venn diagram questions for cat
If 71 students opted for English, 98 students opted for Maths, 68 students opted for Physics and 14 students opted for all the three subjects, find the number of students who opted for exactly two subjects. In this case, x = 0So, the minimum number of students who took all the three tests is 0. 25 people went for a jog. Let the number of students who like both = x. From the 2 equations, we have, b+2c+3d+4e = 99. Correct answers: 2 question: The venn diagram represents the results of a survey that asked participants whether they would want a dog or a cat as a pet. Top-100 TISSNET GK Questions PDF (Most Expected), IIFT 2021 Results Out – Download IIFT Scorecard Here. 9x = 207 => x = 23. a) 2.5%, 92.5% In a college, two-thirds of the students study English, one-fifth of the students study Telugu and one-tenth study both the subjects. What is the number of people in the group who do not drink any beverage at all? Next Types of Triangles Practice Questions. If c = 0, then b = 95, in which case a = 5. a+2b+3c+4d+5e = 25+27+29+33+35 = 149. In a class of 50 students, 25 passed in Physics, 27 in Maths, 29 in Chemistry, 33 in Biology and 35 students passed in Geography. A collection of 9-1 Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas. They did yoga for x-24 days. Question 1: In a school, 150 students have to opt for at least one subject out of English, Physics and Mathematics. The number of people who take exactly 2 types of juices = 2x = 46. CAT Probability Questions cover all the different ways in which question can be asked. In a school there were 800 students. Every question has a detailed solution. Let the number of students who pass in exactly one subject be a, exactly 2 be b, exactly 3 be c, exactly 4 be d and exactly 5 be e. a+b+c+d+e = 50 Consider the following diagram: In the above diagram, we see that there are three groups or sets called ‘A’ ,’B’, and … We dealt with the idea of Minima and Maxima in Set Theory in this post. A Venn diagram can help us determine the total number of students in the class. Because the word “only” is in our problem text, it makes it an easy word problem. • 16 have a cat. Solving the following sample questions will help in understanding the basics of venn diagrams and 4-group venn diagrams. The number of people who drink exactly three beverages is 90. If c = 0, then b = 95, in which case a = 5. 3*first equation - second equation => 2A+B = 84. Let the number of persons who do not take any juice and the number of persons who take all 4 types of juices be ‘x’. LOGICAL VENN DIAGRAMS This section deals with questions which aim at analysing a candidate's ability to relate a certain given group of items and illustrate it diagrammatically. In a group of 1000 people, the number of people who drink tea is 400, the number of people who drink coffee is 500, the number of people who drink ice-tea is 300 and the number of people who drink Horlicks is 200. Venn diagrams is an important topic not just in quants, but also in DI as well. a + b + c = 100 Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. 5-a-day Workbooks. 3 people went for all three. Let ‘c’ be the percentage of residents who read all three newspapers. 1. We know that the total number of students is 150 which can be represented by the union of the three sets A, B and C i.e. If 40 people do not have any of these three pets, what is the minimum possible number of people who own exactly one pet? What is the maximum possible percentage of employees who drink both beverages? The number of people in the group who drink all the four beverages is 40. For dogs, 12 students have dogs, and 5 students have both cats and dogs. Thus the total number of people in the Gym = x + 4x + 2x + x + x = 9x. Many varieties of questions can be framed from this area. The representation would be as follows: The participants here are the 10 kids that I have mentioned in the scenario. So, the fraction of students who study at least one of the two subjects is 17/30 + 1/10 + 1/10 = 23/30. For finding the maximum possible percentage of employees who drink both the beverages, there should be maximum possible overlap between tea and coffee drinkers, Maximum possible overlap = min (78, 64) = 64. Let’s say there are 4 kids with Buzz Lightyear action figures and 7 with Sheriff Woody toys. A Venn diagram, also called primary diagram, set diagram or logic diagram, is a diagram that shows all possible logical relations between a finite collection of different sets. => C= A+16, the minimum value of A can be 0. dog not dog total cat not cat total Some other important properties for Sets and Venn diagrams; Download All Quantitative aptitude formulas of CAT. Let a, b and c be the number of students who chose exactly 2, exactly 3 and all 4 sports respectively.=> 2a + 3b + 4c = 2000=> a + b + c = 800=> b + 2c = 400Here, c can be a maximum of 200. If a conclusion can be deduced from all the possible solutions then that conclusion is true. 30 students are asked if they have a dog or cat. 12 people went for a jog as well as a run. If atleast 1 student failed in both the subjects,find the maximum number of students who passed in only Biology ? Hence, y+2z=70. Enjoy the video and do not forget to share. Take Free Mock Test for CAT 2018. Just learning Set theory formulas for CAT is not enough, practice is more important for exams like CAT, so try this practice questions for CAT. Taking a free CAT mock test to analyse your score and get a national level percentile The above example was a basic one but in exam questions will be more complex and complicated. This means the number of people who take exactly 1 type of juices = 8x – 4x = 4x. From the information given in the question, the following Venn Diagram can be constructed: So, in order to maximize the number of families that own only a bike, we can put the remaining 44 families in ‘only bike’ region. You can solve them on the same lines as the above question using the two step Venn diagram method. • 8 have a dog, but not a cat. If 15 people stop eating pizza and instead start eating burger, then what is the maximum number of people who will be eating only pizza? [3] 2. This is the cornerstone of many a maxima and minima based set. If 2 people read all the three newspapers, find which of the following can be the number of people who read exactly one newspaper? Let the number of students who took exactly one exam be ‘x’.The number of students who took exactly two exams be ‘y’ and the number of students who took exactly three exams be ‘z’.So, x + y + z = 200x + 2y + 3z = 112 + 160 + 128 = 400From these two equations, we get, y + 2z = 200To minimize ‘z’, we have to maximize ‘y’. Let A, B and C be the sets of students who opted for English, Physics and Maths respectively. If the number of students who do not follow the sport is at most 40, find the maximum number of students who are fans of both Sunrisers Hyderabad and Mumbai Indians. Represent these results using a three circle Venn Diagram.” The type of three circle Venn Diagram we will need is the following: Image Source: Passy’s World of Mathematics. Question 5: 207 people who attend “Bold Gym” in Kondapur take four types juices Apple, Orange, Pomegranate and Mango. So, the maximum number of families that own only a bike is 44 and the minimum number of families that own only a bike is 0. There are a few people who do not take any of the juices. If b = 0, a = 89 and c = 11. Let ‘a’ be the percentage of residents who read only one newspaper. Second Equation-2*First Equation = C-A = 16. If the number of people who take all four types of juices is equal to the number of people who do not take any juice at all, what is the number of people who take exactly 2 types of juices? 25 people listened to Hindustani music. In a society with 200 people, 77 people are dog owners, 80 are cat owners and 73 are bird owners. c) 10%, 90% Level 2 – To understand diagrams well, you must also practice. What can be the minimum and maximum percentage of residents who read exactly two newspapers? Changes in CAT Data Interpretation section During the last 5 years, Data Interpretation for CAT has substantially changed. In most of the cases, we are required to find maximum and minimum value in Venn diagram related questions. 16 families have both a car and a bike. How to solve questions based on At least n in Set Theory for CAT Exam? To find the maximum percentage of residents who read exactly two newspapers, ‘b’ has to be maximum and ‘c’ has to be minimum. So, the maximum number of families that own only a bike is 44 and the minimum number of families that own only a bike is 0. Three of those many ways are given below in Venn Diagrams. These diagrams depict elements as points in the plane, and sets as regions inside closed curves. In a survey, it was found that 20 people go for a walk, 3 people went for a walk and a jog but not for a run, 19 people went for a run, 5 people went for a walk and a run but not for a jog. Similarly, in order to minimize the number of families that own only a bike, we can put the remaining 44 families in ‘only scooter’ region. If a = 78, c = 0 and b = 22. Suppose you are given a group of three items. This means the number of people who take exactly 2 types of juices = 4x – x – x = 2x. In a society with 200 people, 77 people are dog owners, 80 are cat owners and 73 are bird owners. Subtracting this from first equation, we get a-c = 78. Maxima Minima Concept based on Set theory or Venn diagram is very important for CAT exam not only in Quant section but more so in LRDI section. These sudden and unexpected changes have made it difficult for the aspirant to find a good source for practicing Logical reasoning questions for the LRDI section of CAT exam. Hence the minimum value of C will be 16. $AUBUC$, $AUBUC = A+B+C-A\bigcap B-B\bigcap C-C\bigcap A+A\bigcap B\bigcap C$, 150 =$71+98+68-A\bigcap B-B\bigcap C-C\bigcap A+A\bigcap B\bigcap C+14$, $A\bigcap B+B\bigcap C+C\bigcap A = 251-150 = 101$. First, for cats, 15 students have cats, and 5 students have both cats and dogs. A Venn diagram is a diagram that describes all the possibilities of overlap and non-overlap of two or more sets. The results of a survey of common allergies was organized into a Venn diagram. Enroll here. Every family owns at least one type of vehicle and the number of families that own exactly one type of vehicle is more than the number of families that own more than one type of vehicle. Venn diagram, also known as Euler-Venn diagram is a simple representation of sets by diagrams. The max value of z is when y=0. Avoid taking several variables when solving such problems. Venn Diagram Questions For CAT PDF Set-2: Download Venn Diagram Questions and Answers for CAT exam PDF set-2 with solutions. Sum = 240-x+x+280-x = 520 - x = 400 - number of students who do not follow the sport. So, 93 - x = 93 - 15 = 78 is the maximum number of people who eat only pizza. Set theory is an important topic for CAT Preparation, CAT Questions from CAT Set theory are available in 2IIMs free CAT Question Bank. Similarly, in order to minimize the number of families that own only a bike, we can put the remaining 44 families in ‘only scooter’ region. 14 students three times. 16 families have both a car and a bike. From the Venn Diagram, the number of people who participated in none of the activities = 46 - 41 = 5. Hence, the number of ways of having the other elements is $$2^{12}$$. As there are ‘2x’ people who take atleast 3 types of juices there should be ‘4x’ people who take atleast 2 types of juices. If the total number of people in the neighborhood is 100 and each of them plays at least one sport, what is the maximum number of people who play exactly one sport? Similarly, for 13 and 2, the number of ways is $$2^{10}$$ We have to get the maximum number of students who passed in at least three subjects, i.e. 60% read Hindu, 80% read Times and 55% read Express. Another method of solving such type of questions is by drawing Venn diagram representing the statements. In a survey, it was found that 14 people read The Hindu, 18 people read the Times and 15 people read the Indian Express. Click here for Answers . Solve all previous papers at your convenience by downloading PDFs. First, we must calculate the number of students who have ONLY cats or ONLY dogs. Since this question is about dogs and cats, it will require a two circle Venn Diagram. Complete the Venn diagram. 2nd Floor, Above Ghanshyam Super Market,Botanical Gardens Road, Sri Ramnagar - Block B,Kondapur, ©2021 Chaya Education Pvt Ltd | In a group of 270 people, 135 eat pizza, 125 eat burger, 115 eat hotdog. Use coupon EARLYBIRD - Get CAT 2021 Complete course for just Rs. Hence max value for x = 120 + 40 = 160. Learn and practice the most important logical reasoning questions & puzzles for CAT/XAT/IIFT and other entrance exams. Subtracting, we get,b+2c = 22. My Tweets. b) 5%, 95% For the following questions answer them individually. Option b) is the correct answer. The intersection of these ellipses represents all those elements that are present in either of the sets. => b + 2c = 95 Each of these 12 numbers can either be in the subset or not. What can be the minimum and maximum percentage of residents who read exactly two newspapers? Many varieties of questions can be framed from this area. Venn Diagram is an important topic which is often seen in all major MBA entrance exams such as CAT, MAT, XAT, NMAT, IIFT, among others. From the options, a can be both 19 and 21. What is the sum of the maximum and minimum number of families that own only a bike? Download Venn Diagram Questions CAT PDF Set-2. value of a = 89. Let the number of people in the group who drink exactly one beverage be ‘a’, the number of people who drink exactly two beverages be ‘b’, the number of people who drink exactly three beverages be ‘c’, the number of people who drink exactly four beverages be ‘d’. 3 people listened to all three genres of music. They played tennis for x-14 days. Download All Quantitative Aptitude important Questions PDF. CAT questions with videos. Primary Study Cards. Question 4: Out of 60 families living in a building, all those families which own a car own a scooter as well. In a survey, it was found that the number of people who play hockey in a neighborhood is 30, the number of people who play cricket is 40 and the number of people who play football is 52. CAT Probability Examples: Example 1: An urn contains 10 white and 15 black balls. In a college consisting of 200 students, 112 students took the Maths Olympiad, 160 students took the Physics Olympiad and 128 students took the Chemistry Olympiad. Since b + 2c = 95, if b = 0, c = 47.5, in which case a = 52.5, So, the minimum percentage is 0% and the maximum percentage is 95%. This three circle word problem is an easy one. CAT Venn Diagrams Questions with Answers. This means the number of people who take exactly 3 types of juices = 2x – x = x. Let the number of people who eat pizza and hotdog but not burger be x.So, adding all the values, we have 93 - x + 12 + 30 + x + 65 + 18 + 67 - x = 270=> x = 15So, the number of people who eat pizza and hotdog but not burger is 15.If these 15 people stop eating pizza and instead start eating burger, the condition in the question is satisfied. Say there is a bunch of 10 kids few of whom have Buzz Lightyear action figures and few who have Sheriff Woody toys. 2x – 38 = 22. a + b + c = 100a + 2b + 3c = 60 + 80 + 55 = 195=> b + 2c = 95To find the maximum percentage of residents who read exactly two newspapers, ‘b’ has to be maximum and ‘c’ has to be minimum. No family has just a scooter and a bike. Question 1: In a school, 150 students have to opt for at least one subject out of English, Physics and … From the information given in the question, the following Venn Diagram can be constructed: So, in order to maximize the number of families that own only a bike, we can put the remaining 44 families in ‘only bike’ region. GCSE Revision Cards. enter your answers in the boxes to complete the two way table based on the given data. What is the minimum percentage of students that play all three sports? Assuming A is the number of students who play exactly 1 game, B is the number of students who play exactly 2 games and C is the number of students who play exactly 3 games. Number of students who like only Sunrisers Hyderabad is 240-x and number of students who like only Mumbai Indians is 280-x. In a locality, residents read at least one of the three newspapers - Hindu, Times and Express. If the number of people surveyed was 46, find the number of people who did not do any of the three. 12 people listened to Hindustani and Western music. 2IIM offers online CAT coaching for CAT and conducts CAT Classes in Chennai. In mathematical language, it represents the intersection of the two groups. So, sum = 44 + 0 = 44. In CAT and other MBA entrance exams, questions asked from this topic involve 2 or 3 variable only. d) 0%, 95%. So, b+2(c+d+e)+d+2e = 99. b =1 and c = 49 and d = e = a = 0 => c + d + e = 49 is the maximum value. Also, ensure you do not panic when you see a question you don’t understand. To find the minimum percentage of residents who read exactly two newspapers, ‘b’ has to be minimum. Hence, when z=0, y=70 and x=90. Method 2- Venn Diagrams. Number of people who drink exactly two beverages is 120. • 21 have a dog. Arun Sharma’s ‘How to Prepare for LIDR for the CAT’ is known to be the best for CAT LIDR training. of students who do not follow the sport in the above equation. Let ‘b’ be the percentage of residents who read exactly two newspapers. Practice Questions; Post navigation. In SSC, IBPS, CAT & Others Exam, questions asked from this topic involve 2 or 3 variable only. Let ‘c’ be the percentage of residents who read all three newspapers. Ten students have only cats. In most of the cases, we are required to find maximum and minimum value in Venn diagram related questions. Very useful for all freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, … Other posts related to Quantitative Aptitude – Modern Maths. I hope that this will help you in solving problems related to Set Theory. Thousands of students have taken Cracku's Free CAT Mock. Previous Transformations of Graphs Practice Questions. In an office, 78% of the employees are tea drinkers and 64% are coffee drinkers. Search for: Contact us. In a survey, it was found that the number of people who listened to Carnatic music was 20, the number of people who listened to Carnatic and Hindustani but not Western music was 3, the number of people who listened to Western Music was 19, 5 people listened to Carnatic and Western music but not Hindustani. Note that the word “only” is extremely important in Venn Diagram word problems. Assuming A is the number of students who play exactly 1 game, B is the number of students who play exactly 2 games and C is the number of students who play exactly 3 games. Privacy Policy. If z = 0, y = 200. Excellent Offers for CAT 2018. It is known that for every person in the Gym who takes atleast ‘N’ types of juices there are 2 persons who take atleast ‘N-1’ juices for N = 2, 3 and 4. What is the sum of the maximum and minimum number of families that own only a bike? What is a Venn Diagram? Permutation and Combination – Fundamental Principle of Counting For minimum overlap between the two sets the union of the two sets should be as large as possible. To be honest, you should be absolutely comfortable with questions dealing with 3 sets and know enough to draw the Venn-diagram in case of 4 sets. Let the number of people who read exactly one newspaper be a, those who read exactly two newspapers be b and those who read exactly 3 newspapers be c. From the given information, a+2b+3c = 47 and c = 2 => a+2b = 41. These ellipses are often drawn inside a rectangle. I hope this article has made Venn diagram questions easier to solve. Here is a Venn diagram. Let the kids with both these toys be 3 in total. Find the maximum number of students that could have chosen all the four sports as their extra-curricular activity? Out of 60 families living in a building, all those families which own a car own a scooter as well. Get all the help you need to crack CAT in one place. If the largest and smallest numbers are 14 and 1, the other elements can be between 2-13. In a school 60% of the students play football, 84% of them play cricket and 72% of them play tennis. What number of people surveyed favoured more than one of the three parties? Therefore, max. CAT Quantitative Aptitude question formula of set theory, venn diagram, set theory problems. What is the minimum possible percentage of employees who drink both beverages? Thus max z, 2z = 70 => z=35. Hence assume that the union of the two sets is 100%. Hence, there are two possibilities with each of the 12 numbers. ... All Venn diagram formulas hold good for probability questions as well. As there are ‘x’ people who take atleast 4 types of juices there should be ‘2x’ people who take atleast 3 types of juices. Here is the type of diagram we will need. Total is $$2^{12}$$ + $$2^{10}$$ + $$2^{8}$$ + $$2^{6}$$ + $$2^{4}$$ + $$2^{2}$$ + $$2^{0}$$ = 5461. Venn Diagrams Practice Questions Click here for Questions . … Data Interpretation for CAT was a part of Quantitative Ability section prior to 2015.There used to be around 10-12 questions out of 50 based on 3-4 DI problems for CAT before 2015, and out of 30 prior to 2013. 60% read Hindu, 80% read Times and 55% read Express. Since b + 2c = 95, if b = 0, c = 47.5, in which case a = 52.5, So, the minimum percentage is 0% and the maximum percentage is 95%. Let ‘b’ be the percentage of residents who read exactly two newspapers. Hence the number of students who chose exactly 2 subjects = 101-(14*3) = 59. If 40 people do not have any of these three pets, what is the maximum possible number of people who own all three pets? Question 2: In an exam conducted for 38 students of class XII 15 passed in Biology and 25 passed in Chemistry. Solving the following sample questions will help in understanding the basics of venn diagrams and 4-group venn diagrams. What is the maximum number of students who passed in at least 3 subjects? Our highly rated app (4.6/5) is a must-have for cracking CAT. we have to maximize c+d+e. No family has just a scooter and a bike. In an office, 78% of the employees are tea drinkers and 64% are coffee drinkers. Quantitative Aptitude important Questions PDF, Ratio And Proportion Questions For Railway Group-D PDF. Suggested Reading : Free Access to CAT Online Classes . The minimum possible value of x is when z is minimum. Learn and practice the most important logical reasoning questions & puzzles for CAT/XAT/IIFT and other entrance exams. Question 3: In a locality, residents read at least one of the three newspapers – Hindu, Times and Express. Then, Let ‘a’ be the percentage of residents who read only one newspaper. So, they did yoga or played tennis for x-14+x-24 = 2x-38 days. What is the fraction of students who study at least one of the two subjects? How many subsets of the set {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20} are present such the sum of the largest and smallest numbers is equal to 15? Save my name, email, and website in this browser for the next time I comment. Using the Venn diagram method and not with the aid of formulas, try answering the questions. So we have to subtract them i.e. Let the number of people who do not drink any beverage be ‘e’.So, a + b + c + d + e = 1000 → (1)a + 2b + 3c + 4d = 400 + 500 + 300 + 200 = 1400 → (2)It is given that d = 40, c = 90 and b = 120So, from equation (2), a = 1400 - 2*120 - 3*90 - 4*40 = 730From equation (1), a + e = 1000 - 120 - 90 - 40 = 750=> e = 20So, the number of people who do not drink any beverage = 20. From the Venn Diagram, the number of people who listened to at least one genre of music = 9+3+3+5+9+2+10 = 41So, number of people who did not listen to any of the three genres of music = 46 - 41 = 5. If each student in the college takes at least one of the three exams, what is the minimum number of students who took all the three exams? In a group of 500 people who participated in a survey, 68% were in favour of at least one of the three parties A, B and C. 40% were in favour of party A, 30% were in favour of party B and 20% were in favour of party C. 5% of the people were in favour of all three parties. This rectangle is supposed to be the master set or the universal set. 9. The Venn diagram method is very interesting and easy. Let x, y, z denote families with 1, 2 and 3 pets. If the number of people who participated in the survey was 46, find the number of people who listened to none of the three genres of music. Here are a few different types of Ven n diagrams with their implications made clear. The number of incidences is nothing but uniqu… How to crack IBPS PO 2018 in First Attempt ? However, it is important that all possible Venn diagrams be drawn. You have entered an incorrect email address! 14999. Download Venn Diagram Questions CAT PDF Set-2, Download All Quantitative Aptitude important Questions PDF. Each of the students chose at least two sports among cricket, football, volleyball and basketball as their extra-curricular activity. Since 2b is even, a has to be odd. Answer the questions about the following sets: D = {x | x is a person allergic to dogs}; C = {x | x is a person allergic to cats}; P = {x | x is a person allergic to pollen} To find the minimum percentage of residents who read exactly two newspapers, ‘b’ has to be minimum. Home; Venn Diagrams; Venn Diagrams. All of the number values for each section of the diagram have been given to us in the question. Important CAT practice questions on Venn diagrams are given below. Important CAT practice questions on Venn diagrams are given below. Maxima Minima Concept based on Set theory or Venn diagram is very important for CAT exam not only in Quant section but more so in LRDI section. Logical Venn Diagrams - Learn and practice with solved Verbal Reasoning Questions and Answers accompanied by easy explanation, diagrams, shortcuts and tricks that help in understanding the concept clearly. Terms and Conditions | Beyond that not much is required, at least for the CAT … A school has 400 students out of which 240 students are fans of Sunrisers Hyderabad and 280 students are fans of Mumbai Indians. CAT logical reasoning questions, in recent years, have been unconventional and of higher difficulty level.. x is maximized when we use the maximum no. So the minimum overlap between the two sets is 78+64-100 = 42%. Venn diagrams is an important topic not just in quants, but also in DI as well. => x = 120+ number of students who do not follow the sport. Answers and Solutions for Venn Diagram Problems and Solutions for CAT PDF: 1) Answer (C) Let the number of days in the vacation be x. The usual depiction makes use of a rectangle as the universal set and circles for the sets under consideration. However, in this rearrangement, the number of people who eat only pizza is not affected. a + 2b + 3c = 60 + 80 + 55 = 195 The number of people playing exactly one sport = a, exactly 2 sports = b and all three sports = c.
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