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Among 250 viewers interviewed who watch at least one of the three TV
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Updated on: 30 Mar 2016, 11:54
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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
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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.




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Re: Among 250 viewers interviewed who watch at least one of the three TV
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12 Oct 2015, 00:47
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)
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Re: Among 250 viewers interviewed who watch at least one of the three TV
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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!



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Re: Among 250 viewers interviewed who watch at least one of the three TV
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17 Dec 2016, 03:45
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



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



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



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Re: Among 250 viewers interviewed who watch at least one of the three TV
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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.
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Re: Among 250 viewers interviewed who watch at least one of the three TV
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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.
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Re: Among 250 viewers interviewed who watch at least one of the three TV
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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
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Re: Among 250 viewers interviewed who watch at least one of the three TV
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24 May 2018, 00:58
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
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