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# ps - 3 sets

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VP
Joined: 30 Sep 2004
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Location: Germany
ps - 3 sets [#permalink]

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30 Oct 2005, 07:23
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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?

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

my question: i know the formula for this problem=>210+240+300-108+2x=600=>x=21.

now i tried to draw a venn diagramm but i just cant get it. i get a diff solution. can someone plz tell me where i am wrong ? thx
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If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

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Director
Joined: 27 Dec 2004
Posts: 894

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30 Oct 2005, 08:42
Chris,

i don't think the use of Venn diagrams is optimal here in the sense that the question stem does not specify which 2 shows the 18% residents watch.
Looking at your venn diagram, you assumed the 18% watch Island Survival and Lovelost Lawyers. However if you assigned the 18% to Lovelost and Medical emergency or medical emergency and Island Survival. i am sure your ansewers would vary. Thus the reason i'd ignore venn diagrams and solve it algrebraically as you have initially done.

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VP
Joined: 30 Sep 2004
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Location: Germany

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30 Oct 2005, 09:10
i just noticed that my venn diagram is right...
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If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

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Manager
Joined: 01 Aug 2005
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30 Oct 2005, 10:23
I seem to be getting C - 42.

Do you have the OE?

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VP
Joined: 22 Aug 2005
Posts: 1111

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Location: CA
Re: ps - 3 sets [#permalink]

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30 Oct 2005, 11:07
christoph 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

my question: i know the formula for this problem=>210+240+300-108+2x=600=>x=21.

now i tried to draw a venn diagramm but i just cant get it. i get a diff solution. can someone plz tell me where i am wrong ? thx

My formula has, change of sign for 2x:
210+240+300-108-2x=600
x = 21

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Manager
Joined: 01 Aug 2005
Posts: 68

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30 Oct 2005, 11:20
How come you guys are writing -2x in your equations, shouldnt it just be x?

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SVP
Joined: 05 Apr 2005
Posts: 1705

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Re: ps - 3 sets [#permalink]

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30 Oct 2005, 21:37
christoph 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

my question: i know the formula for this problem=>210+240+300-108+2x=600=>x=21.

now i tried to draw a venn diagramm but i just cant get it. i get a diff solution. can someone plz tell me where i am wrong ? thx

your venn diagram is perfectly ok and ideal here but the formulae is not. the formulae should be:
600 = 210+240+300-108-2x (you should deduct x twice because x is added thrice; one in 210, another in 240 and the other in 300. actually it should be added only once. so we need to deduct x twice. if it were a case of two component case, we would deduct x once.)

x=21.

if you correctly calculate your formula, x would be in -ve, which is absurd because people cannot be in -ve.

210+240+300-108+2x = 600
2x = 708-750
x =-42/2
x = -21

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Manager
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31 Oct 2005, 13:52
Christoph what book/source is this from? Also if you have the OE please post it. Thanks!

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Senior Manager
Joined: 26 Jul 2005
Posts: 313

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31 Oct 2005, 16:12
Testing my speed, I tried to use logic to solve this problem but think I screwed up. Can someone point out where I'm going wrong?

750 --> total that watched one of the three shows
-600 --> total residents
_______
150 --> watched multiple shows
-108 --> total that watched 2 shows
_______
<b>C. 42</b> watched 3 shows

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Director
Joined: 21 Aug 2005
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31 Oct 2005, 16:42

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Senior Manager
Joined: 26 Jul 2005
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Location: Los Angeles

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31 Oct 2005, 16:47
Makes sense. Thanks gsr!

At least I know many others made the same mistake I made and answered C.

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31 Oct 2005, 16:47
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# ps - 3 sets

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