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Intern
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Of the 600 residents of Clermontville, 35% watch the [#permalink]
 09 Oct 2005, 20:56
Question Stats:
77% (03:20) correct
22% (01:50) wrong based on 18 sessions
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
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Manager
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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.
Whats the OA?
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Intern
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Hi,
I get 42 and here is my method
600 = ((35%*600+50%*600+40%*600) - (18%*600) - sum of people watching all 3
solving we get 42. Do let me know if this is the right answer.
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SVP
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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.
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Manager
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Just modify the formula A + B - both + neither = total:
A + B + C - two shows - three shows = total
35% + 40% + 50% - 18% - x% = 100%
x=7%
600 * .07 = 42
Brendan.
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GMAT Club Legend
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The rules of a venn diagram is if you add each individual sections, you get the total, which is 600 in this case.
So 210 + 240 + 300 - 108 - X = 600 where x represents people who watch all three.
so x = 42
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Senior Manager
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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.
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Intern
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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......
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Director
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OA is D.
Lets see my reasoning.
For a three set problem we have the following formula:
100= A+B+C-AB-AC-BC+ABC, which is the same as the following formula
100= A+B+C+(-AB-AC-BC+ABC+ABC+ABC)-2ABC.
The term between parantheses value 18% so the equation to resolve is
100=35+40+50-18-2ABC
therefore the value of ABC is 3.5% of 600, is 21. D is the correct answer
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Senior Manager
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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.
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Manager
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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?
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Director
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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)]"
600 = 210 + 240 + 300 - 108 - [2 *N(A n B n C)]
=> N(A n B n C) = 21
Hence D
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Manager
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gsr wrote: 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)]"
600 = 210 + 240 + 300 - 108 - [2 *N(A n B n C)]
=> N(A n B n C) = 21
Hence D
Thanks a bunch gsr..... Excellent Explanation!!!!
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Manager
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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.
IS-x-w-y+LL-x-w-z+ME-x-y-z+w+y+x+x=600
Simplify: (IS+LL+ME)+(w+y+z)-2x-2w-2y-2z=600
Simplify: 750+108-2(x+w+y+z)=600
-2(x+w+y+z)=-258
x+(108)=129
x=21
I tried to make my explanation really detailed so that all my steps would be really understandable. How did I do? 
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Manager
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Indeed, the answer is 21:
I = 35%
L = 40%
E = 50%
neither = 0
exactly 2 shows: IL+LE+IE - 3 * ILE = 18%
-> total = I+L+E-(IL+LE+IE)+ILE+neither
100% = 35%+40%+50%-(18%+3*ILE)+ILE+0%
--> ILE = 3.5%
3.5% of 600 people = 21 people
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Senior Manager
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It´s D.
Considering that all 600 ppl watch at least one show:
AUBUC = 100% = A + B + C - (AnB + BnC + CnA) + AnBnC = 35 + 40 + 50 - (18 + 3X) - X (X = AnBnC).
Therefore: 100 = 107 - 2X => X = 3.5%. 600 = 21.
D.
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CEO
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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]
100 = 35 + 40 + 50 – 18 – 2x
100 = 125 – 18 – 2x
100 = 107 – 2x
2x = 7
x = 3.5
3.5% of 600 residents = 600*.035 = 21
This method is MUCH faster than Venn Diagram Approach
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Manager
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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 thus 600=210+240+300-(36+x)-(36+x)-(36+x)+x -42=-2x x=21 D
_________________
Never, never, never give up
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Manager
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After the deductions,I'm getting the ans as 21.
I wud go with option D
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Manager
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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 D for me Just plug the numbers in this equation: Total = A + B + C - N2 - 2*N3
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close
