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CAT 2020 Slot 1 DILR · Set 1 of 5Data InterpretationModerate DifficultyQ1–Q4 · 0 MCQ + 4 TITA

CAT 2020 Slot 1 DILR Set 1: Venn Diagrams (4 Questions) with Solutions

The Venn Diagrams set from the official CAT 2020 Slot 1 DILR paper: the caselet, all 4 questions, the official answer key and a step-by-step solution for each. 100% free, no sign-up.

The Set: Read the Caselet First

CAT 2020 Slot 1 DILR · Questions 1–4
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 В.
6
50 patients were given all the four types of medicines. 75 patients were treated with exactly one type of medicine.
3

In the exam this set competed with 4 others for 40 minutes. Budget about 8 minutes if you attempt it.

Q1. Venn Diagrams

TITA · +3 / 0
How many patients were treated with medicine type B?
Correct Answer
340
Step-by-step solution
📌 Core Concept
Only the 500 treatment-group patients appear in the four-set Venn diagram. Fill every region from the clues, then add up the regions that lie inside B.
🔢 Step-by-Step Solution
1
Clue 6 says 75 patients took exactly one medicine. Clue 2 gives A only = 25, C only = 20 and D only = 10, so B only = 75 − 55 = 20.
2
Clues 3 and 5 give the pair-only regions: AB = 20, AC = 30, AD = 35, CD = 20. They also give the triple regions ABC (without D) = 40 and ACD (without B) = 20. Clue 6 gives all four = 50.
3
Clue 4 says there are 100 patients with exactly three medicines. So ABD + BCD = 100 − 40 − 20 = 40.
4
Use the total for A (clue 1): 25+(20+30+35)+(40+20+ABD)+50=25025 + (20+30+35) + (40+20+\text{ABD}) + 50 = 250. This gives 220+ABD=250220 + \text{ABD} = 250, so ABD only = 30 and BCD only = 10.
5
Use the total for C (clue 1): 20+(30+20+BC)+(40+20+10)+50=21020 + (30+20+\text{BC}) + (40+20+10) + 50 = 210. This gives 190+BC=210190 + \text{BC} = 210, so BC only = 20.
6
The treatment group has 500 patients. The regions add up to 75+(125+BD)+100+50=350+BD=50075 + (125 + \text{BD}) + 100 + 50 = 350 + \text{BD} = 500, so BD only = 150.
7
Add all regions inside B: 20+20+20+150+40+30+10+50=34020 + 20 + 20 + 150 + 40 + 30 + 10 + 50 = 340.
Quick Check
The regions sum to 75+275+100+50=50075+275+100+50 = 500, which matches the treatment group size.
Correct Answer: 340

Q2. Venn Diagrams

TITA · +3 / 0
The number of patients who were treated with medicine types B, C and D, but not type A was:
Correct Answer
10
Step-by-step solution
📌 Core Concept
The region "B, C and D but not A" is one of the exactly-three regions. Clues 4 and 1 together fix it.
🔢 Step-by-Step Solution
1
Clue 4 says 100 patients took exactly three medicines. Clue 5 gives ABC only = 40 and ACD only = 20.
2
The other two triple regions are ABD only and BCD only. They share 100−40−20=40100 - 40 - 20 = 40 patients.
3
Use the total for A in clue 1. The regions inside A are: A only 25, AB only 20, AC only 30, AD only 35, ABC 40, ACD 20, ABD (unknown), and all four 50. So 25+20+30+35+40+20+50+ABD=25025 + 20 + 30 + 35 + 40 + 20 + 50 + \text{ABD} = 250, which gives 220+ABD=250220 + \text{ABD} = 250 and ABD only = 30.
4
Then BCD only = 40−30=1040 - 30 = 10.
Quick Check
The exactly-three regions are 40+20+30+10=10040 + 20 + 30 + 10 = 100, which matches clue 4.
Correct Answer: 10

Q3. Venn Diagrams

TITA · +3 / 0
How many patients were treated with medicine types B and D only?
Correct Answer
150
Step-by-step solution
📌 Core Concept
Only the 500 treatment patients are in the Venn diagram. Once every other region is known, the 500 total fixes the B-and-D-only region.
🔢 Step-by-Step Solution
1
Exactly one medicine: 75 patients (clue 6).
2
Exactly three medicines: 100 patients (clue 4).
3
All four medicines: 50 patients (clue 6).
4
Pair-only regions from clue 3 are AD 35, AB 20, AC 30 and CD 20. BC only still has to be found.
5
Use the total for C (210). The regions inside C are: C only 20, AC 30, CD 20, BC, ABC 40, ACD 20, BCD, and all four 50. Here BCD = 10, found from clue 4 and the total for A (A = 250 gives ABD = 30, so BCD = 40 − 30). So 20+30+20+BC+40+20+10+50=21020 + 30 + 20 + \text{BC} + 40 + 20 + 10 + 50 = 210, which gives 190+BC=210190 + \text{BC} = 210 and BC only = 20.
6
Known pair-only regions add up to 35+20+30+20+20=12535 + 20 + 30 + 20 + 20 = 125.
7
The treatment group has 500 patients, so 75+125+BD+100+50=50075 + 125 + \text{BD} + 100 + 50 = 500. This gives 350+BD=500350 + \text{BD} = 500 and BD only = 150.
Quick Check
The B total then comes to 340, and the D total to 325. Both are consistent with the other counts.
Correct Answer: 150

Q4. Venn Diagrams

TITA · +3 / 0
The number of patients who were treated with medicine type D was:?
Correct Answer
325
Step-by-step solution
📌 Core Concept
Fill every region of the four-set Venn diagram for the 500 treatment patients, then add the regions inside D.
🔢 Step-by-Step Solution
1
Clue 2 gives D only = 10. Clue 3 gives AD only = 35 and CD only = 20. Clue 6 gives all four = 50.
2
Clue 5 gives ACD (without B) = 20.
3
Clues 4 and 1 give the other triples. ABC = 40 and ACD = 20, so ABD + BCD = 40. The total for A (250) then gives ABD = 30 and BCD = 10.
4
The total for C (210) gives BC only = 20. Then the 500 total gives BD only = 150. Here the other regions sum to 75+125+100+50=35075 + 125 + 100 + 50 = 350, so BD only is 500−350500 - 350.
5
Add all regions inside D: 10+35+20+150+20+30+10+50=32510 + 35 + 20 + 150 + 20 + 30 + 10 + 50 = 325.
Quick Check
The regions sum to 75+275+100+50=50075 + 275 + 100 + 50 = 500, which matches the treatment group size.
Correct Answer: 325
Timed Practice

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CAT 2020 Slot 1 DILR at a Glance

Sets in this section5
Questions in this section24
Section time40 minutes
Convenor IIMIIM Indore

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