Venn Diagram Question in CUET 2022 Slot 2

Q1-2. In a housing society, 50 households subscribe to newspaper 1, 60 households subscribe to newspaper 2 and 70 households subscribe to newspaper 3. Further 25 households subscribe to both 1 and 2, 20 households to both 2 and 3 and 10 households to both 1 and 3. Also there are five households which subscribe to all the three newspapers?

1. If 20 households do not subscribe to any of the three mentioned newspapers, then what is the total number of households in the society?

(1) 200

(2) 180

(3) 155

(4) 170

EXPLANATION

Let’s use the principle of inclusion and exclusion to find the total number of households in the society.

Let:

• ( A ) be the set of households subscribing to newspaper 1,
• ( B ) be the set of households subscribing to newspaper 2,
• ( C ) be the set of households subscribing to newspaper 3.

We are given the following information:

• ( |A| = 50 ),
• ( |B| = 60 ),
• ( |C| = 70 ),
• 

2. What is the number of households that subscribe to only one newspaper?

(1) 90

(2) 45

(3) 76

(4) 180

EXPLANATION

Let’s denote the number of households subscribing to each newspaper as follows:

• A: households subscribing to newspaper 1 (|A| = 50)
• B: households subscribing to newspaper 2 (|B| = 60)
• C: households subscribing to newspaper 3 (|C| = 70)

Now, we are given the following information:

3. A batch of students at a college are planning a winter vacation trip. Three options have been proposed as destinations – Shimla, Goa and Jaisalmer. While some students are fixated with only one choice, some are okay with more than one choice and some don’t mind going to either of the three destinations. It was found that 40 students are ready for both Goa and Shimla, 10 students are ready to go to any of the three destinations, and 30 students are ready for both Shimla and Jaisalmer. If 25 students want to go to Shimla only, total how many students are willing to go to Shimla?

(1) 95

(2) 70

(3) 85

(4) 70

EXPLANATION

Let’s use the principle of inclusion and exclusion to find the total number of students willing to go to Shimla.

Let:

• G: students willing to go to Goa
• S: students willing to go to Shimla
• J: students willing to go to Jaisalmer

Given information:

∣S∣=80+30−20

∣S∣=90

Therefore, the correct answer is: (1) 95