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# Of the 300 patients who suffered from at least one symptom of A, B, an

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Senior Manager
Joined: 10 Dec 2004
Posts: 254
Of the 300 patients who suffered from at least one symptom of A, B, an  [#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?
Math Expert
Joined: 02 Sep 2009
Posts: 56307
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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20 Aug 2010, 08:43
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+40-10-2*{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 100-10-5=85% --> in numbers 300*85%=255.

Check for more on this formula at: formulae-for-3-overlapping-sets-69014.html#p729340

Hope it helps.
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Manager
Joined: 28 Aug 2004
Posts: 194
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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21 May 2005, 00:10
1
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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Joined: 18 Apr 2005
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Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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21 May 2005, 02:38
2
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
Intern
Joined: 10 May 2005
Posts: 2
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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27 May 2005, 00:17
2
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  [#permalink]

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11 May 2010, 10:17
1
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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Posts: 98
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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23 Jun 2010, 07:38
2
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  [#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

Attachments

vennUntitled.png [ 12.05 KiB | Viewed 4327 times ]

Senior Manager
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Posts: 253
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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20 Aug 2010, 03:51
1
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: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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25 Sep 2014, 03:24
Refer diagram below:
Attachment:

lap.png [ 10.19 KiB | Viewed 1501 times ]

We require to find the total of pink shaded region

Total = 300

White Region = 30

Remaining = 270 = Total Pink Region + Green Region

Total Pink Region = 270 - Green Region

Setting up the equation:

105 + 120-(q+r+x)+r+135-(p+r+x) = 300

x = 15

Total Pink region = 270-15 = 255
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Posts: 105
Re: Of the 300 patients who suffered from at least one symptom of A, B, an  [#permalink]

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19 Mar 2018, 15:10
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 $$Total= A+B+C-Sum of exactly2+2Exactly3+N$$ and then you use the first formula to find Sum of Exactly1

Exactly3=AnBnC

Hope it helps !
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08 Jul 2019, 12:21
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Re: Venn Diagram Question   [#permalink] 08 Jul 2019, 12:21
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