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04 Nov 2021, 08:15
Kudos
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Difficulty:
35%
(medium)
Question Stats:
73% (02:16) correct
27%
(02:24)
wrong
based on 206
sessions
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In a study done among 120 people at a Medical Centre, it was found that each person was suffering from at least one of the following diseases among abnormal blood pressure, diabetes and heart disease. There were 60 people who were diabetic, 40 had heart disease and 80 had abnormal blood pressure. How many of them were suffering from at least two of the above three diseases if 20 people were suffering from all the three diseases?
A) 30
B) 40
C) 50
D) 60
E) 70
A) 30
B) 40
C) 50
D) 60
E) 70
04 Nov 2021, 10:20
Kudos
Bookmarks
Let I = number of people suffering from at least 1 disease = Union = all 120 people
Let II = number of people suffering from at least 2 diseases (includes exactly 2 and exactly 3)
Let III = number of people suffering from at least 3 diseases (just those with exactly 3)
It must be that case that:
I >/= II >/= III
Since everyone suffers from at least one disease:
If we added up the entire “circle” of people suffering from Diabetes
+
If we added to this the entire “circle” of people suffering from heart disease
+
And if we adding to those two values the entire “circle” of people suffering from high blood pressure
_____________________________
The SUM TOTAL would equal =
I + II + III
Therefor we have:
I + II + III = (60) + (40) + (80) = 180
I = number of people suffering from at least 1 disease = all 120 people
III = number of people suffering from at least 3 disease = 20 people
Plug the values in:
(120) + II + (20) = 180
II = 40
Answer
40 people suffer from at least 2 diseases (either have 2 diseases or 3 diseases)
40
Method 2:
Let:
A = # of ppl who suffer from exactly 1 disease
B = # of ppl who suffer from exactly 2 diseases
C = # of ppl who suffer from exactly 3 diseases
We are given that C = 20 ppl
Since all 120 people suffer from at least 1 disease, we can write equation 1 for the unique number of people:
A + B + C = 120 ——- equation 1
And, to account for all the “tallies” of each disease:
1(A) + 2(B) + 3(C) = (60) + (40) + (80) = 180 ————— equation 2
Subtract equation 1 from equation 2:
1(A) + 2(B) + 3(C) = 180
(-) [ A + B + C = 120 ]
___________________________
B + 2(C) = 60
We are given that C = number of ppl who have exactly 3 diseases = 20
B + 2(20) = 60
B = 60 - 40 = 20
Answer:
Number of people suffering from at least 2 diseases = (# of ppl suffering from exactly 2) + (# of ppl suffering from exactly 3) = B + C = 20 + 20 =
40
Posted from my mobile device
Let II = number of people suffering from at least 2 diseases (includes exactly 2 and exactly 3)
Let III = number of people suffering from at least 3 diseases (just those with exactly 3)
It must be that case that:
I >/= II >/= III
Since everyone suffers from at least one disease:
If we added up the entire “circle” of people suffering from Diabetes
+
If we added to this the entire “circle” of people suffering from heart disease
+
And if we adding to those two values the entire “circle” of people suffering from high blood pressure
_____________________________
The SUM TOTAL would equal =
I + II + III
Therefor we have:
I + II + III = (60) + (40) + (80) = 180
I = number of people suffering from at least 1 disease = all 120 people
III = number of people suffering from at least 3 disease = 20 people
Plug the values in:
(120) + II + (20) = 180
II = 40
Answer
40 people suffer from at least 2 diseases (either have 2 diseases or 3 diseases)
40
Method 2:
Let:
A = # of ppl who suffer from exactly 1 disease
B = # of ppl who suffer from exactly 2 diseases
C = # of ppl who suffer from exactly 3 diseases
We are given that C = 20 ppl
Since all 120 people suffer from at least 1 disease, we can write equation 1 for the unique number of people:
A + B + C = 120 ——- equation 1
And, to account for all the “tallies” of each disease:
1(A) + 2(B) + 3(C) = (60) + (40) + (80) = 180 ————— equation 2
Subtract equation 1 from equation 2:
1(A) + 2(B) + 3(C) = 180
(-) [ A + B + C = 120 ]
___________________________
B + 2(C) = 60
We are given that C = number of ppl who have exactly 3 diseases = 20
B + 2(20) = 60
B = 60 - 40 = 20
Answer:
Number of people suffering from at least 2 diseases = (# of ppl suffering from exactly 2) + (# of ppl suffering from exactly 3) = B + C = 20 + 20 =
40
Posted from my mobile device
