Logical Reasoning – 1000 patients currently suffering from a disease



1000 patients currently suffering from a disease were selected to study the effectiveness of treatment of four types of medicines — A, B, C and D. These patients were first randomly assigned into two groups of equal size, called treatment group and control group. The patients in the control group were not treated with any of these medicines; instead they were given a dummy medicine, called placebo, containing only sugar and starch. The following information is known about the patients in the treatment group.

  1. . A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
  2. 25 patients were treated with type A medicine only. 20 patients were treated with type C medicine only. 10 patients were treated with type D medicine only.
  3. 35 patients were treated with type A and type D medicines only. 20 patients were treated with type A and type B medicines only. 30 patients were treated with type A and type C medicines only. 20 patients were treated with type C and type D medicines only.
  4. 100 patients were treated with exactly three types of medicines.
  5. 40 patients were treated with medicines of types A, B and C, but not with medicines of type D. 20 patients were treated with medicines of types A, C and D, but not with medicines of type B.
  6. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
Q.1 How many patients were treated with medicine type B?

Answer: 340

Q.2 The number of patients who were treated with medicine types B, C and D, but not type A was:?

Answer: 10

Q.3 How many patients were treated with medicine types B and D only?

Answer: 150

Q.4 The number of patients who were treated with medicine type D was:?

Answer: 325

Solutions:
As the given questions are based on only second group that is treatment group also there are a lot of data given . So it will be easier to make a venn diagram and fill all the given data and then solve the questions for missing values.
as the given question are based on
Given ,
From statement f) 75 patients were treated with exactly one type of medicine.
So 10+20+x+25 = 75
x = 20
From statement a) A total of 250 patients were treated with type A,
So 25+20+30+40+35+20+50 + y = 250
220 + y = 250
y = 30
From statement d) 100 patients were treated with exactly three types of medicines.
40+20+y+z = 100
60+30+z = 100
z = 10
From statement a) total of 210 patients were treated with type C medicine. So,
20+20+20+30+40+50+b+z = 210
180+b + 10= 210
b = 20
Now as there were total 500 patient in treatment group , so
250+x+b+z+a +20+20+10 = 500
300+20+20+10 + a = 500
a + 350 = 500
a = 150
Q1 – Number of patients were treated with medicine type B = 20+40+50+y + x+z+a+b = 110+20+30+10+150+20= 340
Q2. The number of patients who were treated with medicine types B, C and D, but not type A = z = 10
Q3. The number of patients were treated with medicine types B and D only = a = 150
Q4. The number of patients who were treated with medicine type D = 20+50+35+y + a+ z + 20+10 = 135+30+10+150 = 325


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