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17 May 2005, 08:20
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
48% (02:50) correct
52%
(02:32)
wrong
based on 108
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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?
A. 235
B. 240
C. 245
D. 250
E. 255
A. 235
B. 240
C. 245
D. 250
E. 255
20 Aug 2010, 08:43
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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.
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.
General Discussion
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
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
