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

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

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New post Updated on: 30 Mar 2016, 11:54
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  25% (medium)

Question Stats:

81% (02:41) correct 19% (02:51) wrong based on 171 sessions

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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

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  [#permalink]

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New post 12 Oct 2015, 00:47
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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  [#permalink]

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

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New post 17 Dec 2016, 03:45
1
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
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Re: Among 250 viewers interviewed who watch at least one of the three TV  [#permalink]

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

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

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

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

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New post 13 May 2018, 17:52
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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  [#permalink]

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New post 24 May 2018, 00:58
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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


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Re: Among 250 viewers interviewed who watch at least one of the three TV &nbs [#permalink] 24 May 2018, 00:58
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