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Of the 300 patients who suffered from at least one symptom [#permalink]
 17 May 2005, 08:20
Question Stats:
40% (01:50) correct
60% (02:59) wrong based on 2 sessions
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..
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Director
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Christoph,
are you assuming that nobody had all 3 symptoms?
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thearch wrote: 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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Senior Manager
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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
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Manager
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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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Director
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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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Director
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Is it possible to take this problem further and deduce the exact number of patients who suffers only from A, only from B and only from C ?
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Director
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Please explain this problem ....I didnt get the solution.....
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Director
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gmat2me2 wrote: 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.
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can someone explain this to me,plz !
i calculated it the folowing way:
35%-x-10%-0+40%-x-0-10%+45%-0-0-x=100%
x=all 3 symptoms
where am i wrong ?
Attachments
venn2.JPG [ 9.36 KiB | Viewed 3183 times ]
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christoph wrote: can someone explain this to me,plz !
i calculated it the folowing way:
35%-x-10%-0+40%-x-0-10%+45%-0-0-x=100%
x=all 3 symptoms
where am i wrong ?
chris, you're subtracting x 3 times; A, B and C all include ABC, so you've to subtract x = ABC only twice to keep one ABC in the loop.
Also you're subtracting 10% twice; should be once otherwise double coutning.
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thx,dan.
A=35%=105 and B=40%=135 and C=45%=120
105-(AB+AC+ABC)+135-(AB+BC+ABC)+120-(BC+AC+ABC)+(AB+AC+BC+ABC)=300
=>
105-(30+0+ABC)+135-(30+0+ABC)+120-(0+0+ABC)+(30+0+0+ABC)=300
=>
105-30-ABC+135-30-ABC+120-ABC+30+ABC=300
=>
330-2ABC=300 => ABC=15 => 300-30-15=255 
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Director
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Chris, see those areas where you have 10%, 0, and 0? Their sum has to be equal to 10%, not just one area as it is on your diagram.
Venn diagram is the most powerful way to sort out simple set and probability problems.
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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: PS - Venn Diag [#permalink]
24 Oct 2009, 23:47
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.. 255 Sol: First find N3 : 100 = 35 + 45 + 40 - 10 - 2*N3 N3 = 5% Second find N1: 100 = N1 + N2 + N3 = N1 + 10 + 5 N1 = 85% or 255 Cheers
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Re: PS - Venn Diag [#permalink]
11 May 2010, 10:17
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: PS - Venn Diag [#permalink]
22 Jun 2010, 16:58
300= 105 + 135 + 120 - (Both) + (all 3)
lets call (all 3) = x
exactly 2: 30 = Both - 3(x)
Both = 30 + 3x
300 = 360 -(both) + x
= 360 -(30-3x) + x
= 330 - 2x
x= 15
15 in all 3
75 in Both
exactly 1 = 360 - 2(both) + 3(x)
= 360 - 150 + 45
= 255
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...
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Re: PS - Venn Diag [#permalink]
23 Jun 2010, 07:38
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: PS - Venn Diag [#permalink]
24 Jun 2010, 17:34
I thinks the Venn diagram should look like this , since no patients have all 3 so answer should be 200
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vennUntitled.png [ 12.05 KiB | Viewed 689 times ]
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Re: PS - Venn Diag [#permalink]
20 Aug 2010, 03:51
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: PS - Venn Diag
[#permalink]
20 Aug 2010, 03:51
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