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Of the 300 patients who suffered from at least one symptom [#permalink]

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17 May 2005, 08:20

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Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

Christoph, are you assuming that nobody had all 3 symptoms?

i assume that 30 have exactly two symptoms and 30 have all three symptomps. A+B+C=360. so 30 have i.e. AB and 30 have ABC. so its A-ABC-AB+(B-ABC-AB)+(C-ABC)=105-30-30+135-30-30+120-30=210. is it ?
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If your mind can conceive it and your heart can believe it, have faith that you can achieve it.

Please explain this problem ....I didnt get the solution.....

gmat, use Venn diagram, draw three intersecting circles representing A B C, there will be 3 areas where only to sets intersect, and 1 where all three intersect. Solution should be clear if you do that. Sorry I have no idea how to draw things on my comp, otherwise I would do it.

(A intersect B) + (B intersect C) + (C intersect A) - (A intersect B intersect C) = 10%.300 = 30

T = A + B + C - (A inter B) - (B inter C) - (C inter A) + (A inter B inter C)
= A + B + C - 30 - 2 (A inter B inter C)
<--> 300 = 105 + 135 +120 - 30 - 2 (A inter B inter C)
--> (A inter B inter C) = 15

Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

We know from Venn Diag that (AUBUC) = A+B+C - (AB) - 2(ABC) 100 = 35+45+40 - 10 -2(g)

Therefore, g = 5%

Putting g = 5% in eq (1), we get a+b+c = 85% = (85/100)x300 = 255.

Hope this is useful.
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the trick here is to remember 4 main equations union of three sets = (sum of 3) - (sum of 2) + (all 3) exactly 2 = (sum of 2) - 3(all 3) at least 2 = (sum of 2) - 2(all 3) only 1 = (sum of 3) -2(sum of 2) + 3(all 3)

of course add neither to each one of these if not everyone is in a set...

Of the 300 patients who suffered from at least one symptom of A, B, and C, 35 % suffered from A, 45% suffered from B, 40 % suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom?

Pls explain answer choice..

deferred solution till OA is out, but here it goes..

T = A + B + C - (2 of them) - 2 * (ABC) + neither

300 = 105 + 135 + 120 -30 -2*ABC

ABC = 15.

a + 2*b + 3*c = 105 + 135 + 120 = 360 a + 2*30 + 3*15 = 360