MCQ
Reasoning: Venn Diagrams MCQ - Practice Questions with Answers
Solve 25 Reasoning: Venn Diagrams questions for RAS/RPSC preparation.
Practice questions
Q1Match each word group with the Venn relation it represents. I. Square, Rectangle, Shape II. Tea, Coffee, Beverage III. Doctors, Women, Singers Relations: 1. Three partly overlapping circles 2. Three circles one inside another 3. Two separate small circles inside a larger circle
A square is a type of rectangle, and every rectangle is a shape, so Square, Rectangle and Shape form three circles one inside another. Tea and coffee are different drinks, and both belong to the wider group Beverage; this gives two separate small circles inside a larger circle. Doctors, women and singers are independent human groups: a person may belong to any one, any two, or all three. So they are best shown by three partly overlapping circles.
Q2In a class, 32 students like Mathematics, 28 like Science and 12 like both subjects. If 5 students like neither subject, how many students are there in the class?
First find the number of students who like at least one of the two subjects. In a two-set Venn diagram, the common part is included in both 32 and 28, so it has been counted twice. Therefore, students liking at least one subject = 32 + 28 - 12 = 48. The 5 students who like neither subject lie outside both circles. Adding them gives the total class strength: 48 + 5 = 53.
Q3In a group of 30 candidates, 16 candidates solved the Mathematics question, 12 candidates solved the Reasoning question and 5 candidates solved both questions. Which statement is incorrect according to the Venn diagram?
The common part, 5, is included in both given totals. Candidates who solved only Mathematics are 16 - 5 = 11, and candidates who solved only Reasoning are 12 - 5 = 7. The number who solved at least one question is 16 + 12 - 5 = 23. Therefore the number who solved neither question is 30 - 23 = 7, not 5. Hence the incorrect statement is that 5 candidates solved neither question.
Q4In a class of 40 students, 22 students like tea, 18 students like coffee and 8 students like both tea and coffee. Using the Venn diagram idea, how many students like neither tea nor coffee?
In a two-circle Venn diagram, students who like at least one of the two drinks are counted by adding both groups and subtracting the common part once. So the number who like tea or coffee is 22 + 18 - 8 = 32. These 32 students are inside one or both circles. The class has 40 students in all, so the students outside both circles are 40 - 32 = 8. Therefore 8 students like neither tea nor coffee.
Q5Match each group of words with the most suitable Venn diagram relation. Relations: 1 = two separate small circles inside one larger circle; 2 = three separate circles; 3 = three circles overlapping each other. I. Mango, Apple, Fruit II. Teachers, Women, Doctors III. Pen, Stationery, Pencil
Use the meanings of the word groups. Mango and apple are two separate kinds inside the larger group fruit, so I matches relation 1. Teachers, women, and doctors can overlap because a woman may be a teacher, a doctor, or both, so II matches relation 3. Pen and pencil are two separate kinds inside stationery, so III also matches relation 1. The correct matching is I-1, II-3, III-1.
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More questions
6In a Venn diagram, circle P lies completely inside circle Q. Circle R also lies completely inside circle Q, but circle R does not touch circle P. Which statement is definitely correct?
7In a survey of 60 students, 32 like tea, 28 like coffee and 12 like both. Consider the statements: I. 20 students like only tea. II. 16 students like only coffee. III. 48 students like at least one of tea and coffee. IV. 10 students like neither tea nor coffee. Which statements are correct?
8In an activity club of 50 students, 26 joined music, 24 joined drama, and 10 joined both music and drama. Consider the statements: I. Only music students are 16. II. Only drama students are 14. III. Students in neither activity are 8. Which statements are correct?
9In a list, there are some poets. All poets are writers. No writer is illiterate. Which conclusion is incorrect? I. No poet is illiterate. II. Some writers are poets. III. Some illiterate persons are writers.
10In a Venn diagram, circle M represents students who like music and circle P represents students who like painting. Circles M and P overlap. Both circles are completely inside rectangle S, which represents all students. A part of S lies outside both circles. Which statement is incorrect?
11In a class of 40 students, 18 play cricket, 15 play kabaddi and 7 play both games. How many students play neither cricket nor kabaddi?
12Match List I with List II according to the most suitable Venn relation. List I: I. Squares and rectangles II. Nurses and women III. Tables and chairs IV. Vehicles and buses List II: 1. First group completely inside the second group 2. Two groups partly overlap 3. Two separate groups 4. Second group completely inside the first group
13In a class of 60 students, 32 students like tea, 28 students like coffee and 12 students like both tea and coffee. Which statement is correct?
14Read the assertion and reason for the Venn diagram of cats, animals and chairs. Assertion: The circle for cats should be completely inside the circle for animals, and separate from the circle for chairs. Reason: All cats are animals, and no chair is an animal. Choose the correct option.
15Read the assertion and reason. In a survey of 40 students, 25 read a Hindi newspaper, 18 read an English newspaper and 7 read both. Assertion: Exactly 4 students read neither newspaper. Reason: Students reading at least one newspaper = 25 + 18 - 7 = 36, so students reading neither = 40 - 36 = 4.