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