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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

Attachments

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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.

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

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

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