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Of the 300 patients who suffered from at least one symptom

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Re: PS - Venn Diag [#permalink] New post 20 Aug 2010, 07:43
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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?

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.

Answer: 255.

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

Hope it helps.
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Re: PS - Venn Diag [#permalink] New post 29 Aug 2011, 10:55
total = A+B+C -(two symptoms) -2(three symptoms)
300 = 105+135+120 -30 -2(all three)
all three = 15

suffering from exactly one symptom = 300 -15 -30 = 255
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Re: Of the 300 patients who suffered from at least one symptom [#permalink] New post 24 Sep 2014, 22:53
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Re: Of the 300 patients who suffered from at least one symptom [#permalink] New post 25 Sep 2014, 02:24
Refer diagram below:
Attachment:
lap.png
lap.png [ 10.19 KiB | Viewed 208 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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Re: Of the 300 patients who suffered from at least one symptom   [#permalink] 25 Sep 2014, 02:24

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