CAT 2020 Slot 1 — DILR Question 1
Answer the next 4 questions based on the information given below.
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.
- A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
- 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.
- 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.
- 100 patients were treated with exactly three types of medicines.
- 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.
- 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
How many patients were treated with medicine type B?
Answer & solution
Answer: 340
We can draw the following Venn diagram according to the information given in the question.
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75 patients were treated with exactly one type of medicine.
∴ 25 + a + 20 + 10 = 75
⇒ a = 20
250 patients were treated with type A medicine
∴ 25 + 30 + 20 + 35 + 20 + 40 + 50 + e = 250.
⇒ e = 30
100 patients were treated with exactly three types of medicines.
∴ 20 + 40 + c + e = 100
⇒ c = 10
210 patients were treated with type C medicine
∴ 30 + 40 + b + 20 + 20 + 50 + c + 20 = 210
⇒ b = 20
Since patients were equally in treatment group and control group hence, there were total 500 patients who were in the treatment group and 500 in control group (who were not given any medicine).
Total patient in treatment group = 500 = 25 + 30 + 20 + 35 + 20 + 40 + 50 + e + a + b + c + d + 20 + 20 + 10.
⇒ d = 150
The completed Venn diagram:
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∴ 340 patients were treated with Type B medicine.
Hence, 340.