# CAT Questions | CAT LR Questions: Venn Diagram

### CAT Verbal Ability

A very important branch of mathematics with a wide variety of applications is Set Theory. It is a very basic and simple concept, but in Algebra, Logic, Combinatorics, Probability, etc., it has considerable use. Therefore, knowing venn diagram math and venn diagram formula is of serious importance for the same purpose in solving different venn diagram questions in competitive exams such as MBA entrance exams.

For solving venn diagram problems basic representation of venn diagram sets is the Venn diagram, also known as the Euler-Venn diagrams is used. For the sets under consideration, the regular representation makes use of a rectangle as the universal set and circles.

Distribution in competitive exams

 Year No of Questions Good attempt Difficulty 2019 Slot 1 1 1 Moderate Slot 2 2 1 Difficult 2018 Slot 1 1 1 Easy Slot 2 1 0 – 1 Moderate

 Year No of Questions Good attempt Difficulty 2020 2 2 Moderate 2019 2 1 Moderate

#### SNAP :

 Year No of Questions Good attempt Difficulty 2019 2 2 Easy-Moderate 2018 3 2 Moderate

## List of concepts in Venn Diagram

A rectangle representing the universal set starts with each Venn diagram. Then a circle represents each set of values in the problem. In the sections where the circles overlap, any values which belong to more than one set will be put. Some venn diagram examples as follows:

## CAT Logical Reasoning questions | CAT LR : Venn Diagram

Q1. Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is     (CAT 2018)

Let the number of students who studying only H be h, only E be e, only H and P but not E be x, only E and P but not H be y

Given only P = 0 All three = 10; Studying only H and E but not P = 20 Given number of students studying H = Number of students studying E

= h + x + 20 + 10

= e + y + 20 + 10

h + x = e + y total number of students = 74 Therefore, h + x + 20 + 10 + e + y = 74

h + x + e + y = 44 h + x + h + x = 44 h + x = 22

Therefore, the number of students studying H = h + x + 20 + 10 = 22 + 20 + 10 = 52.

Q2. A survey on a sample of 25 new cars being sold at a local auto dealer was conducted to see which of the three popular options — air conditioning, radio and power windows were already installed.

(CAT 2003)

Following were the observation of the survey:

What is the number of cars that had none of the options?

1. 4 2. 3      3. 1        4.2

Total = 4 + 6 + 2 + 2 + 3 + 1 + 5 = 23

Cars having none of the option = 25 – 23 = 2.

(11) Power Windows

Q3: In a college, 200 students are randomly selected. 140 like tea, 120 like coffee, and 80 like both tea and coffee.

• How many students like only tea?
• How many students like only coffee?
• How many students like neither tea nor coffee?
• How many students like only one of tea or coffee?
• How many students like at least one of the beverages?

The given information may be represented by the following Venn diagram, where T = tea and C = coffee.

Number of students who like only tea = 60

Number of students who like only coffee = 40

Number of students who like neither tea nor coffee = 20

Number of students who like only one of tea or coffee = 60 + 40 = 100

Number of students who like at least one of tea or coffee = n (only Tea) + n (only coffee) + n (both Tea & coffee) = 60 + 40 + 80 = 180

Q4. In a survey of 500 students of a college, it was found that 49% liked watching football, 53% liked watching hockey and 62% liked watching basketball. Also, 27% liked watching football and hockey both, 29% liked watching basketball and hockey both and 28% liked watching football and basketball both. 5% liked watching none of these games.

• How many students like watching all the three games?
• Find the ratio of the number of students who like watching only football to those who like watching only hockey.
• Find the number of students who like watching only one of the three given games.
• Find the number of students who like watching at least two of the given games.

n(F) = percentage of students who like watching football = 49%

n(H) = percentage of students who like watching hockey = 53%

n(B)= percentage of students who like watching basketball = 62%

n ( F ∩ H) = 27% ; n (B ∩ H) = 29% ; n(F ∩ B) = 28%

Since 5% like watching none of the given games so, n (F ∪ H ∪ B) = 95%.

Now applying the basic formula,

95% = 49% + 53% + 62% -27% – 29% – 28% + n (F ∩ H ∩ B)

Solving, you get n (F ∩ H ∩ B) = 15%.

Now, make the Venn diagram as per the information given.

Note: All values in the Venn diagram are in percentage.

The number of students who like watching all the three games = 15 % of 500 = 75.

The ratio of the number of students who like only football to those who like only hockey = (9% of 500)/(12% of 500) = 9/12 = 3:4.

The number of students who like watching only one of the three given games = (9% + 12% + 20%) of 500 = 205

The number of students who like watching at least two of the given games=(number of students who like watching only two of the games) +(number of students who like watching all the three games)= (12 + 13 + 14 + 15)% i.e. 54% of 500 = 270

## How to prepare for CAT, XAT, GMAT, SNAP, and NMAT Venn Diagrams

Level 1 –

In the form of a Venn diagram, it is necessary to carefully list the conditions given in the query. MBAP CAT E Book (Concept Theory) study material and MBAP Live Lecture Recording (Basic) on basic concept can be referred for the best approach. Avoid taking several variables when solving such problems. Using the Venn diagram method and not with the aid of formulas, try answering the questions by solving MBAP CAT E Book (Practise Questions) and MBAP lecture Assignment.

Level 2 –

To understand diagrams well, you must also practice. Arun Sharma’s ‘How to Prepare for LIDR for the CAT’ is known to be the best for CAT LIDR training. It is elaborate and easy to understand the examples given in it. To help you organize your training accordingly, it is also split into three stages of difficulty using MBAP Topic wise Previous Year CAT Question.

Level 3 –

Including all the above levels make sure you go through all the different Venn Diagram questions from the previous years of different exams using MBAP Previous year CAT paper, since so many questions are based on the concepts that have appeared in previous entrance exams. Spend lots of time per day to practice LIDR in general and measurement for the entrance test you intend to appear in particular with MBAP CAT Advance E books. The more time you spend on the questions, the more familiar they’ll get.

Counselling Session
By IIM Mentor

#### Words From Our Students

Nihar Mehta
Calls from IIMs, SPJIMR & MDI
During my CAT preparation, I enrolled at MBA Pathshala for classroom coaching. Abhijit Sir & Haider Sir guided me through the process of planning & executing the strategies I had to use to succeed in the test. I received regular feedback on my progress during the GD and PI preparations after CAT. I received calls from IIMs, SPJIMR, and MDI. MBAP played a huge role in this, and I cannot thank them enough for their efforts.
Ishan Rathod
Calls from IIM I, S, and all New And Baby IIM's.
MBAP is a great place to prepare for MBA-CET, CAT, and CMAT, and the faculty are unbeatable. Most importantly, they pay personal attention to each student. Most faculty members come from IIMs. One-on-one interaction helped me improve as the exams approached, as well as get calls from IIMs I, S, and all New and Baby IIMs. Interview sessions were very beneficial for me to convert IIM S.
Sanskriti Reja
Calls from IIMs, XLRI, XIMB
I am glad I chose MBA Pathshala for my MBA coaching. The faculty here is excellent and very competent. If I had any questions or needed extra classes, they always gave me one. I got through my GD-PIs too after the exams with their help. Thanks to MBAP, I was able to pass CAT and other entrance exams. Among others, I received calls from XLRI, XIMB, and IIMs. A few of the colleges I've converted are KJ Somaiya, TAPMI, IIM Sambalpur, and IIM Sirmaur.
Parth Kanakia
Converted SPJIMR
MBAP prepared me for GD, WAT, and PI. Abhijit Singh, Haider, and other MBAP faculty provided excellent training. Good knowledge was imparted from the very beginning. Regular mock interviews were conducted. As a former SPJIMR, I would recommend students to join MBAP.
Ronit jaiswal
Calls from IIM-A/B/C & SNAP 98.12%ile
Coaching offers me personalized attention and a competitive environment. Because the preparation was so rigorous, I eventually began to perform at my best. The mock interviews/GD/WATs were conducted by anonymous panels, and it really boosted my confidence. Although I got a call from SCMHRD (SNAP-98.12), Abhijeet sir felt that I should try again and aim for IIM-A/B/C. It has been your pleasure to have been your mentor.
Maitreya Khanapurkar
Calls From IIMs
You will get good support from the faculty until you get into a B-School. The shortcut techniques you will learn will be extremely useful. You will be able to resolve doubts at any time. If you plan on taking CAT CET or any other entrance exam, go for MBA Pathshala. With the help of MBAP tutors, I received a call from IMT Ghaziabad.
Yash Dandavate
GMAT Score - 660
GMAT prep with MBAP was the best I've ever experienced. With Rohan Kulkarni Sir's Verbal Guidance, I scored 85th percentile in my GMAT exam as I was very weak in English. I always found Haider Sir and Abhijeet to answer my questions and to develop strategies and shortcuts to tackle GMAT problems for me. MBAP is a great option for GMAT and CAT prep.