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All questions of Venn Diagram for Super TET Exam

Directions to Solve
Study the following figure and answer the questions given below.
Question -
If hospital management requires only married trained nurses for operation theater, which part of diagram should be chosen by him ?
  • a)
    7
  • b)
    4
  • c)
    5
  • d)
    6
Correct answer is option 'C'. Can you explain this answer?

Kiran Reddy answered
because the question is only married trained nurses, so the diagram circle, triangle (represents nurses in hospital) and rectangle where intersect is the married trained nurses to the hospital. So the answer is 5 only.

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.
Question -
Which of the following diagrams indicates the best relation between Elephant, Carnivorous and Tiger ?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Nidhi Rane answered
Tiger is carnivorous but Elephant is different from these two.

Directions to Solve
Study the following figure and answer the questions given below.
Question -
By which numbers trained nurses are represented ?
  • a)
    3, 6
  • b)
    7, 5
  • c)
    5, 6
  • d)
    1, 5
Correct answer is option 'C'. Can you explain this answer?

Kiran Reddy answered
Option A = 3, 6 ; Here 3 is 'just only a married population'.
Option B = 7, 5 ; Here 7 is 'married nurses in hospital but not trained'.
Option D = 1, 1 ; Here 1 is 'nurses in hospital but not trained'.
But, Option C = 5, 6 ; Here both 5 & 6 are covered with 'Trained nurses'. Hence the required answers.
 

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?

Iq Funda answered
The best relation between Travelers, Train, and Bus can be represented in a Venn diagram, where Travelers are represented as a larger circle containing both Train and Bus circles. This is because travelers can choose either train or bus as their mode of transportation, and some may use both. Here's the explanation:
Travelers
- Travelers are people who move from one place to another for various reasons, such as work, leisure, or other purposes.
Train
- A train is a mode of transportation that runs on a railway track and can carry passengers or goods.
- Some travelers may choose to travel by train due to various factors such as cost, comfort, or availability.
Bus
- A bus is a mode of transportation that runs on roads and can carry passengers.
- Some travelers may choose to travel by bus due to factors such as cost, convenience, or accessibility.
Venn Diagram: Option C
- In option C, we have a large circle representing Travelers, which includes two smaller circles representing Train and Bus.
- This diagram shows that there are travelers who use trains, travelers who use buses, and some travelers who may use both modes of transportation.
- This representation captures the relationship between travelers and their choice of transportation, whether it's by train, bus, or both.

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?

G.K Academy answered
We know that x + y + z = T and x + 2y + 3z = R, where
x = number of members belonging to exactly 1 set = 70
y = number of members belonging to exactly 2 sets
z = number of members belonging to exactly 3 sets = 10
T = Total number of members
R = Repeated total of all the members = (40 + 50 + 60) = 150
Thus we have two equations and two unknowns. Solving this we get y = 25
So, 25 people belong to exactly 2 clubs.

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.

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?

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 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).

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?

Given Information:
- Total number of students admitted to the 2018-19 MBA batch = 400
- Number of students who did not choose "Business Statistics" = 200
- Number of students who did not choose "International Management" = 100
- Number of students who did not choose either subject = 80

Calculations:
Let's denote:
- Number of students who chose both "Business Statistics" and "International Management" as x
- Number of students who chose only "Business Statistics" as y
- Number of students who chose only "International Management" as z
From the given information, we can create the following equations:
x + y = 200 (Total number of students who chose "Business Statistics")
x + z = 100 (Total number of students who chose "International Management")
x + y + z + 80 = 400 (Total number of students admitted)
Now, we can solve these equations to find the values of x, y, and z.
From the first two equations:
y = 200 - x
z = 100 - x
Substitute these values in the third equation:
x + (200 - x) + (100 - x) + 80 = 400
300 - x + 80 = 400
380 - x = 400
-x = 20
x = 20
Therefore, the number of students who chose both "Business Statistics" and "International Management" is 20.
Therefore, the correct answer is option B) 180.

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?

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?

Understanding the Problem
To solve the problem, we need to set up variables for the number of students in each category of elective subjects.
Given Data
- Total students = 360
- Students not taking any subject = 72
- Students taking Green Supply Chain (G) = 120
- Students taking Corporate Governance (C) = 124
- Students taking all three subjects = 12
- Let:
- x = Students taking G and C but not Global Climate Change (X)
- y = Students taking G and X but not C
- z = Students taking X and C but not G
Relationships between the groups
- According to the problem:
- \( x = 2y \)
- \( x = z \)
- \( y = 12 \) (since 12 students take all three subjects)
Calculating Students in Each Category
Using the relationships:
- \( y = 12 \) (students taking all three)
- \( x = 2y = 2 \times 12 = 24 \)
- \( z = x = 24 \)
Calculating Total Students Taking Each Subject
Using the inclusion-exclusion principle:
- Total taking G and C = \( 120 + 124 - (x + y + z + 12) \)
Set the equation:
- \( 120 + 124 - (24 + 12 + 24 + 12) = 360 - 72 \)
- Solve for students taking Global Climate Change only:
Final Calculation
Total students studying:
- \( G + C + X - G \cap C - G \cap X - C \cap X + G \cap C \cap X = 288 \)
Thus, the students studying Global Climate Change only = \( 360 - 72 - (students in G + C + both) = 104 \).
Conclusion
The number of students studying Global Climate Change & Business only is:
Answer: 104 (Option B).

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.

Directions to Solve
Study the following figure and answer the questions given below.
Question -
What is represented by the number 7 ?
  • a)
    Married nurses in the hospital
  • b)
    Trained nurses
  • c)
    Unmarried trained nurses
  • d)
    Married trained nurses
Correct answer is option 'A'. Can you explain this answer?

Vikram Mehta answered
Answer: Option A
Explanation:
  • As triangle represents the nurses in hospital.
  • And circle represents the married population.
  • 7 is in intersecting point of circle and triangle
  • So, No 7 repersents mazrried nurses in the hospital.

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