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Test: Venn Diagram - Mechanical Engineering MCQ


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10 Questions MCQ Test - Test: Venn Diagram

Test: Venn Diagram for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Test: Venn Diagram questions and answers have been prepared according to the Mechanical Engineering exam syllabus.The Test: Venn Diagram MCQs are made for Mechanical Engineering 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Venn Diagram below.
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Test: Venn Diagram - Question 1
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At a certain school, each of the 160 students takes atleast one of the 3 classes. The 3 classes available are English, Hindi and Spanish. 54 students study English, 86 study Hindi and 61 study Spanish. If 8 students take all 3 classes, how many take exactly 2 classes?

Detailed Solution for Test: Venn Diagram - Question 1

Let us consider following diagram –

We know that

a+b+c+x+y+z+8 = 160

a+b+c+x+y+z = 152

Also, a+b+c+2*(x+y+z)+3*8 = 54+86+61

a+b+c+2*(x+y+z) = 177

Solving both equation we have, x+y+z = 177-152 = 25 students

So 25 students took exactly 2 subjects.
Hence, option B is the right answer.

Test: Venn Diagram - Question 2
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Instructions

There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

  1. 75 students selected only management and physics.
  2. 84 students selected only management and history.
  3. 52 students selected only physics and history.
  4. The number of students who selected only history is 137 less the number of students who selected only management.
  5. In total 238 students selected management as an elective.
  6. In total 240 students selected history as an elective.

Q. How many students selected both management and physics as elective?

Detailed Solution for Test: Venn Diagram - Question 2

Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,

y + x + 84 + 75 = 238

x + y = 79

Considering students who took history as an elective we have,

137 – y + x + 84 + 52 = 240

y – x = 33

Adding both the equation we get,

2y = 112

y = 56

So, x = 23

So, number of students who took all the three electives = 23

Number of students who took only management = 56

Number of students who took only history = 137 – 56 = 81

So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79

Thus, we get following venn diagram –

Number of students who selected both management and physics as elective = 75 + 23 = 98
Hence, option E is the correct choice.

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Test: Venn Diagram - Question 3
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Instructions

There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

  1. 75 students selected only management and physics.
  2. 84 students selected only management and history.
  3. 52 students selected only physics and history.
  4. The number of students who selected only history is 137 less the number of students who selected only management.
  5. In total 238 students selected management as an elective.
  6. In total 240 students selected history as an elective.

Q. How many students selected the only history as an elective?

Detailed Solution for Test: Venn Diagram - Question 3

Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,

y + x + 84 + 75 = 238

x + y = 79

Considering students who took history as an elective we have,

137 – y + x + 84 + 52 = 240

y – x = 33

Adding both the equation we get,

2y = 112

y = 56

So, x = 23

So, number of students who took all the three electives = 23

Number of students who took only management = 56

Number of students who took only history = 137 – 56 = 81

So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79

Thus, we get following venn diagram –

Hence, option C is the correct choice.

Test: Venn Diagram - Question 4
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Instructions

There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

  1. 75 students selected only management and physics.
  2. 84 students selected only management and history.
  3. 52 students selected only physics and history.
  4. The number of students who selected only history is 137 less the number of students who selected only management.
  5. In total 238 students selected management as an elective.
  6. In total 240 students selected history as an elective.

Q. How many students selected only physics as an elective?
Detailed Solution for Test: Venn Diagram - Question 4

Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,

y + x + 84 + 75 = 238

x + y = 79

Considering students who took history as an elective we have,

137 – y + x + 84 + 52 = 240

y – x = 33

Adding both the equation we get,

2y = 112

y = 56

So, x = 23

So, number of students who took all the three electives = 23

Number of students who took only management = 56

Number of students who took only history = 137 – 56 = 81

So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79

Thus, we get following venn diagram –

Hence, option B is the correct choice.

Test: Venn Diagram - Question 5
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Instructions

There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

  1. 75 students selected only management and physics.
  2. 84 students selected only management and history.
  3. 52 students selected only physics and history.
  4. The number of students who selected only history is 137 less the number of students who selected only management.
  5. In total 238 students selected management as an elective.
  6. In total 240 students selected history as an elective.

Q. How many students selected only management as an elective?
Detailed Solution for Test: Venn Diagram - Question 5

Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,

y + x + 84 + 75 = 238

x + y = 79

Considering students who took history as an elective we have,

137 – y + x + 84 + 52 = 240

y – x = 33

Adding both the equation we get,

2y = 112

y = 56

So, x = 23

So, number of students who took all the three electives = 23

Number of students who took only management = 56

Number of students who took only history = 137 – 56 = 81

So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79

Thus, we get following venn diagram –

Hence, option A is the correct choice.

Test: Venn Diagram - Question 6
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Instructions

There are 450 students in a college. Each student has to choose one or more elective out of management, history and physics. Further following information is also known –

  1. 75 students selected only management and physics.
  2. 84 students selected only management and history.
  3. 52 students selected only physics and history.
  4. The number of students who selected only history is 137 less the number of students who selected only management.
  5. In total 238 students selected management as an elective.
  6. In total 240 students selected history as an elective.

Q. How many students select all the three electives?
Detailed Solution for Test: Venn Diagram - Question 6

Let ‘x’ be the number of students who took all the three electives and ‘y’ be the number of students who took only management as an elective.
We get following venn diagram –

Considering students who took management as an elective we have,

y + x + 84 + 75 = 238

x + y = 79

Considering students who took history as an elective we have,

137 – y + x + 84 + 52 = 240

y – x = 33

Adding both the equation we get,

2y = 112

y = 56

So, x = 23

So, number of students who took all the three electives = 23

Number of students who took only management = 56

Number of students who took only history = 137 – 56 = 81

So, the number of students who took only physics = 450 – 240 – 56 – 75 = 79

Thus, we get following venn diagram –

Hence, option D is the correct option.

Test: Venn Diagram - Question 7
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In a locality consisting of 400 families, each family reads at least one newspaper. It is known that 200 families read ‘The Hindu’. 150 families read ‘Indian Express’ and 180 families read ‘Times of India’. If it is known that exactly 40 families read all three newspapers then how many families read exactly two newspapers?
Detailed Solution for Test: Venn Diagram - Question 7

Let there be ‘a’ people who read exactly one newspaper, ‘b’ people who read exactly ‘2’ newspapers and ‘c’ people who read all three newspaper. So we have
a + b + c = 400
a + 2b + 3c = 150 + 180 + 200 = 530
Subtracting both the equations we get
b + 2c = 130
We have been given that c = 40
Hence, b = 130 – 80 = 50
Thus, 50 people read exactly two newspapers.

Test: Venn Diagram - Question 8
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Instructions
350 people are living in a particular village. There are three drinks Tea, Coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that:

  1. In total 120 people like Tea and 160 people like Coffee.
  2. 46 people like all the three drinks.
  3. 62 people like both Tea and Hot chocolate.
  4. 53 people like both Hot chocolate and Coffee.
  5. 89 people like both Tea and Coffee.

Q. How many people like only Tea?
Detailed Solution for Test: Venn Diagram - Question 8

46 people like all the three drinks. We make following venn diagram –

Since 62 people like both Tea and Hot chocolate

62 – 46 = 16 people like only Tea and Hot chocolate

Since 53 people like both Hot chocolate and Coffee

53 – 46 = 7 people like only Hot chocolate and Coffee

Since 89 people like both Tea and Coffee

89 – 46 = 43 people like only Tea and Coffee.

Thus, number of people who like only Tea = 120 – 46 – 16 – 43 = 15

Thus, number of people who like only Coffee= 160 – 43 – 46 – 7 = 64

Number of people who like only Hot chocolate = 350 – 160 – 16 – 15 = 159

We get following venn diagram –

Hence, option E is the correct choice.

Test: Venn Diagram - Question 9
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Instructions
350 people are living in a particular village. There are three drinks Tea, Coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that:

  1. In total 120 people like Tea and 160 people like Coffee.
  2. 46 people like all the three drinks.
  3. 62 people like both Tea and Hot chocolate.
  4. 53 people like both Hot chocolate and Coffee.
  5. 89 people like both Tea and Coffee.

Q. How many people like only Coffee and Hot chocolate?
Detailed Solution for Test: Venn Diagram - Question 9

46 people like all the three drinks. We make following venn diagram –

Since 62 people like both Tea and Hot chocolate

62 – 46 = 16 people like only Tea and Hot chocolate

Since 53 people like both Hot chocolate and Coffee

53 – 46 = 7 people like only Hot chocolate and Coffee

Since 89 people like both Tea and Coffee

89 – 46 = 43 people like only Tea and Coffee.

Thus, number of people who like only Tea = 120 – 46 – 16 – 43 = 15

Thus, number of people who like only Coffee= 160 – 43 – 46 – 7 = 64

Number of people who like only Hot chocolate = 350 – 160 – 16 – 15 = 159

We get following venn diagram –

Hence, option C is the correct choice.

Test: Venn Diagram - Question 10
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Instructions
350 people are living in a particular village. There are three drinks Tea, Coffee and Hot chocolate available in the village. Each citizen has to vote for one or more of the three drinks which he/she like. It is known that:

  1. In total 120 people like Tea and 160 people like Coffee.
  2. 46 people like all the three drinks.
  3. 62 people like both Tea and Hot chocolate.
  4. 53 people like both Hot chocolate and Coffee.
  5. 89 people like both Tea and Coffee.

Q. How many people like only Hot chocolate?
Detailed Solution for Test: Venn Diagram - Question 10

46 people like all the three drinks. We make following venn diagram –

Since 62 people like both Tea and Hot chocolate
62 – 46 = 16 people like only Tea and Hot chocolate

Since 53 people like both Hot chocolate and Coffee
53 – 46 = 7 people like only Hot chocolate and Coffee

Since 89 people like both Tea and Coffee
89 – 46 = 43 people like only Tea and Coffee.

Thus, number of people who like only Tea = 120 – 46 – 16 – 43 = 15

Thus, number of people who like only Coffee= 160 – 43 – 46 – 7 = 64

Number of people who like only Hot chocolate = 350 – 160 – 16 – 15 = 159

We get following venn diagram –

Hence, option B is the correct choice.

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