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Senior Manager
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Of the 300 patients who suffered from at least one symptom of A, B, an
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17 May 2005, 07:20
Question Stats:
50% (03:40) correct 50% (01:57) wrong based on 42 sessions
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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?



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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20 May 2005, 23:10
I 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
==> a = 255



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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21 May 2005, 01:38
I got 255 as well.
Venn diagram is very helpful here
knowing that 30 people suffered from two symptoms
number of ppl suffereing exactly from 1 and 3 symptoms is (360  2*30 (since 2 sets intersect)  3 (ABC) (since 3 sets intersect)) + ABC = 300  30 = 270
so ABC = 15
300  30 15 = 255



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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26 May 2005, 23:17
T=300
A=35%.300=105
B=135
C=120
(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
> answer = 300  30 15 = 225.



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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11 May 2010, 09:17
I have a different way to solve this using venn diag. Let take the variables as: a = exactly one for A, b = exactly one for B, c = exactly one for C, d = exactly two from A and B, e = exactly two from B and C, f = exactly two from C and A g = all three from A, B and C We are given d+e+f = 10%, so lets solve in % terms. a+b+c+(d+e+f)+g = 100 >>>> a+b+c+g = 90 (eq 1) Now, we need g to find the required (a+b+c). 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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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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23 Jun 2010, 06:38
255. 100 = 35 + 45 + 40  10  2x x all common x = 15 percent Required = 100  ( 10 + 15 ) = 85 percent of 300 = 255
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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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24 Jun 2010, 16:34
I thinks the Venn diagram should look like this , since no patients have all 3 so answer should be 200
Attachments
vennUntitled.png [ 12.05 KiB  Viewed 3905 times ]



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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20 Aug 2010, 02:51
pb_india wrote: 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 ==> a = 255 pls explain the step in the red color



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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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20 Aug 2010, 07:43
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?Total=A+B+C  {People who suffered from exactly 2 symptoms}  2*{People who suffered from exactly 3 symptoms} + {People who suffered from neither of symptoms}; 100=35+45+40102*{People who suffered from exactly 3 symptoms}+0 > {People who suffered from exactly 3 symptoms}=5%; So as {People who suffered from exactly 2 symptoms}=10% and {People who suffered from exactly 3 symptoms}=5% then {People who suffered from exactly one symptom} is 100105=85% > in numbers 300*85%=255. Answer: 255. Check for more on this formula at: formulaefor3overlappingsets69014.html#p729340Hope it helps.
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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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25 Sep 2014, 02:24
Refer diagram below: Attachment:
lap.png [ 10.19 KiB  Viewed 1081 times ]
We require to find the total of pink shaded regionTotal = 300
White Region = 30
Remaining = 270 = Total Pink Region + Green Region
Total Pink Region = 270  Green RegionSetting up the equation: 105 + 120(q+r+x)+r+135(p+r+x) = 300 x = 15 Total Pink region = 27015 = 255
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Re: Of the 300 patients who suffered from at least one symptom of A, B, an
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19 Mar 2018, 14:10
HowManyToGo wrote: Dan wrote: 255 I too got 255. Does anyone know the forumla based soln. I did it with V diagrams and no matter how many times I do such problems , I take eons. HMTG yes it is \(Total = Sum of Exactly1+ Sum of Exactly2+ Exactly3\) In this kind of problems you find the Exactly 3 from the formula \(Total= A+B+CSum of exactly2+2Exactly3+N\) and then you use the first formula to find Sum of Exactly1 Exactly3=AnBnC Hope it helps !
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Re: Of the 300 patients who suffered from at least one symptom of A, B, an &nbs
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