Treatment
CAT 2020 Slot 1 · DILR · Hard · Data Interpretation
Passage / data set
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.
Question 1 of 4
How many patients were treated with medicine type B?
340
Explanation
Using 4-set Venn diagram calculations for the treatment group (500 patients): Total in A = 250. Components of A:
- A only = 25
- AB only = 20
- AC only = 30
- AD only = 35
- ABC = 40
- ACD = 20
- ABD = x
- ABCD = 50 Sum of A components = 25 + 20 + 30 + 35 + 40 + 20 + x + 50 = 220 + x = 250 => x = 30 (ABD = 30).
Total in C = 210:
- C only = 20
- AC only = 30
- BC only = y
- CD only = 20
- ABC = 40
- ACD = 20
- BCD = z
- ABCD = 50 Sum of C = 20 + 30 + y + 20 + 40 + 20 + z + 50 = 180 + y + z = 210 => y + z = 30.
Exactly three types = 100: ABC (40) + ACD (20) + ABD (30) + BCD (z) = 100 => 90 + z = 100 => z = 10. Since y + z = 30 => y = 20 (BC only = 20).
Exactly one type = 75: A only (25) + C only (20) + D only (10) + B only (b) = 75 => 55 + b = 75 => b = 20 (B only = 20).
BD only = w. Total patients = 500. Sum of all 15 regions = 500 => w = 150.
Now, Total patients treated with medicine type B: B = B only (20) + AB (20) + BC (20) + BD (150) + ABC (40) + ABD (30) + BCD (10) + ABCD (50) = 340.
Question 2 of 4
The number of patients who were treated with medicine types B, C and D, but not type A was:
10
Explanation
This represents the region BCD (patients treated with B, C, D but not A). From our Venn diagram solution, z = 10.
Question 3 of 4
How many patients were treated with medicine types B and D only?
150
Explanation
This represents the region BD only (w). From the total set equation, w = 150.
Question 4 of 4
The number of patients who were treated with medicine type D was:
325
Explanation
Total D = D only (10) + AD (35) + CD (20) + BD (150) + ACD (20) + ABD (30) + BCD (10) + ABCD (50) = 325.
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