# CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram

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

Apti4All offered four subjects – QA, DILR, VA and RC. Students studying at Apti4All had the option of attending classes for one, two or three subjects but not all the four as the classes of RC and VA were conducted at the same time and the students had to choose one of the two. The following details give the number of students who were attending tuition in different subjects.

- Students attending tuitions in VA = 72
- Students attending tuitions is VA and DILR = 16
- Students attending tuitions in QA and VA = 26
- Students attending tuitions in VA, QA and DILR = 16
- Students attending tuitions in QA = 108
- Students attending tuitions in QA and RC = 44
- Students attending tuitions in RC and DILR = 38
- Students attending tuitions in QA, DILR and RC = 24
- Students attending tuitions in RC = 98
- Students attending tuitions in QA and DILR = 54
- Students attending tuitions in DILR = 80

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

What is the total number of students attending classes at Apti4All?

Answer: 220

**Explanation** :

From the given data, we get the following diagram.

∴ Number of students studying only QA = 108 – (10 + 20 + 14 + 16 + 24) = 24.

∴ Number of students studying only DILR = 80 – (14 + 16 + 24 + 14) = 12.

∴ Number of students studying only VA = 72 – (10 + 16) = 46.

∴ Number of students studying only RC = 98 – (20 + 24 + 14) = 40.

Hence, we get the final diagram.

∴ The total number of students at Apti4All = 24 + 10 + 20 + 14 + 16 + 24 + 12 + 14 + 46 + 40 = 220.

Hence, 220.

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

The number of students attending tuitions for exactly three subjects are?

Answer: 40

**Explanation** :

Consider the solution for the first question of this set.

Number of students attending tuitions for exactly three subjects = 0 + 16 + 0 + 24 = 40.

Hence, 40.

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

The number of students attending tuitions for exactly one subject are?

Answer: 122

**Explanation** :

Consider the solution for the first question of this set.

Number of students attending tuitions for exactly one subject = 24 + 12 + 46 + 40 = 122.

Hence, 122.

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

The number of students attending tuitions for exactly only DILR and RC are?

Answer: 14

**Explanation** :

Consider the solution for the first question of this set.

Number of students attending tuitions for only DILR and RC = 14.

Hence, 14.

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

The number of students attending tuitions for QA or DILR but not RC?

Answer: 76

**Explanation** :

Consider the solution for the first question of this set.

Number of students attending tuitions for QA or DILR but not RC = 24 + 14 + 12 + 10 + 16 = 76.

Hence, 76.

Workspace:

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

In a colony, residents can watch four different OTT platforms – Hotstar, Netflix, SonyLiv and Prime. 20% of them do not watch any OTT platform. The four platforms given in the above order are watched by 460, 360, 360 and 440 people respectively. The number of people watching exactly 2 platforms for any two platforms is 40. There are 60 people who watch all the four platforms but there is nobody who watches exactly three out of the four platforms.

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

How many people watch exactly two platforms?

- A.
240

- B.
300

- C.
160

- D.
180

Answer: Option A

**Explanation** :

From the given data, we get the following diagram.

∴ Number of people watching only Hotstar = 460 – 3 × 40 – 60 = 280

∴ Number of people watching only Netflix = 360 – 3 × 40 – 60 = 180.

∴ Number of people watching only SonyLiv = 360 – 3 × 40 – 60 = 180.

∴ Number of people watching only Prime = 440 – 3 × 40 – 60 = 260.

Hence, we get the following complete diagram.

Number of people who watch exactly two platforms is 6 × 40 = 240.

Hence, option (a).

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

How many people watched exactly one platform?

- A.
1200

- B.
900

- C.
1500

- D.
700

Answer: Option B

**Explanation** :

Consider the solution for the first question of this set.

Total Number of people watching exactly one platform = 280 + 180 + 180 + 260 = 900.

Hence, option (b).

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

How many people do not watch any platform at all?

- A.
75

- B.
100

- C.
225

- D.
150

Answer: Option D

**Explanation** :

Consider the solution for the first question of this set.

Total number of people watching at least one platform = 900 + 240 + 60 = 1200.

This represents 80% of the total number of the people.

So, total number of people = 1200/0.8 = 1500.

∴ Number of people who do not watch any platform = 20% of 1500 = 300.

Hence, option (d).

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

What percentage of the people watching Netflix also watch at least one other platform?

- A.
35%

- B.
55%

- C.
50%

- D.
65%

Answer: Option C

**Explanation** :

Consider the solution for the first question of this set.

Number of Netflix people watching at least one more platform.

= exactly two platforms + all four platforms = 3 × 40 + 60 = 180.

As a percentage of all the people watching Netflix, this is 180/360 × 100 = 50%.

Hence, option (c).

Workspace:

**CRE 3 - 4 Set Venn Diagram | LR - Venn Diagram**

If all the people in the college including those who do not watch any platform watch at least one more platform, (out of the four platforms above) which they do not watch at present, then what is the least number of people watching all the four platforms?

- A.
120

- B.
50

- C.
30

- D.
60

Answer: Option D

**Explanation** :

Consider the solution for the first question of this set.

Least increase in the number of people who watched all platforms will come only if each student watches exactly one additional platform.

But, since the number of people who watched exactly three platforms in zero, there will not be any addition to the figure of 60 people who watched all four platforms.

Hence, the answer is 60.

Hence, option (d).

Workspace:

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