Question

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. A total of 250 patients were treated with type A medicine and a total of 210 patients were treated with type C medicine.
b. 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.
c. 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.
d. 100 patients were treated with exactly three types of medicines.
e. 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.
f. 50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
The number of patients who were treated with medicine types B, C and D, but not type A was: [This Question was asked as TITA]

• A. 13
• B. 22
• C. 12
• D. 10

Answer 1

The Correct Option is D

A study was conducted with 1000 subjects. 500 subjects received actual treatment, while the other 500 received a placebo. This formed the sample set. Subsequently, four medications (A, B, C, and D) were administered to the 500 treated individuals. Based on the provided data, the following Venn diagram can be constructed.

According to the problem statement, 250 patients received medication type A. Using this information, we can determine the number of patients who received medications A, B, and D, but not C. The calculation is 250 - (25 + 20 + 30 + 40 + 20 + 50 + 35) = 30. Condition (d) states that exactly three different medications were administered to 100 patients. Therefore, the number of patients who received only B, C, and D, excluding A, can be determined. This value is 100 - 20 - 40 = 40. Condition (f) specifies that 75 patients received precisely one type of medication. This allows us to calculate the number of patients who received only medication B: 75 - (25 + 20 + 10) = 20. We are also informed that 210 patients received medication type C. This enables us to calculate the number of patients treated solely with drugs B and C. The calculation is 210 - (30 + 20 + 40 + 50 + 10 + 20 + 20) = 20. Filling in the Venn diagram with this information results in the following graph.

The total number of patients considered for treatment was 500. Therefore, the sum of all regions in the Venn diagram should equal 500. Using this, we can calculate the value of x, which represents the number of individuals who received only drugs B and D. x = 500 - (25 + 20 + 20 + 30 + 40 + 20 + 20 + 20 + 50 + 10 + 20 + 35 + 30 + 10) = 150.

The number of patients treated with medicine types B, C, and D, but not type A, is 10.