Venn Diagram MCQ Quiz - Objective Question with Answer for Venn Diagram - Download Free PDF

Hockey players who play football is shown below:

Number of hockey players who play football = 22 + 19 = 41

Hence, ‘41’ is the correct answer.

Mistake Points

i) In the question, it is mentioned that Hockey players who play football but it is not mentioned that we do not have to include players who play cricket. So unless mentioned we have to consider all the categories.

ii) Here the word "only" is not used. If only words have used in the question then the answer would have been 22 but as and is used answer will be 41.

The shaded part represents the number of banks are not office.

The number of banks are not office  = 11

Hence, ‘11’ is the correct answer.

The logic follows here is:

From the diagram given below

The shaded part represents red bird = 7 + 5 = 12

Hence the correct answer is “12”

Given the ratio:

\( (a + b + c) : (d + e + f) : g = 15 : 3 : 2 \)

Total number of students in the school = \( 900 \)

Calculations:

\( a + b + c = 900 \times \frac{15}{20} = 675 \)

\( d + e + f = 900 \times \frac{3}{20} = 135 \)

\( g = 900 - 675 - 135 = 90 \)

Definitions:

Number of students who play:

• Hockey = \( h = c + e + f + g \)
• Football = \( h + 45 = b + f + g + d \)
• Cricket = \( (h + 45) \times 1.5 = 1.5h + 67.5 = a + d + e + g \)

Equation Setup:

\( h + (h + 45) + (1.5h + 67.5) = a + b + c + 2d + 2e + 2f + 3g = 675 + 270 + 270 = 1215 \)

Simplification:

\( 3.5h + 112.5 = 1215 \)

\( 35h + 1125 = 12150 \)

\( 35h = 11025 \)

h = 315.

Number of students who play Hockey = h = c + d + f + g = 315
Number of students who play Football = h + 45 = b + d + g + e = 315 + 45 = 360
Number of students who play Cricket = (h + 45) × 1.5 = a + e + d + g = 360 × 1.5 = 540.

a = 360; a + e + d + g = 540; v = 90; thus, e + d = 540 – 360 – 90 = 90
e + d + f = 135 ⇒ f = 135 – 90 = 45.

Given the ratio:

\( (a + b + c) : (d + e + f) : g = 15 : 3 : 2 \)

Total number of students in the school = \( 900 \)

Calculations:

\( a + b + c = 900 \times \frac{15}{20} = 675 \)

\( d + e + f = 900 \times \frac{3}{20} = 135 \)

\( g = 900 - 675 - 135 = 90 \)

Definitions:

Number of students who play:

• Hockey = \( h = c + e + f + g \)
• Football = \( h + 45 = b + f + g + d \)
• Cricket = \( (h + 45) \times 1.5 = 1.5h + 67.5 = a + d + e + g \)

Equation Setup:

\( h + (h + 45) + (1.5h + 67.5) = a + b + c + 2d + 2e + 2f + 3g = 675 + 270 + 270 = 1215 \)

Simplification:

\( 3.5h + 112.5 = 1215 \)

\( 35h + 1125 = 12150 \)

\( 35h = 11025 \)

h = 315.

Number of students who play Hockey = h = c + d + f + g = 315
Number of students who play Football = h + 45 = b + d + g + e = 315 + 45 = 360
Number of students who play Cricket = (h + 45) × 1.5 = a + e + d + g = 360 × 1.5 = 540.

c + d + f + g = 315; d + e + f = 135; g = 90
If e = 20; d + f = 135 – 20 = 115
c = 315 – 115 – 90 = 110.

Total number of persons = 200

Number of persons who likes coffee = 108

Number of persons who likes tea = 90

Number of persons who like both tea and coffee = 46

Number of persons who like only tea = 90 – 46 = 44

Number of persons who like only coffee = 108 – 46 = 62

Persons who like neither tea nor coffee = 200 – (44 + 62 + 46) = 48

Failed in 2 subjects i.e passed in 1 subject only.

Ireland is a country and Dublin is its capital, whereas Greece is a country.

So the possible relationship diagram would be:

Hence, figure a is the correct answer.

The shaded part represents is the number of players who play football or cricket but not basketball.

 n(A∪B) = n(A) + n(B) - n(A⋂B)

The number of players who play football or cricket but NOT basketball = Number of player who play cricket and football – (Number of player who play both basketball and cricket + Number of player who play both Basketball and football + Number of player who play Basketball, Cricket and football)

And

Number of player who play cricket and football = The number of players who play football + The number of players who play cricket - The number of players who play both football and cricket

Number of player who play cricket and football = 50 + 40 - (14 + 5) = 71

So,

The number of players who play football or cricket but not basketball =

= 71 – (9 + 7 + 5)

= 71 – 21

= 50

Hence, ‘50’ number of players who play football or cricket but NOT basketball.

Additional Information

Players who play only Football = 50 - (14 + 7 + 5) = 24

Players who play only Cricket= 40 - (14 + 9 + 5) = 12

Players who play only Basketball = 30 - (9 + 7 + 5) = 9

Check all the options

Option 1: Fathers, Brothers, Males

• All fathers and brothers are males

​

Option 2: Mothers, Aunts, Doctors

• Some mothers are Aunts and some mothers and aunties are doctors

Option 3: Literates, Engineers, Farmers

• All engineers are Literates and some farmers are Literates.

Option 4: Grandfathers, Fathers, Males

• All grandfathers are fathers
• All grandfathers and fathers are male.

Hence, ‘option4’ is the correct answer.

Hockey players who play football is shown below:

Number of hockey players who play football = 22 + 19 = 41

Hence, ‘41’ is the correct answer.

Mistake Points

i) In the question, it is mentioned that Hockey players who play football but it is not mentioned that we do not have to include players who play cricket. So unless mentioned we have to consider all the categories.

ii) Here the word "only" is not used. If only words have used in the question then the answer would have been 22 but as and is used answer will be 41.

The Venn diagram that best illustrates the relationship between Ministers, Farmers and Engineers is shown below:

Some Ministers can be Farmers and Engineers, Some Farmers can be Ministers and Engineers and Some Engineers can be Ministers and Farmers.

Hence, ‘option 3’ is the correct answer.

The Venn diagrams best represent the relationship between - Women, Gynaecologists, Doctors figures are shown below:

All Gynaecologists are doctors, some women are doctors and some women are Gynaecologists.

Hence, ‘option 2’ is the correct answer.

Mistake PointsAthletics is a Game, Athlete is a person, so solve it accordingly.

Given:

Cricket, Athlete, Sport

The Venn diagram for the given classes is:

Cricket is a type of sport and an athlete is a person who plays sport.

Hence, the correct answer is "Option (3)".

Total number of people taken Italian food = 150

Total number of people taken Indian food = 200

Total number of people taken Continental food = 100

Total number of people taken only both Italian and Indian food = 14

Total number of people taken only both Italian and Continental food = 10

Total number of people taken only both Continental and Indian food = 15

Total number of people taken all three kind of food = 6

Total number of people invited in the party = 500

Total number of people taken only Indian food = 200 - 14 - 15 - 6 = 165

Total number of people taken only Italian food = 150 - 14 - 10 - 6 = 120

Total number of people taken only Continental food = 100 - 10 - 15 - 6 = 69

So,

Total Number of people who did not attend the party

= 500 - (120 + 10 + 6 +14 + 69 + 15 +165) = 500 - 399 = 101

Hence, 101 people did not attend party.