joined: 05 Jul 2006
Posts: 1734

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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 = 2505025 = 175



Intern
Joined: 30 Jan 2016
Posts: 7

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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
Joined: 11 Aug 2016
Posts: 47
Location: India
Concentration: Operations, General Management
GPA: 3.95
WE: Design (Manufacturing)

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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
Joined: 01 Dec 2016
Posts: 119
Concentration: Finance, Entrepreneurship
WE: Investment Banking (Investment Banking)

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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 600650 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
Joined: 14 Oct 2012
Posts: 176

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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/threetable ... 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 [ 600.44 KiB  Viewed 1006 times ]



Target Test Prep Representative
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
13 May 2018, 17:52
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 WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Status: It's near  I can see.
Joined: 13 Apr 2013
Posts: 960
Location: India
Concentration: International Business, Operations
GPA: 3.01
WE: Engineering (Consulting)

Re: Among 250 viewers interviewed who watch at least one of the three TV [#permalink]
Show Tags
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






