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
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:
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.
Following were the observation of the survey:
15 had air conditioning
2 had air conditioning and power windows but no radios
12 had radio
6 had air conditioning and radio but no power windows
11 had power windows
4 had radio and power windows
3 had all three options
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.
(15) Air Conditioning (12) Radio
(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.
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.
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
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.