This EduRev document offers 10 Multiple Choice Questions (MCQs) from the topic Set Theory (Level - 1). These questions are of Level - 1 difficulty and will assist you in the preparation of CAT & other MBA exams. You can practice/attempt these CAT Multiple Choice Questions (MCQs) and check the explanations for a better understanding of the topic.
Question for Practice Questions Level 1: Set Theory - 1
Try yourself:In a group of 50 persons, everyone takes either tea or coffee. If 35 take tea and 25 take coffee, then the number of persons who take tea only (and not coffee) is
Explanation
Let A be the set of persons who take tea and B be the set of those who take coffee. We are given that n(A ∪ B) = 50, n(A) = 35 and n(B) = 25.
⇒ 50 = 35 + 25 – n(A ∩ B)
⇒ (A ∩ B) = 10
Hence, n(A – B) = n(A) – n(A ∩ B) = 35 – 10 = 25
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:Let A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}. Then, A ∩ B is given by
Explanation
A ∩ B = Elements that belong to both A and B
∴ Elements of A ∩ B should be multiples of 3 and 5 or we can say that elements of A ∩ B are multiples of 15.
Hence, A ∩ B = {x | x is a multiple of 15} = {15, 30, 45, ...}
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:Let A denote the set of integers between 1 and 1000 which are divisible by 12 and B denote the set of integers between 1 and 1000 which are divisible by 18. How many elements are there in the set A B?
Explanation
n(A) = [1000/12] = 83 (A is a set of integers between 1 to 1000 is divisible by 12.)
n(B) = [1000/18] = 55 (B is a set of integers between 1 to 1000 divisible by 18, where [x] is the greatest integer function.)
A ∩ B = Set of integers between 1 and 1000 which are divisible by 12 and 18 both, i.e. divisible by 36
n(A ∩ B) = [1000/36] = 27
n(A B) = n(A) + n(B) – n(A ∩ B) = 83 + 55 – 27 = 111
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:Directions: Study the following information and answer the question.
In Foodpur, where a person has to eat either vegetarian food or non-vegetarian food, there are 600 people who eat non-vegetarian food, 400 people who eat vegetarian food and 150 people who eat both. Of the people who eat non-vegetarian, there are 300 who eat mutton, 400 who eat chicken and 200 who eat both these types of meat.
Q. How many people eat non-vegetarian food, but do not eat mutton or chicken?
Explanation
Number of people who eat non-vegetarian food, but do not eat mutton or chicken = 600 – 200 – 200 – 100 = 100
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:Directions: Study the following information and answer the question.
A newsagent sells the dailies Hindu, Express and Mail in equal number to 906 persons. 21 persons buy Express and Mail, 36 buy Hindu and Mail, 27 buy Hindu and Express, and buy 9 all the three dailies.
Q. The numbers of persons buying Hindu and Express only, Hindu and Mail only, and Express and Mail only form a ratio
Explanation
Since the dailies are sold in equal number, the total sale of each may be taken as x.
Hence, from the diagram, if we add up all the ''only'' regions, we get:
(x - 54) + (x - 48) + (x - 39) + 9 + 27 + 18 + 12 = 906
⇒ x = 327
Number of persons buying Hindu and Express only = 18
Number of persons buying Hindu and Mail only = 27
Number of persons buying Express and Mail only = 12
Required ratio = 18 : 27 : 12 = 6 : 9 : 4
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:Members of a group of 400 people speak either Hindi or English or both. If 270 speak Hindi only and 50 speak both Hindi and English, then how many of them speak English only?
Explanation
Number of people in the group = 400
270 + 50 + x = 400
x = 80
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:In a town with population of 5000, 3200 people are egg-eaters, 2500 meat eaters and 1500 eat both egg and meat. How many are pure vegetarians i.e. neither meat-eaters nor egg-eaters?
Explanation
Total number of egg or meat eaters
= 1700 + 1500 + 1000 = 4200
Number of pure vegetarians = 5000 – 4200 = 800
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?
Explanation
Total number of people in the group = 70
Number of people who like coffee = 37
Number of people who like tea = 52
Number of people who like both coffee and tea = x
So, 70 = [37 - x + x + 52 - x]
x = 19
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:In a community, 56% of the total families use mixers and 66% of the total use air conditioners.
What is the highest number of families not using either a mixer or an air conditioner?
Explanation
Highest number of families not using either a mixer or an air conditioner = 100 - 66 = 34%
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Question for Practice Questions Level 1: Set Theory - 1
Try yourself:In a written test, out of number of students who appeared, 49% passed section A and 35% passed section B. Find the percentage of students who appeared but failed in both the sections of the test if 25% of the students passed both sections A and B.
Explanation
From the Venn diagram,
(24 + 25 + 10) i.e. 59% passed in one or both.
∴ 41% failed in both.
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