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

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Senior Manager
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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?

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17 May 2005, 09:28
Christoph,
are you assuming that nobody had all 3 symptoms?

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17 May 2005, 09:44
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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21 May 2005, 00:01
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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21 May 2005, 00:10
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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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21 May 2005, 02:38
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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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25 May 2005, 15:41
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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25 May 2005, 20:51
Please explain this problem ....I didnt get the solution.....

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25 May 2005, 22:08
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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26 May 2005, 05:13
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 5745 times ]

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26 May 2005, 05:23
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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26 May 2005, 14:34
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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26 May 2005, 15:43
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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27 May 2005, 00:17
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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]

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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?

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]

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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]

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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]

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23 Jun 2010, 07:38
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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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Manager
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Re: PS - Venn Diag [#permalink]

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24 Jun 2010, 17:34
I thinks the Venn diagram should look like this , since no patients have all 3

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vennUntitled.png [ 12.05 KiB | Viewed 3354 times ]

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Senior Manager
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Re: PS - Venn Diag [#permalink]

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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?

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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