# PE 2 - Venn Diagram | LR - Venn Diagram

**Answer the next 4 questions based on the information given below.**

A survey was conducted in a society to determine number of newspaper subscriptions. 300 people were surveyed who have subscribed for at least one of the following newspapers i.e., TOI, Hindustan Times, Bhaskar, Business Standard and Financial Express. Any person who subscribed TOI also subscribed Bhaskar, while any person who subscribed Financial Express also subscribed Business Standard. Any person who subscribed for Hindustan Times also subscribed for TOI, while no person who subscribed for Business Standard subscribed for TOI.

It is also known that

- The number of persons who subscribed for Hindustan Times was thrice the number of persons who subscribed for only Business Standard.
- The number of persons who subscribed for only Bhaskar was ten less than the number of persons who subscribed for exactly one newspaper.
- The number of persons who subscribed for Financial Express was twenty-nine more than the number of persons who subscribed for TOI.
- The number of persons who subscribed for at least three newspapers was 140.
- The number of persons who subscribed for TOI was hundred more than the number of persons who subscribed for only Business Standard.
- The number of persons who subscribed for Bhaskar was eighty-six more than the number of persons who subscribed for Business Standard.

**PE 2 - Venn Diagram | LR - Venn Diagram**

We can draw the following Venn diagram from the information given in the question.

Answer: 25

**Explanation** :

We can draw the following Venn diagram from the information given in the question.

From (1): a = 3g …(1)

From (2): c = (c + g) – 10

⇒ g = 10

⇒ a = 30 [From (1)]

From (3): e + f = a + b + 29

⇒ e + f = 59 + b …(2)

From (4): a + e = 140

⇒ 30 + e = 140

⇒ e = 110

From (5): a + b = g + 100

⇒ 30 + b = 10 + 100

⇒ b = 80

⇒ e + f = 59 + b = 139 …(3) [From equation (2)]

⇒ 110 + f = 139

⇒ f = 29

From (6): a + b + c + d + e = d + e + f + g + 86

⇒ a + b + c = f + g + 86

⇒ 30 + 80 + c = f + 10 + 86

⇒ c = f - 14

⇒ c = 15

Now, total number of people surveyed is 300.

∴ a + b + c + d + e + f + g = 300

⇒ 30 + 80 + 15 + d + 110 + 29 + 10 = 300

⇒ d = 26

∴ The final Venn diagram is:

∴ Number of people who subscribed for exactly one newspaper = c + g = 15 + 10 = 25.

Hence, 25.

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

How many persons subscribed for Bhaskar and exactly one other newspaper?

Answer: 106

**Explanation** :

Consider the solution to first question of this set.

Number of people who subscribed for Bhaskar and exactly one other newspaper = b + d = 80 + 26 = 106.

Hence, 106.

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

Among the persons who subscribed for Bhaskar, how many persons subscribed for Business Standard?

Answer: 136

**Explanation** :

Consider the solution to first question of this set.

Number of persons who subscribed for Bhaskar as well as Business Standard = d + e = 26 + 110 = 136.

Hence, 136.

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

How many persons subscribed for both Financial Express and TOI?

Answer: 0

**Explanation** :

Consider the solution to first question of this set.

As can be seen from the Venn diagram, there is no overlapping region for Financial Express and TOI.

Hence, 0.

Workspace:

**Answer the next 5 questions based on the information given below:**

In a colony, a survey was conducted regarding the ownership of three different types of jeans – Straight-fit, Ripped and Low-waist.

- The number of residents owning all three types of jeans is the same as those owning none.
- The number of residents owning exactly two of any type of jeans are same which is also same as the number of residents owning none of the three types of jeans.
- The number of residents owning only low-waist jeans is half the number of residents owning either only straight-fit or only low-waist
- Number of residents who own only low-waist jeans is same as the number of residents who own at least one more type of jeans.

**PE 2 - Venn Diagram | LR - Venn Diagram**

If the number of residents who own only low-waist is 120, then what is the total number of residents in the colony?

- (a)
400

- (b)
800

- (c)
600

- (d)
1000

Answer: Option B

**Explanation** :

Let the number of residents who own all three types of jeans = x.

From (1): The number of residents who own none of the three types of jeans = x

From (2): The number of residents who own exactly two of any type of jeans = x

Let the number of residents who own only low-waist jeans = y

From (3): The number of residents who own only straight-fit or only ripped jeans = 2y

From (4): x + x + x = y

⇒ 3x = y

Total number of residents = 2y + 2y + y + x + x + x + x + x = 5y + 5x = 15x + 5x = 20x.

If the number of residents who own only low-waist i.e., y is 120, then x = 40.

∴ Total number of residents = 20 × 40 = 800.

Hence, option (b).

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

What percentage of the residents who own straight-fit jeans, also own at least one more type of jeans?

- (a)
66.67%

- (b)
13.67%

- (c)
28.56%

- (d)
33.33%

Answer: Option D

**Explanation** :

Consider the solution to first question of this set.

Number of residents who own straight-fit jeans = 2y + x + x + x = 2y + 3x = 9x

Number of residents who own straight-fit jeans and also own at least one more type of jeans = x + x + x = 3x

∴ Required % = 3x/9x × 100 = 33.33) %.

Hence, option (d).

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

If 22 residents do not own any of the three vehicles, then how many residents are there in the colony?

Answer: 440

**Explanation** :

Consider the solution to first question of this set.

Given, x = 22

∴ Total number of residents = 20x = 20 × 22 = 440.

Hence, 440.

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

What percentage of the colony residents own exactly one type of jeans?

Answer: 75%

**Explanation** :

Consider the solution to first question of this set.

Number of residents who own exactly one type of jeans = 2y + 2y + y = 5y = 15x.

Total number of residents = 20x.

∴ Required percentage = 15x/20x × 100 = 75%

Hence, 75.

Workspace:

**PE 2 - Venn Diagram | LR - Venn Diagram**

What percentage of the residents own straight fit or low-waist jeans?

Answer: 80

**Explanation** :

Consider the solution to first question of this set.

Number of residents owning a low-waist or ripped jeans = 4y + 4x = 16x

∴ Required percentage = 16x/20x × 100 = 80%

Hence, 80.

Workspace:

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