ThinkCAT Logo
ThinkCAT
Sign up
QuestionsMocksResourcesAnalytics
CAT 2020 Slot 1 DILR · Set 5 of 5Data InterpretationEasy DifficultyQ21–Q24 · 4 MCQ

CAT 2020 Slot 1 DILR Set 5: 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 21–24
Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
The following facts are known about these ten musicians.
1
Both A and B are experts in mridangam, but only one of them is also an expert in tabla.
2
D is an expert in both tabla and ghatam.
3
Both F and G are experts in tabla, but only one of them is also an expert in mridangam.
4
Neither I nor J is an expert in tabla.
5
Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam

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

Q21. Venn Diagrams

MCQ · +3 / −1
Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam?
  1. A) C
  2. B) F
  3. C) H
  4. D) A
Correct Answer
C) H
Step-by-step solution
📌 Core Concept
The region counts fix every musician's group. Only 1 person is in ghatam alone, and no one is in mridangam and ghatam, or in all three.
🔢 Step-by-Step Solution
1
The regions listed total 3+3+1+2+1=103+3+1+2+1=10. So the regions "mridangam and ghatam only" and "all three" are empty.
2
Fact 4: I is not in tabla. Fact 5: I is not in mridangam. Each musician is in at least one instrument, so I is in ghatam only. That is the single ghatam-only expert.
3
Fact 5 says exactly one of H and I is in ghatam. I is, so H is not. H is also not in mridangam, so H is in tabla only.
4
C is not forced. C and E share the one remaining tabla-only place and the one remaining mridangam-only place, so either could be tabla-only. F could be a tabla-and-mridangam expert, since Fact 3 says only one of F and G is also in mridangam.
5
Only H is definitely in tabla but not in mridangam or ghatam.
Why Not the Others
A: A is in mridangam, so A is never tabla-only.
C: C may be mridangam-only.
F: F may also be in mridangam.
Correct Answer: C

Q22. Venn Diagrams

MCQ · +3 / −1
Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam?
  1. A) B
  2. B) E
  3. C) J
  4. D) G
Correct Answer
C) J
Step-by-step solution
📌 Core Concept
The region counts fix most musicians' groups. Then check who is forced into mridangam alone.
🔢 Step-by-Step Solution
1
The regions total 3+3+1+2+1=103+3+1+2+1=10. So the regions "mridangam and ghatam only" and "all three" are empty.
2
Fact 4 says J is not in tabla. J is not the ghatam-only expert, because I fills that place (Fact 4 and Fact 5 force I into ghatam only). Mridangam and ghatam together is impossible. So J is in mridangam only.
3
Fact 1: A and B are both in mridangam, and exactly one is also in tabla. So one of them is mridangam-only and the other is tabla-and-mridangam. Which is which is not fixed, so neither is definite.
4
Fact 3: F and G are both in tabla and exactly one is also in mridangam. So neither is mridangam-only.
5
E is not forced. C and E share one tabla-only and one mridangam-only place.
6
Only J is definitely mridangam-only.
Why Not the Others
B: B may be the tabla-and-mridangam expert.
E: E may be tabla-only.
G: G is in tabla, so G is not mridangam-only.
Correct Answer: C

Q23. Venn Diagrams

MCQ · +3 / −1
Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?
  1. A) A and B
  2. B) F and G
  3. C) C and E
  4. D) C and F
Correct Answer
C) C and E
Step-by-step solution
📌 Core Concept
The two tabla-and-mridangam places are already taken by two of the named pairs, so the leftover pair cannot contain such a musician.
🔢 Step-by-Step Solution
1
There are exactly 2 tabla-and-mridangam (not ghatam) experts.
2
Facts 1 and 3 each put one of their pair there. Exactly one of A and B is in both tabla and mridangam. Exactly one of F and G is in both. That fills both places.
3
The groups of the others follow. D is tabla and ghatam. I is ghatam only (Fact 4 and Fact 5). H is tabla only (Fact 5). J is mridangam only (Fact 4).
4
The remaining places are one tabla-only and one mridangam-only. They go to the other of A and B, the other of F and G, and to C and E. The tabla-only places are H, the other of F and G, and one more. The mridangam-only places are J, the other of A and B, and one more. So C and E take one tabla-only and one mridangam-only place.
5
Neither C nor E can be in both tabla and mridangam.
6
A and B contain one such musician. F and G contain one such musician. C and F can contain one only if F is that musician, which is possible.
Why Not the Others
A and B: one of them must be tabla-and-mridangam.
F and G: one of them must be tabla-and-mridangam.
C and F: F can be tabla-and-mridangam.
Correct Answer: C

Q24. Venn Diagrams

MCQ · +3 / −1
If C is an expert in mridangam and F is not, then which are the three musicians who are experts in tabla but not in either mridangam or ghatam?
  1. A) E, F and H
  2. B) C, G and H
  3. C) E, G and H
  4. D) C, E and G
Correct Answer
A) E, F and H
Step-by-step solution
📌 Core Concept
Place the fixed musicians first. Then use the new condition to settle C, E, F and G.
🔢 Step-by-Step Solution
1
The region counts total 10, so "mridangam and ghatam only" and "all three" are empty.
2
D is tabla and ghatam (Fact 2). I is ghatam only. H is tabla only. J is mridangam only (Facts 4 and 5).
3
Exactly one of A and B is tabla and mridangam. Exactly one of F and G is tabla and mridangam. Those are the two such experts. C and E therefore fill one tabla-only place and one mridangam-only place.
4
Given: C is in mridangam, so C is mridangam-only. Then E is tabla-only.
5
Given: F is not in mridangam. By Fact 3, F is tabla-only and G is tabla and mridangam.
6
The tabla-only experts are therefore H, E and F. That is 3, as required.
Quick Check
Mridangam-only: C, J and the other of A and B, which is 3. Tabla and mridangam: G and one of A and B, which is 2. All counts match.
Correct Answer: A
Timed Practice

Attempt the full CAT 2020 Slot 1 paper as a free mock

All three sections, 120 minutes, in the TCS iON-style simulator. Free, no sign-up.

Start Free Mock

CAT 2020 Slot 1 DILR at a Glance

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

More CAT DILR Sets with Solutions