Venn – Diagram – Railway Reasoning part – 1

Total Questions: 50

1. In the following figure, rectangle represents students, circle represents girls, oval represents arts faculty, and triangle represents sports. The numbers given in different parts represent the number of persons belonging to that part. How many girl-students have opted for arts faculty, and they do not participate in sports, and how many students who participate in sports, but are not girls, and have opted for arts faculty? [Group - D 17/08/2022 (Afternoon)]

Correct Answer: (a) 211 and 178, respectively
Solution:

Number of girl-students who have opted for arts stream, and they do not participate in sports = 211
Students who participate in sports, but are not girls, and have opted for arts stream= 178

2. Study the diagram and answer the question that follows. A = Academicians, E = Teachers, D = Women, B = Men and C = Doctors. The numbers inside the shapes indicate number of the respective persons. What is the sum total mumber of the following: [Group - D 17/08/2022 (Evening)]

i) women academicians who are teachers
ii) teachers who are doctors and
iii) men who are NEITHER teachers NOR academicians?

Correct Answer: (d) 67
Solution:

From the given diagram
i. Number of women academicians who are teachers = 19
ii. Number of teachers who are doctors = 20
iii. Number of men who are neither teachers nor academicians = 28.
Hence, Required Number = 19 + 20 + 28 = 67

3. Study the given diagram carefully and answer the question. The numbers in different sections indicate the number of persons. [Group - D 22/08/2022 ( Afternoon)]

Which of the following statements is correct on the basis of the above diagram?

Correct Answer: (b) The number of graduates who are also coffee lovers but not soldiers is 65.
Solution:

Number of graduates who are also Coffee lovers but not soldiers = 65.

4. Study the Venn Diagram given below and answer the question that follows. [Group - D 02/09/2022 ( Morning)]

How many volunteers are supervisors but neither donors nor field workers?

Correct Answer: (c) 0
Solution:

There are no supervisors who are volunteers but neither donors nor field workers.

5. Study the given diagram carefully and answer the question. The numbers in different sections indicate the number of persons. What does region '13' represent? [Group - D 22/09/2022 ( Morning)]

Correct Answer: (d) The number of painters who are plumbers and also watchmen but not carpenters.
Solution:

Here, 13 represents the number of painters who are plumbers and also watchman but nor carpenters.

6. In the given venn diagram, assuming that the shaded areas do not exist, determine which conclusion can be validly drawn? [NTPC CBT - I 30/12/2020 (Morning)]

Correct Answer: (b) All artists are cartoonists
Solution:

In the given venn diagram, the conclusion that can definitely be drawn is – all artists are cartoonists.

7. Last year,there were three sections in a competitive exam. Out of them 33 students cleared the cut-off in Section A, 34 students cleared the cut-off in Section B and 32 students cleared the cut-off in Section C. 10 students cleared the cut-off in section A and section B. 9 cleared the cut-off in section B and section C and 8 cleared the cut-off in section A and section C. The number of students who cleared only one section was equal and was 21 for each section. How many students cleared all the three sections? [RRB NTPC 07/01/2021 (Morning)]

Correct Answer: (a) 6
Solution:From the above diagram, we can observe that students who cleared cut off of all three sections = 6

8. Study the given Venn diagram and answer the questions that follows. [NTPC CBT - I 13/01/2021 (Morning)]

A state has 7500 officers. Among them 62% officers are punctual (P), 58% officers are honest (H) and 70% officers are brave (B), 38% officers are punctual (P) and honest (H), 48% are honest (H) and brave (B) and 36% are punctual (P) and brave (B). What percentage of the officers are punctual (P), Honest (H) and brave (B)?

Correct Answer: (c) 32%
Solution:

Concept used is : n(AᴜBᴜC)
= n(A) + n(B) + n(C) – n(A∩B) – n(B∩C) – n(C∩A) + n(A∩B∩C)
So, 100 = 62 + 58+ 70 - 38 - 48 - 36 + n(A∩B∩C)
100 = 190 - 122 + n(A∩B∩C)
n(A∩B∩C) = 222 - 190 = 32%

9. L and A are classmates as well as good friends. In a class of 30 students, L has 10 unique friends and 5 friends who are common to A. A has a total of 17 friends in the class. How many students are friends with neither L nor A ? [NTPC CBT - I 16/01/2021 (Evening)]

Correct Answer: (b) 3
Solution:

Total no. of student = 30
Student are friends of L and A
= 10 + 17 = 27
students are friends with neither L nor A
= 30 − 27 = 3

10. In a class of 65 students, 20 students like only maths. 25 students like only English and 15 students like both English and maths. 8 students like computers and 3 students like all three subjects. There are no students who like only computers and English. Also, there are no students who like only Maths and Computers. How many students like only computers? [NTPC CBT - I 17/01/2021 (Evening)]

Correct Answer: (a) 5
Solution: