# DILR Venn Diagram

At Quantifiers, we understand the pivotal role of Venn diagrams in the Data Interpretation and Logical Reasoning section of the CAT exam. Our comprehensive curriculum and expert guidance empower students to conquer this critical aspect of the test.

## Unlocking CAT Success with Venn Diagram Mastery

Venn diagrams are indispensable tools for visualizing and solving complex problems involving sets and their relationships. At Quantifiers, we prioritize the significance of Venn diagrams within the CAT syllabus, ensuring our students are well-equipped to navigate through these questions with confidence and precision.

##### Benefits of Venn Diagram Proficiency
• Enhanced Problem-Solving Abilities: Proficiency in Venn diagrams cultivates logical reasoning and analytical thinking, crucial for success not only in the CAT exam but also in various other competitive assessments.

• Time Management: Efficiently navigating Venn diagram-based questions helps optimize time during the exam, allowing candidates to focus on other sections.

At Quantifiers, we recognize the significance of Venn diagrams in the CAT exam and are dedicated to ensuring our students excel in this area. Our holistic approach, personalized attention, and result-oriented strategies make us the ideal partner in your CAT exam journey.

## Practice Questions for CAT with Solutions

### 1. CAT - Sets & Venn Diagram

The following information pertains to a group of students writing three tests CAT, XAT and MAT:

1. Out of every four students writing CAT, there are three students appearing for XAT also.
2. For every five students appearing for both CAT and XAT, there are two students appearing for XAT but not for CAT.
3. Half of the students who are writing either XAT but not CAT or CAT but not XAT, appear for MAT also.
4. The number of students who write only MAT is same as the number of students who write exactly one other exam along with MAT.
5. Out of every three students who write XAT and CAT, one writes MAT also.
6. Out of every two students who write CAT but not XAT, one student writes MAT also.
7. It is known that on the whole 120 students appeared for CAT.

Q1. What is the number of students who write only MAT or only XAT or only CAT?

Q2. How many students appeared for at least one of XAT and MAT but not for CAT?

Q3. What is the number of students who wrote exactly two tests?

Q4. What is the number of students who wrote MAT but not CAT?

66

69

93

51

### 2. CAT - Venn Diagram

In a popular vegetable market, vendors sell tomatoes, cabbages, onions and potatoes. 56 sell tomatoes, 41 sell cabbages, 44 sell onions and 60 sell potatoes. The number of vendors selling only potatoes is four times the number of vendors selling only cabbages. The number of vendors selling only tomatoes is thrice the number of vendors selling only onions. The number of vendors selling only onions and potatoes is twice the number of vendors selling only tomatoes and cabbages. The number of vendors selling only potatoes and tomatoes is twice the number of vendors selling only onions and cabbages. The number of vendors selling only cabbages and potatoes is twice the number of vendors selling only onions and tomatoes. The number of vendors selling any three of the vegetables is equal. There is at least one vendor who sells only tomatoes. 35 vendors sell only one of these vegetables and 10 vendors sell all four.

Q1. How many vendors sell tomatoes and potatoes?

Q2. How many vendors did not sell potatoes?

Q3. How many vendors were there in the market?

Q4. How many vendors sell atmost three vegetables?

30

40

100

90

### 3. CAT - Venn Diagram

An engineering college invited 600 students for the counselling round. Two-thirds of the students were rejected right away for insufficient documents and the rest were given a choice of atleast one branch out of A, B and C. For every two students who were given the choice of only branch A, one more was given the choice of only branch B. For every five students who were given the choice of only branch C, three less were given the choice of only branch B. The number of students who got the choice of both B and C was 60 and the ratio of students who got the choice of both A and C to those who got the choice of both A and B was 5 : 7.

Q1. The number of students who got exactly two choices was 60 and the ratio of the number of students who got the choice of both C and B but not A to the number of students who got the choice of both A and C but not B is 2 : 1. How many students got a choice of all three branches
1. 45
2. 35
3. 40
4. 30
Q2. What is the maximum number of students who were given the choice of only branch C?
1. 45
2. 90
3. 75
4. 60
Q3. How many students were given exactly one choice? (Refer to the data from the first question of the set, if required.)
1. 110
2. 130
3. 120
4. None
Q4. 20 students who got a choice for only C switched to only A. 5 students who got a choice for only A and only B category respectively switched to only C. What is the ratio of students who now had the choice of branches A, B and C respectively? Assume data from the first question.
1. 109:111:121
2. 117:125:133
3. 111:109:123
4. 111:109:120

c. 40

d. 60

d. None

d. 111:109:120

### 4. CAT - Sets & Venn Diagram

A class of 100 students was asked choose from Quizzing, Painting and Reading as vacation activities. Each student picked at least one of the three activities. The number of students who picked painting, quizzing and reading was pq and r respectively

Q1. If each activity was picked by distinct number of students, the maximum possible number of students in the activity that has the least students is:
1. 92
2. 27
3. 33
4. None of these
Q2. pqr are distinct and p < q < r. If the value of p is the maximum possible, what can be the maximum number of students who have picked up both quizzing and reading, but not painting?
1. 49
2. 47
3. 43
4. 50
Q3. If the students are allowed to not pick even a single activity, the sum of the number of students who have opted for the three activities is equal to the total number of students. What is the maximum possible number of students who have not picked any activity?
1. 33
2. 66
3. 99
4. 49
Q4. The number of students who selecting quizzing was 60% more than the number of students who selected painting while the number of students who selected reading was only 40% more than the number of students who selected painting. The sum of students who selected atleast one activity was the same as the total number of students. If there were atmost 3 students in every possible combination of multiple activities, what is the maximum possible number of students who selected only reading?
1. 35
2. 32
3. 26
4. 29

d. None of these

d. 50

b. 66

a. 35

0

4) None of these

0

640

### 6. CAT - Sets & Venn Diagram

On Republic day 550 students of model high school were present for a special assembly. Once the assembly was over, principal asked the students to pick chocolates of their choice from 3 boxes kept at corner of the ground. Boxes 1, 2 and 3 contained chocolates Milkybar, DAIRY MILK and 5 STAR respectively. Owing to lack of teachers, students went havoc and picked as many chocolates as they could.

A. 237 students picked DAIRY MILK, 246 students picked Milkybar and 275 students picked 5 STAR.

B. 44 students picked all three types. No one picked more than one from any box. 45 students were disappointed to see all boxes empty

Q1. If the number of students who picked both DAIRY MILK and Milkybar but not 5 STAR is 79, then how many students picked only 5 STAR?

Q2. If the number of students who picked only Milkybar is 87, how many students picked both DAIRY MILK and 5 STAR? (Use data from previous question if necessary.)

Q3. Number of students who picked only 5 STAR is greater than the number of students who picked only Milkybar. Also, the number of students who picked only Milkybar is greater than number of students who picked only DIARY MILK.

What is the maximum number of students who picked both 5 STAR and Milkybar but not DAIRY MILK?

Q4. Fifty DAIRY MILK, fifty Milkybars and fifty 5 STARs expired. At least ten expired chocolates of each kind had gone to children picking more than one chocolate. If students do not eat expired chocolates, what will be the difference between the maximum and the minimum number of students who could not eat chocolates?

145

94

69

135