Set Theory Questions for CAT

Out of 120 students, 60 know Java, 50 know Python, 40 know C++. 20 know Java and Python, 15 know Python and C++, 10 know Java and C++, and 5 know all three. How many know only Java?

Among 250 students, 150 like Physics (P), 120 like Chemistry (C), 80 like both. How many like at least one?

In the Indian athletic squad sent to the Olympics, 21 athletes were in the triathlon team; 26 were in the pentathlon team; and 29 were in the marathon team. 14 athletes can take part in triathlon and pentathlon; 12 can take part in marathon and triathlon; 15 can take part in pentathlon and marathon; and 8 can take part in all the three games. How many players are there in all?

In the CBSE Board Exams last year, $53\%$ passed in Biology, $61\%$ passed in English, $60\%$ in Social Studies, $24\%$ in Biology & English, $35\%$ in English & Social Studies, $27\%$ in Biology and Social Studies and $5\%$ in none. If the number of students in the class is 300, what will be the $\%$ change in the number of passes in only two subjects, if the original number of students is 200?

In a locality, 28 people read the Hindu and 32 people read the Times of India. What is the highest possible number of people in the locality who read the Times of India but not the Hindu?

Among 100 workers, 40 know Welding (W), 30 know Carpentry (C), 20 know both. How many know at least one?

In a survey of 1000 people regarding newspaper subscriptions for four newspapers A, B, C, and D, the following information is provided: I) The number of readers for newspapers A, B, and C is 350, 300, and 250, respectively. II) Each person reads a maximum of two newspapers. III) The number of readers for only A, B, C, and D is 100, 75, 50, and 25, respectively. IV) The number of readers for both A and B is 100, which is the same as the number of readers for both A and C. V) The number of readers for both C and D is 25. Determine the number of people who read newspaper D.

What must necessarily happen after the withdrawal of volunteers (from three to two projects)?

In an exam, students practiced four sections: QA, LR, DI, and RC. 90% practiced QA, 80% practiced RC, 70% practiced LR, and 60% practiced DI. Each student practiced exactly three sections. What percentage practiced QA, LR, and DI but not RC?

In the Stafford Public School, students had an option to study none or one or more of three foreign languages viz: French, Spanish and German. The total student strength in the school was 2116 students out of which 1320 students studied French and 408 students studied both French and Spanish. The number of people who studied German was found to be 180 higher than the number of students who studied Spanish. It was also observed that 108 students studied all three subjects. What is the minimum possible number of students who did not study any of the three languages?

In a company, 45% of the employees are male and 60% of the males earn more than ₹30,000. If 42% of all employees earn more than ₹30,000, what fraction of female employees earn at most ₹30,000?

In the Stafford Public School, students had an option to study none or one or more of three foreign languages viz: French, Spanish and German. The total student strength in the school was 2116 students out of which 1320 students studied French and 408 students studied both French and Spanish. The number of people who studied German was found to be 180 higher than the number of students who studied Spanish. It was also observed that 108 students studied all three subjects. What is the maximum possible number of students who did not study any of the three languages?

A new drug for treating depression is tested on 280 volunteers to identify potential side effects. The drug is administered to both men and women, and data is collected separately for those with diabetes. The two Venn diagrams below provide information about all the volunteers involved.

What is the ratio of the total number of diabetic patients experiencing side effects to the number of non-diabetic patients experiencing side effects?

Out of 300 book readers, 160 read Fiction, 140 Non-Fiction, 120 Biographies. If 70 read exactly two genres and 30 all three, how many read exactly one?

In a survey of 120 employees:

• 68 know Python
• 75 know Java
• 55 know C++ Some may not know any language. Find the difference between the maximum and minimum possible number of employees who know all three languages.

In a school, students study VA, DI, and QA. P(VA) = 11/30, P(only DI) = 9/30, and P(none) = 17/120. What is P(QA)?

In a survey of 250 people, 150 like Movies, 120 like Music, and 100 like Sports. If 80 like both Movies and Music, 60 like both Music and Sports, and 70 like both Movies and Sports, find the number of people who like exactly two activities if 40 people like all three.

The complement of set A, denoted as A′, consists of all elements in the universal set that are not in A. How many of the following statements must be true? i. (A ∪ B)' = (A' ∩ B') ii. If A ∩ B = ∅, then A' ∪ B' = the universal set iii. If A ∪ B = the universal set, then A' ∩ B' = ∅ iv. If A ⊂ B, then A' ∪ B' = (A ∩ B)'

Set A includes all three-digit numbers that are multiples of 5, Set B includes all three-digit even numbers that are multiples of 3, and Set C includes all three-digit numbers that are multiples of 4. What is the total number of elements in {A ∪ B ∪ C}?

A set S has 10 elements. How many subsets contain at least one odd and one even element?