At Quantifiers, we understand the pivotal role of DILR Venn diagram 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.

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

**Enhanced Problem-Solving Abilities:**Proficiency in DILR Venn diagram 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.

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

- Out of every four students writing CAT, there are three students appearing for XAT also.
- For every five students appearing for both CAT and XAT, there are two students appearing for XAT but not for CAT.
- Half of the students who are writing either XAT but not CAT or CAT but not XAT, appear for MAT also.
- The number of students who write only MAT is same as the number of students who write exactly one other exam along with MAT.
- Out of every three students who write XAT and CAT, one writes MAT also.
- Out of every two students who write CAT but not XAT, one student writes MAT also.
- 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?**

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?**

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.

- 45
- 35
- 40
- 30

- 45
- 90
- 75
- 60

- 110
- 130
- 120
- None

- 109:111:121
- 117:125:133
- 111:109:123
- 111:109:120

**Correct Answer 1**

c. 40

**Correct Answer 2**

d. 60

**Correct Answer 3**

d. None

**Correct Answer 4**

d. 111:109:120

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 *p*, *q* and *r* respectively

- 92
- 27
- 33
- None of these

- 49
- 47
- 43
- 50

- 33
- 66
- 99
- 49

- 35
- 32
- 26
- 29

**Correct Answer 1**

d. None of these

**Correct Answer 2**

d. 50

**Correct Answer 3**

b. 66

**Correct Answer 4**

a. 35

**Correct Answer 1**

0

**Correct Answer 2**

4) None of these

**Correct Answer 3**

0

**Correct Answer 4**

640

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.

Some more information is given below.

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?**

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