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Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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09 Oct 2005, 19:56

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4

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00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

66% (03:08) correct
34% (02:35) wrong based on 273 sessions

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Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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09 Oct 2005, 20:07

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I get (C) 42

of the 600 residents, 210, 240 and 300 watch Island Survival,
Lovelost Lawyers and Medical Emergency respectively. this adds up to 750. we also know that 108 (18%) watch 2 shows, which leaves 642. therefore 42 watch all three shows.

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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09 Oct 2005, 20:15

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tingle wrote:

Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

(A) 150 (B) 108 (C) 42 (D) 21 (E) -21

Why am I getting E

210 watch IS
300 watch ME
240 watch LL
108 watch any two.

The number of viewers watch more than 1 programe is 210+300+240 -600= 150
------> the number of viewers watch all three programe is 150-180=42
C.

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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09 Oct 2005, 23:46

It is
240 + 300 + 210 - 108 - X = 600,
Where 240 watch Island Survival
300 watch Lovelost lawyers
210 watch medical emergency
108 watch 2 of those shows
X # who watch all the 3 shows
600 - Total # of residents.
Solving the equn we get x = 42.

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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10 Oct 2005, 05:59

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OA is D....

Here's the explanation:-

I+L+M-(IL+LM+IM)-2ILM= 600
210+240+300-(108)-2ILM= 600
ILM = 21

Why are we deducting 2ILM from the total???? shouldnt we be adding it back to the total as we already have deducted ILM thrice while deducting 108 from the equation. Pls explain......

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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10 Oct 2005, 06:48

I got 42.

I drew a venn diagram and split all the of shows. So, I got 210+240+300 = 750. Then reduced this by 18% ie 108 to get 642. Since there are only 600 residents, that must mean than 42 watch all the shows.

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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10 Oct 2005, 08:01

tingle wrote:

OA is D....

Why are we deducting 2ILM from the total???? shouldnt we be adding it back to the total as we already have deducted ILM thrice while deducting 108 from the equation. Pls explain......

18% is the list of people that watch *exactly 2 shows*.

I still don't get it. Why are we dividing 42 by 2?

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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10 Oct 2005, 19:31

By Set theory, for three sets intersecting each other,

Total = N(A) + N(B) + N(C) - (N(A n B) + N(A n C) + N(C n B)) +
N(A n B n C)
Where,
N = Number of -
n = 'Intersection'

We need to find out N(A n B n C)
The sum "N(A n B) + N(A n C) + N(C n B)" includes the value "N(A n B n C)" three times.

Per the question, "N(A n B) + N(A n C) + N(C n B)" - "3 * N(A n B n C)" = 18% So, "N(A n B) + N(A n C) + N(C n B)" = 18% + "3 * N(A n B n C)"
Therefore,
Total = N(A) + N(B) + N(C) - "18% + [3 * N(A n B n C)]" + N(A n B n C)]"

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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27 Apr 2007, 11:35

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I got 21 my first try too, but after so many 42s I thought I was wrong. Here is my reasoning:

IS=210
LL=240
ME=300
w=# shared between IS and LL
y=# shared between IS and ME
z=# shared between LL and ME
x=# shared between all three shows (this is the # we're trying to find)

We have to break the total # of residents into 3 groups:
1) those who only watch 1 show-->IS-x-w-y
LL-x-w-z
ME-x-y-z
2) those who watch only 2 shows-->w+y+z (which we know from the stem is 108)
3)those who watch all three shows-->x

So, add these three groups together and you get your 600 residents.

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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27 Nov 2007, 06:50

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tingle wrote:

Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

(A) 150 (B) 108 (C) 42 (D) 21 (E) -21

Why am I getting E

Triple Set Theory
100 = A + B + C – [AB + AC + BC] – [2*ALL]

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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20 Sep 2009, 03:03

used both methods. drew Venn diagram+used formula.

35% from 600=210 40% from 600=240 50% from 600=300 18% from 600=108 (108/3=36. 36 people by 3 groups. watching two of the shows) x - no of people watching all three

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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24 Oct 2009, 22:38

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tingle wrote:

Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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15 Jan 2010, 15:11

Prometoh wrote:

tingle wrote:

Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

(A) 150 (B) 108 (C) 42 (D) 21 (E) -21

D for me

Just plug the numbers in this equation:

Total = A + B + C - N2 - 2*N3

please let me know if my logic is sound if we introduce a change to the original question: instead of 18% watch exactly 2 of these shows, let's change it to: 18% watch at least 2 of these shows

would the answer then be

Total = A + B + C - N2 - N3 => 42 answer C?

I'm using the set theory that: # in exactly 2 sets = N2 - 3*N3 # in two or more sets = N2 - 2*N3

So for the total: Total = A + B + C - N2 + N3 now becomes: Total = A + B + C - (18 + 2*N3) + N3 Total = A + B + C - 18 - N3 Total = 35 + 40 + 50 - 18 - N3 = 100 N3 = 7% = 42

Re: Of the 600 residents of Clermontville, 35% watch the television show [#permalink]

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14 Feb 2010, 23:28

xiao85yu wrote:

Prometoh wrote:

tingle wrote:

Of the 600 residents of Clermontville, 35% watch the television show Island Survival, 40% watch Lovelost Lawyers and 50% watch Medical Emergency. If all residents watch at least one of these three shows and 18% watch exactly 2 of these shows, then how many Clermontville residents watch all of the shows?

(A) 150 (B) 108 (C) 42 (D) 21 (E) -21

D for me

Just plug the numbers in this equation:

Total = A + B + C - N2 - 2*N3

please let me know if my logic is sound if we introduce a change to the original question: instead of 18% watch exactly 2 of these shows, let's change it to: 18% watch at least 2 of these shows

would the answer then be

Total = A + B + C - N2 - N3 => 42 answer C?

I'm using the set theory that: # in exactly 2 sets = N2 - 3*N3 # in two or more sets = N2 - 2*N3

So for the total: Total = A + B + C - N2 + N3 now becomes: Total = A + B + C - (18 + 2*N3) + N3 Total = A + B + C - 18 - N3 Total = 35 + 40 + 50 - 18 - N3 = 100 N3 = 7% = 42

HI xiao85yu,

As per the set theory formula Total = g1+g2+g3 - (sum of all two groups) -2(sum of all three) + neither 600 = 210+240+300 - (108) - 2(sum of all three) + 0 2(sum of all three) = 750 - 600 - 108 2(sum of all three) = 42 (sum of all three) = 21

that's why its D.

I think you missed to divide the answer with 2.

Cheers!
_________________

--Action is the foundational key to all success.

gmatclubot

Re: Of the 600 residents of Clermontville, 35% watch the television show
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14 Feb 2010, 23:28

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