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All questions of Venn Diagrams for Bank Exams Exam

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Each of these questions given below contains three elements. These elements may or may not have some inter linkage. Each group of elements may fit into one of these diagrams at (A), (B), (C), (D) and/or (E). You have to indicate the group of elements which correctly fits into the diagrams.
Q.
Which of the following diagrams indicates the best relation between Travelers, Train and Bus ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?

Geetika Kulkarni answered
To find the number of even integers n, where 100 < n="" />< 1000,="" we="" can="" count="" the="" number="" of="" even="" hundreds,="" tens,="" and="" ones="" />

For the hundreds digit, there are 9 possible even digits: 2, 4, 6, 8, 10, 12, 14, 16, and 18.

For the tens digit, there are 10 possible even digits: 0, 2, 4, 6, 8, 10, 12, 14, 16, and 18.

For the ones digit, there are 5 possible even digits: 0, 2, 4, 6, and 8.

Therefore, the total number of even integers n is 9 * 10 * 5 = 450.

Note that we include the number 100 in this count because it is an even integer.

Shyam visited Ram during his brief vacation. In the mornings they both would go for yoga. In the evenings they would play tennis. To have more fun, they indulge only in one activity per day, i.e. either they went for yoga or played tennis each day. There were days when they were lazy and stayed home all day long. There were 24 mornings when they did nothing, 14 evenings when they stayed at home, and a total of 22 days when they did yoga or played tennis. For how many days Shyam stayed with Ram?
  • a)
    32
  • b)
    24
  • c)
    30
  • d)
    None of these
Correct answer is option 'C'. Can you explain this answer?

Shreya Basu answered
Given Information:
- Shyam visited Ram during his brief vacation.
- In the mornings, they both would go for yoga.
- In the evenings, they would play tennis.
- They indulge only in one activity per day, either yoga or tennis.
- There were days when they were lazy and stayed home all day long.
- There were 24 mornings when they did nothing.
- There were 14 evenings when they stayed at home.
- In total, they did yoga or played tennis on 22 days.

Approach:
- Let's assume the number of days Shyam stayed with Ram is x.
- We need to find the value of x.

Solution:

Mornings:
- There were 24 mornings when they did nothing.
- Since there are 7 days in a week, the number of weeks they did nothing in the mornings = 24/7 = 3 weeks.
- So, the number of mornings they did yoga or played tennis = 7 - 3 = 4 mornings per week.
- Therefore, the total number of mornings they did yoga or played tennis = 4 * (x/7) = 4x/7.

Evenings:
- There were 14 evenings when they stayed at home.
- Similarly, the number of evenings they did yoga or played tennis = 7 - 14/7 = 7 - 2 = 5 evenings per week.
- Therefore, the total number of evenings they did yoga or played tennis = 5 * (x/7) = 5x/7.

Total number of days they did yoga or played tennis:
- According to the given information, the total number of days they did yoga or played tennis = 22.
- So, the equation is 4x/7 + 5x/7 = 22.
- Combining like terms, we get 9x/7 = 22.
- Multiplying both sides by 7/9, we get x = (22 * 7) / 9.
- Simplifying, x = 154/9.
- Since x represents the number of days, we round it up to the nearest whole number.
- Therefore, the number of days Shyam stayed with Ram is 17.

Final Answer:
- Shyam stayed with Ram for 17 days.
- None of the given options (a, b, c, d) matches the correct answer.

Out of 60 families living in a building, all those families which own a car own a scooter as well. No family has just a scooter and a bike. 16 families have both a car and a bike. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. What is the sum of the maximum and minimum number of families that own only a bike?
  • a)
    24
  • b)
    34
  • c)
    54
  • d)
    44
Correct answer is option 'D'. Can you explain this answer?

Learning Education answered
From the information given in the question, the following Venn Diagram can be constructed:

So, in order to maximize the number of families that own only a bike, we can put the remaining 44 families in ‘only bike’ region.
Similarly, in order to minimize the number of families that own only a bike, we can put the remaining 44 families in ‘only scooter’ region.
So, the maximum number of families that own only a bike is 44 and the minimum number of families that own only a bike is 0.
So, sum = 44 + 0 = 44

A premier B-school, which is in process of getting an AACSB accreditation, has 360 second year students. To incorporate sustainability into their curriculum, it has offered 3 new elective subjects in the second year namely Green Supply Chain, Global Climate Change & Business and Corporate Governance. Twelve students have taken all the three electives, and 120 students study Green Supply Chain. There are twice as many students who study Green Supply Chain and Corporate Governance but not Global Climate Change and Business, as those who study both Green Supply Chain and Global Climate Change & Business but not Corporate Governance, and 4 times as many who study all the three. 124 students study Corporate Governance. There are 72 students who could not muster up the courage to take up any of these subjects. The group of students who study both Green Supply Chain and Corporate Governance but not global Climate Change & Business is exactly the same as the group made up to the students who study both Global Climate Change & Business and Corporate Governance. How many students study Global Climate Change & Business only?
  • a)
    176
  • b)
    104
  • c)
    152
  • d)
    188
Correct answer is option 'B'. Can you explain this answer?

Iq Funda answered
The number of students who study each combination of subjects (based on the direct data) given is as shown below:

It is given that: (GSC and CG but not GCCB) = 4 times (all three electives)
∴ 2x = 4(12) i.e. x = 24
Also: (GSC and CG but not GCCB) = (all three electives) + (GCCB and CG but not GSC) 
∴ (GCCB and CG but not GSC) = 2x − 12 = 2(24) − 12 = 36
So, the figure becomes:

Now, CG only = 124 − (48 + 12 + 36) = 28 
∴ GCCB alone = 360 − 120 − 36 − 28 − 72 = 104
Hence, option (b).

290 students of MBA (International Business) in a reputed Business School have to study foreign language in Trimesters IV and V. Suppose the following information are given
(i) 120 students study Spanish
(ii) 100 students study Mandarin
(iii) At least 80 students, who study a foreign language, study neither Spanish nor Mandarin
Then the number of students who study Spanish but not Mandarin could be any number from
  • a)
    20 to 110
  • b)
    80 to 100
  • c)
    50 to 80
  • d)
    80 to 170
Correct answer is option 'A'. Can you explain this answer?

G.K Academy answered
Atleast 80 students study neither Spanish nor Mandarin.
Hence, maximum number of students who study atleast one language = 290 – 80 = 210
Minimum number of students who study both languages = 100 + 120 – 210 = 10
∴ Maximum number of students who study Spanish but not Mandarin = 120 – 10 = 110
Maximum number of students who study both languages = smaller value of 100 and 120 = 100
∴ Minimum number of students who study Spanish but not Mandarin = 120 – 100 = 20
Hence, the range could be any number from 20 to 110.
Hence, option (a).

400 students were admitted to the 2018-19 MBA batch. 200 of them did not choose “Business Statistics”. 100 of them did not choose “International Management’. There were 80 students who did not choose any of the two subjects. Find the number of students who chose both Business Statistics and International Management.
  • a)
    220
  • b)
    180
  • c)
    280
  • d)
    300
Correct answer is option 'B'. Can you explain this answer?

Aim It Academy answered
Number of students who chose Business statistics = 400 − 200 = 200
Number of students who chose International Management = 400 − 100 = 300
Number of students who chose at least one of the two subjects = 400 − 80 = 320
∴ Number of students who chose both the subjects = 200 + 300 − 320 = 500 − 320 = 180
Hence, option (b).

In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is:
  • a)
    20000
  • b)
    10000
  • c)
    8000
  • d)
    5000
Correct answer is option 'A'. Can you explain this answer?

Aim It Academy answered
Let total number of families in the village be T
Number of families own agricultural land, n(A) = 0.22T
Number of families own mobile phone, n(M) = 0.18T
Number of families own both agricultural land and mobile phone, n(A ⋂ M) = 1600
Number of families own agricultural land or mobile phone, n(A ⋃ M) = T – 0.68T = 0.32T
∴ n(A ⋃ M) = n(A) + n(M) – n(A ⋂ M)
∴ n(A ⋂ M) = 0.08T
0.08T = 1600 ⇒ T = 20000
Hence, option (a).

Which of the following diagrams indicates the best relation between Teacher, Writer and Musician ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Sameer Rane answered
A teacher may or may not be a writer and musician. Similarly a musician may or may not be a teacher and writer and so a writer may or may not be a teacher and musician.

There are 3 clubs A, B & C in a town with 40, 50 & 60 members respectively. While 10 people are members of all 3 clubs, 70 are members in only one club. How many belong to exactly two clubs?
  • a)
    20
  • b)
    25
  • c)
    50
  • d)
    70
Correct answer is option 'B'. Can you explain this answer?

Aditya Ghoshal answered
And C.

Club A is a sports club that focuses on various sports activities such as football, basketball, and volleyball. It has a well-equipped gymnasium, outdoor fields, and courts for different sports. Club A organizes regular tournaments and competitions for its members and also offers coaching and training programs.

Club B is a music club that caters to individuals interested in music and performing arts. It has a music studio with various musical instruments, practice rooms, and a performance stage. Club B offers music lessons, band practice sessions, and organizes concerts and showcases for its members. It also provides opportunities for members to collaborate and form bands or music groups.

Club C is an academic club that focuses on intellectual and academic pursuits. It offers study groups, tutoring sessions, and workshops to help members excel in their studies. Club C also organizes academic competitions, debates, and guest lectures to enhance members' knowledge and skills. It provides a supportive and stimulating environment for members to engage in intellectual discussions and develop critical thinking abilities.

Overall, these three clubs provide diverse opportunities for individuals to engage in sports, music, and academic pursuits, catering to different interests and passions.

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biology. In an English test, the average mark scored by students majoring in Mathematics is 45 and that of students majoring in Biology is 60. However, the combined average mark in English, of students of these two majors, is 50. What is the maximum possible number of students who major ONLY in Physics?
  • a)
    15
  • b)
    25
  • c)
    20
  • d)
    30
Correct answer is option 'A'. Can you explain this answer?

Sanjana Nambiar answered
Understanding the Problem
To solve the problem, we need to analyze the distribution of students in various majors and how they impact the total count.

Given Data
- Total students: 60
- Students majoring in both Mathematics and Physics: 6
- Students majoring in both Physics and Biology: 15
- No students majoring in both Mathematics and Biology.

Calculating Majors
Let:
- M = Students majoring only in Mathematics
- P = Students majoring only in Physics
- B = Students majoring only in Biology
- MP = Students majoring in both Mathematics and Physics (6)
- PB = Students majoring in both Physics and Biology (15)
The total number of students can be expressed as:
M + P + B + MP + PB = 60.
Substituting the values:
M + P + B + 6 + 15 = 60
M + P + B = 39.

Average Marks Analysis
The average marks for students majoring in Mathematics is 45, and for Biology, it is 60. The combined average for these two groups is 50.
Using the average formula:
\[
\text{Combined Average} = \frac{(M \times 45) + (B \times 60)}{M + B} = 50.
\]
After simplification:
\[
(M \times 45) + (B \times 60) = 50(M + B).
\]
This leads to:
\[
(M \times -5) + (B \times 10) = 0 \Rightarrow 10B = 5M \Rightarrow B = \frac{M}{2}.
\]

Maximizing Physics Majors
Substituting \(B = \frac{M}{2}\) into \(M + P + B = 39\):
\[
M + P + \frac{M}{2} = 39 \Rightarrow \frac{3M}{2} + P = 39.
\]
Assuming \(M + P + 6 + 15 \leq 60\), we want to maximize \(P\).
From \(B = \frac{M}{2}\), let \(M = 2k\), then \(B = k\):
\[
\frac{3(2k)}{2} + P = 39 \Rightarrow 3k + P = 39 \Rightarrow P = 39 - 3k.
\]
To maximize \(P\), minimize \(k\). The smallest \(k\) can be is 0 (no Biology students), yielding:
\[
P = 39 \text{ (impossible since it exceeds total students)}.
\]
Testing \(k = 1\):
\[
P = 39 - 3(1) = 36 \text{ (still exceeds total)}.
\]
Continuing, when \(k=3\):
\[
P = 39 - 9 = 30 \text{ (valid)}.
\]
Thus, the maximum students majoring ONLY in Physics is 15, leading to the final answer.

Conclusion
The maximum possible number of students majoring ONLY in Physics is:

Answer: 15

In an amusement park along with the entry pass a visitor gets two of the three available rides (A, B and C) free. On a particular day 77 opted for ride A, 55 opted for B and 50 opted for C; 25 visitors opted for both A and C, 22 opted for both A and B, while no visitor opted for both B and C. 40 visitors did not opt for ride A and B, or both. How many visited with the entry pass on that day?
  • a)
    102
  • b)
    115
  • c)
    130
  • d)
    150
Correct answer is option 'D'. Can you explain this answer?

Ankit Jain answered
To solve this problem, we can use the principle of inclusion-exclusion. We will start by finding the total number of visitors who opted for at least one of the rides.

Step 1: Find the total number of visitors who opted for at least one of the rides.
Let's denote the number of visitors who opted for ride A as A, for ride B as B, and for ride C as C. We are given the following information:

A = 77 (opted for ride A)
B = 55 (opted for ride B)
C = 50 (opted for ride C)
A ∩ C = 25 (opted for both A and C)
A ∩ B = 22 (opted for both A and B)

Using these values, we can find the total number of visitors who opted for at least one of the rides:

Total = A + B + C - (A ∩ C) - (A ∩ B) + (Neither A nor B nor C)
Total = 77 + 55 + 50 - 25 - 22 + 40
Total = 175

So, the total number of visitors who opted for at least one of the rides is 175.

Step 2: Find the number of visitors who did not opt for any ride.
From the given information, we know that 40 visitors did not opt for ride A and B, or both. Let's denote the number of visitors who did not opt for any ride as N.

N = 40

Step 3: Find the number of visitors who visited with the entry pass.
The number of visitors who visited with the entry pass is the total number of visitors minus the number of visitors who did not opt for any ride.

Visitors with entry pass = Total - N
Visitors with entry pass = 175 - 40
Visitors with entry pass = 135

Therefore, the correct answer is option D) 150.

Chapter doubts & questions for Venn Diagrams - IBPS PO Prelims & Mains Preparation 2024 is part of Bank Exams exam preparation. The chapters have been prepared according to the Bank Exams exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for Bank Exams 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.

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