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ps - 3 sets

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VP
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ps - 3 sets [#permalink] New post 30 Oct 2005, 06:23
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 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

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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 [#permalink] New post 30 Oct 2005, 07:42
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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 [#permalink] New post 30 Oct 2005, 08:10
i just noticed that my venn diagram is right... :idea:
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 [#permalink] New post 30 Oct 2005, 09:23
I seem to be getting C - 42.

Do you have the OE?
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Re: ps - 3 sets [#permalink] New post 30 Oct 2005, 10:07
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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 [#permalink] New post 30 Oct 2005, 10:20
How come you guys are writing -2x in your equations, shouldnt it just be x?
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Re: ps - 3 sets [#permalink] New post 30 Oct 2005, 20:37
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 8-)
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 [#permalink] New post 31 Oct 2005, 12:52
Christoph what book/source is this from? Also if you have the OE please post it. Thanks!
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 [#permalink] New post 31 Oct 2005, 15:12
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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 [#permalink] New post 31 Oct 2005, 15:42
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 [#permalink] New post 31 Oct 2005, 15:47
Makes sense. Thanks gsr!

At least I know many others made the same mistake I made and answered C.
  [#permalink] 31 Oct 2005, 15:47
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