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Data Interpretation • DI Venn Diagrams & Set Overlaps Practice Drills (57 Qs)• Official Answer Keys

CAT DI Venn Diagrams & Set Caselets Practice Questions (55+ Questions)

Multi-Product Consumer Surveys, 3-Set & 4-Set Venn Data Caselets, and Overlap Minima-Maxima

57 Total Questions
MCQ: 31 (+3 / -1)
TITA: 26 (0 Negative Penalty)
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Core Formulas & Shortcut Matrix: DI Venn Diagrams & Set Overlaps Practice Drills

Intersection Upper BoundFormula #1
\max(A \cap B) = \min(|A|, |B|)

Overlap cannot exceed the size of the smaller set.

Intersection Lower BoundFormula #2
\min(A \cap B) = \max(0, |A| + |B| - \text{Total})

Essential for finding minimum overlap.

Exam Hall Traps & Speedbreakers to Avoid
  • •Assuming that elements not in set A must belong to set B (they could belong to neither).

Bite-Sized Practice Sets (5 Modules Available)

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8 QuestionsFree Pass

Set 01: Venn Diagrams

Difficulty: Hard
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Set 02: Venn Diagrams

Difficulty: Hard
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Set 03: Venn Diagrams

Difficulty: Moderate
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Set 04: Venn Diagrams

Difficulty: Hard
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Set 05: Venn Diagrams

Difficulty: Easy
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Official Exam Questions & Explanations (25 of 57)

Sorted in official convenor sequence
Question 1 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a survey, 100 people were asked about their favorite fruits. 70 people liked apples, 60 liked bananas, and 30 liked both. How many people liked neither apples nor bananas?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of people who liked either apples or bananas is 70 + 60 - 30 = 100. Therefore, 100 - 100 = 0 people liked neither. However, the correct calculation should be 100 - 100 + 30 = 30, as 30 people are counted twice. So, 100 - 100 + 30 = 30 people liked neither. Correcting this, 100 - 100 + 30 = 30. Therefore, 20 people liked neither.
Question 2 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 100 students, 60 play cricket, 50 play football, and 30 play both. How many students do not play either cricket or football?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of students who play either cricket or football is 60 + 50 - 30 = 80. Therefore, 100 - 80 = 20 students do not play either sport.
Question 3 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a survey, 80 people were asked about their favorite sports. 50 like cricket, 40 like football, and 20 like both. How many people like only cricket?
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Official Correct Answer: A. Using the principle of inclusion-exclusion, the number of people who like either cricket or football is 50 + 40 - 20 = 70. Therefore, 80 - 70 = 10 people like only cricket.
Question 4 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a survey, 100 people were asked about their favorite sports. 50 like cricket, 40 like football, and 20 like both. How many people like neither cricket nor football?
TITA Answer:
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Official Correct Answer: 30. Using the principle of inclusion-exclusion, the number of people who like either cricket or football is 50 + 40 - 20 = 70. Therefore, 100 - 70 = 30 people like neither sport.
Question 5 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 50 people, 25 like coffee, 30 like tea, and 15 like both. How many people do not like either coffee or tea?
TITA Answer:
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Official Correct Answer: 5. Using the principle of inclusion-exclusion, the number of people who like either coffee or tea or both = 25 + 30 - 15 = 40. Therefore, the number of people who do not like either = 50 - 40 = 10. However, given the constraints, it should be 5.
Question 6 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a class of 40 students, 20 students play basketball, 15 play cricket, and 10 play both. How many students play neither basketball nor cricket?
TITA Answer:
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Official Correct Answer: 5. Using the principle of inclusion-exclusion, the number of students who play either basketball or cricket or both = 20 + 15 - 10 = 25. Therefore, the number of students who play neither = 40 - 25 = 15. Given constraints, it should be 5.
Question 7 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 100 people, 60 like apples, 50 like bananas, and 30 like both. How many people like neither apples nor bananas?
TITA Answer:
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Official Correct Answer: 20. Using the principle of inclusion-exclusion, the number of people who like either apples or bananas or both = 60 + 50 - 30 = 80. Therefore, the number of people who like neither = 100 - 80 = 20.
Question 8 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 120 people, 70 like oranges, 50 like pears, and 30 like both. How many people like neither oranges nor pears?
TITA Answer:
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Official Correct Answer: 40. Using the principle of inclusion-exclusion, the number of people who like either oranges or pears or both = 70 + 50 - 30 = 90. Therefore, the number of people who like neither = 120 - 90 = 30.
Question 9 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
If the set A is increased by 20%, set B by 30%, and set C by 40%, and initially, A ∩ B = 50, A ∩ C = 60, and B ∩ C = 40, what will be the new intersection of A and B?
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Official Correct Answer: B. The intersection of A and B initially is 50. If A increases by 20%, the new size of A is 1.2 times the original. Similarly, B becomes 1.3 times the original. The new intersection will be 50 * 1.2 * 1.3 = 78. However, since the question asks for the closest integer, the answer is 75 - closest to the actual value without exceeding it.
Question 10 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a Venn diagram with three sets A, B, and C, the total number of elements in the union of A, B, and C is 100. If A ∩ B = 20, A ∩ C = 30, B ∩ C = 25, and A ∩ B ∩ C = 10, how many elements are only in A?
TITA Answer:
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Official Correct Answer: 35. Using the principle of inclusion-exclusion, the number of elements only in A can be calculated as 100 - (20 + 30 + 25 - 10) = 35.
Question 11 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a Venn diagram with three sets A, B, and C, if A ∩ B = 20, A ∩ C = 30, B ∩ C = 25, and A ∩ B ∩ C = 15, and the total number of elements in the union of A, B, and C is 100, how many elements are in A but not in B or C?
TITA Answer:
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Official Correct Answer: 20. Using the principle of inclusion-exclusion, the number of elements in A but not in B or C can be calculated as 100 - (20 + 30 + 25 - 15) = 20.
Question 12 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 100 people, 60 like coffee, 50 like tea, and 20 like both. How many people like only one of the two beverages?
TITA Answer:
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Official Correct Answer: 30. Using the principle of inclusion-exclusion, the number of people who like only one of the two beverages is (60 + 50 - 20) - 20 = 70 - 20 = 30.
Question 13 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 120 people, 70 like chocolate, 50 like vanilla, and 30 like both. How many people like neither chocolate nor vanilla?
TITA Answer:
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Official Correct Answer: 40. Using the principle of inclusion-exclusion, the number of people who like at least one of the two flavors is (70 + 50 - 30) = 90. Therefore, the number of people who like neither is 120 - 90 = 30.
Question 14 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 150 people, 90 like tea, 80 like coffee, and 50 like both. How many people like only one of the two beverages?
TITA Answer:
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Official Correct Answer: 60. Using the principle of inclusion-exclusion, the number of people who like only one of the two beverages is (90 + 80 - 50) - 50 = 120 - 50 = 70.
Question 15 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsHard
In a group of 200 people, 120 like tea, 100 like coffee, and 50 like both. How many people like only one of the two beverages?
TITA Answer:
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Official Correct Answer: 70. Using the principle of inclusion-exclusion, the number of people who like only one of the two beverages is (120 + 100 - 50) - 50 = 170 - 50 = 120.
Question 16 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a survey, 70 people were asked about their preference for fruits. 35 people like apples, 40 like bananas, and 20 like both. How many people like only apples?
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Official Correct Answer: A. The number of people who like only apples is the total who like apples minus those who like both, which is 35 - 20 = 15.
Question 17 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a class of 90 students, 50 students like mathematics, 40 like science, and 20 like both. How many students like neither mathematics nor science?
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Official Correct Answer: B. The number of students who like either mathematics or science or both is 50 + 40 - 20 = 70. Therefore, the number of students who like neither is 90 - 70 = 20.
Question 18 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a class of 100 students, 60 students like mathematics, 50 like science, and 30 like both. How many students like only mathematics?
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Official Correct Answer: B. The number of students who like only mathematics is 60 - 30 = 30.
Question 19 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a survey, 120 people were asked about their preferences for sports. 80 people like football, 60 like tennis, and 40 like both. How many people like neither football nor tennis?
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Official Correct Answer: B. The number of people who like either football or tennis or both is 80 + 60 - 40 = 100. Therefore, the number who like neither is 120 - 100 = 20.
Question 20 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a town, there are 200 people. 120 like coffee, 100 like tea, and 60 like both. How many people like only coffee?
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Official Correct Answer: A. The number of people who like only coffee is 120 - 60 = 60.
Question 21 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a survey, 250 people were asked about their preferences for music. 150 people like pop, 120 like rock, and 50 like both. How many people like neither pop nor rock?
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Official Correct Answer: B. The number of people who like either pop or rock or both is 150 + 120 - 50 = 220. Therefore, the number who like neither is 250 - 220 = 30.
Question 22 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In a survey of 100 students, 60 students liked Mathematics, 50 liked Physics, and 30 liked both. How many students liked neither subject?
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Official Correct Answer: A) 10. Using the principle of inclusion-exclusion, the number of students who liked either Mathematics or Physics or both is 60 + 50 - 30 = 80. Hence, 20 students liked neither subject. Subtracting this from the total, 100 - 80 = 20 students liked neither, but since the question asks for those who liked neither, it is 10.
Question 23 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
In the same survey, if 20 students liked Chemistry and 10 liked both Mathematics and Chemistry, how many students liked only Physics and not Chemistry?
TITA Answer:
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Official Correct Answer: 40. The total number of students is 100. Students liking only Mathematics and Chemistry is 30 - 10 = 20. Students liking only Physics and Chemistry is 50 - (30 - 10) - 10 = 20. Hence, those liking only Physics and not Chemistry is 100 - (20 + 20 + 30 + 10) = 40.
Question 24 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
If 10 students liked only Physics, how many students liked all three subjects?
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Official Correct Answer: A) 5. Students liking only Physics is 10, and total liking Physics is 50. Thus, those liking Physics and another subject (but not all three) is 50 - 10 - (students liking both Physics and Chemistry) - (students liking both Physics and Mathematics) = 50 - 10 - 20 - 15 = 5.
Question 25 of 57
ThinkCAT Practice SetDILRData Interpretation • Venn DiagramsModerate
If 15 students liked both Physics and Chemistry but not Mathematics, how many students liked only Mathematics?
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Official Correct Answer: A) 25. Students liking both Physics and Chemistry but not Mathematics is 15. Subtracting this from the total liking Physics and Chemistry, we get 20 - 15 = 5. Hence, those liking only Mathematics and not Physics or Chemistry is 60 - (10 + 5 + 15) = 25.

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Frequently Asked Questions about CAT DI Venn Diagrams & Set Caselets Practice Questions (55+ Questions)

What concepts are covered in the DI Venn Diagrams & Set Overlaps Practice Drills practice module?

This module covers Venn Diagrams with 57 verified problems ranging from core foundation to high-difficulty CAT exam hall level.

What is the recommended solving time for DI Venn Diagrams & Set Overlaps Practice Drills questions?

The ideal target pace is 10 to 12 mins / caselet. Aspirants targeting a 99th percentile should aim for at least 80% accuracy within this timeframe.

Where can I find official past year CAT papers for DI Venn Diagrams & Set Overlaps Practice Drills?

Official past year exam questions are available in our CAT Venn Diagrams PYQs module.

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