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sharadGmat
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Of the 600 residents of Clermontville, 35% watch the 03 Jul 2006, 19:21
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45. 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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Of the 600 residents of Clermontville, 35% watch the 03 Jul 2006, 21:18
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I am getting -42. But people count can't be -ve. :roll: :roll: :roll:

35+40+50-18+x = 100

So x = -7. Total number = -7*6 = -42
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acfuture
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Of the 600 residents of Clermontville, 35% watch the 03 Jul 2006, 21:27
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600 = .35(600)+.40(600)+300-.18(600)-ALL

ALL = 42

C
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ps_dahiya
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Of the 600 residents of Clermontville, 35% watch the 03 Jul 2006, 21:31
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acfuture
600 = .35(600)+.40(600)+300-.18(600)-ALL

ALL = 42

C
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Formula is A+B+C-AB-BC-CA+ABC. Instead, you took -ABC.
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Of the 600 residents of Clermontville, 35% watch the 04 Jul 2006, 01:41
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ps_dahiya
acfuture
600 = .35(600)+.40(600)+300-.18(600)-ALL

ALL = 42

C

Formula is A+B+C-AB-BC-CA+ABC. Instead, you took -ABC.
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True formula is A+B+C-(AB+BC+AC)+ABC

hence

600 = 210+240-108+ABC
ABC = 42
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Of the 600 residents of Clermontville, 35% watch the 04 Jul 2006, 03:12
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I am getting D.... as per the formula given by Honghu .
OA please...
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Of the 600 residents of Clermontville, 35% watch the 04 Jul 2006, 03:31
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Remember, for three sets A,B and C

TOTAL= n(A)+n(B)+n(C)-( n(A and B and not C)+n(B and C and not A)+n(A and C and not B)) - 2n(A and B and C)+ n(not A and not B and not C)

So, if x= percent who watch all three,

100%= 35% + 40% + 50% - 18% - 2x + 0%

and x=3.5%

So n(A and B and C)= 3.5% of 600= 21

Remember for other questions

TOTAL= n(A)+n(B)+n(C)- (n(A and B)+n(A and C)+ n(B and C))+n( A and B and C)+n(not A and not B and not C)
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Of the 600 residents of Clermontville, 35% watch the 04 Jul 2006, 06:51
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amansingla4
I am getting D.... as per the formula given by Honghu .
OA please...
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if you don't mind, can you post the formula that you are refering to?

ps_dahiya,
again thanks ... :oops:
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amartin6165
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Of the 600 residents of Clermontville, 35% watch the 04 Jul 2006, 11:05
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please tell me if I am wrong, but the answer cannot be 42 because you are then counting the same person 3 times, once for each of the three shows they watch. thus the answer must be 21...

i would also like to see the formula -- i worked it out slightly differently.

(35/100)*(600) = 210 watch I.S.
(4/10)*600 = 240 watch L.L.
300 watch M.E.

750 counts of shows watched

(18/100)(600) = 108 watch 2 shows; 750 - 108 = 642

Answer is NOT 42 because we're looking at counts of shows watched rather than number of people, thus answer must be 21 to count each person once.



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