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Test Level 1: Set Theory - 1 - CAT MCQ


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10 Questions MCQ Test - Test Level 1: Set Theory - 1

Test Level 1: Set Theory - 1 for CAT 2024 is part of CAT preparation. The Test Level 1: Set Theory - 1 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Set Theory - 1 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Set Theory - 1 below.
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Test Level 1: Set Theory - 1 - Question 1
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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  

Detailed Solution for Test Level 1: Set Theory - 1 - Question 1

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

Test Level 1: Set Theory - 1 - Question 2
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Let A = {x : x is a multiple of 3} and B = {x : x is a multiple of 5}. Then, A ∩ B is given by  

Detailed Solution for Test Level 1: Set Theory - 1 - Question 2

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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Test Level 1: Set Theory - 1 - Question 3
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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?  

Detailed Solution for Test Level 1: Set Theory - 1 - Question 3

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

Test Level 1: Set Theory - 1 - Question 4
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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?
Detailed Solution for Test Level 1: Set Theory - 1 - Question 4


Number of people who eat non-vegetarian food, but do not eat mutton or chicken = 600 – 200 – 200 – 100 = 100

Test Level 1: Set Theory - 1 - Question 5
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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
Detailed Solution for Test Level 1: Set Theory - 1 - Question 5

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

Test Level 1: Set Theory - 1 - Question 6
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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?
Detailed Solution for Test Level 1: Set Theory - 1 - Question 6


Number of people in the group = 400
270 + 50 + x = 400
x = 80

Test Level 1: Set Theory - 1 - Question 7
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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?  
Detailed Solution for Test Level 1: Set Theory - 1 - Question 7


Total number of egg or meat eaters
= 1700 + 1500 + 1000 = 4200
Number of pure vegetarians = 5000 – 4200 = 800

Test Level 1: Set Theory - 1 - Question 8
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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?  
Detailed Solution for Test Level 1: Set Theory - 1 - Question 8


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

Test Level 1: Set Theory - 1 - Question 9
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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?  
Detailed Solution for Test Level 1: Set Theory - 1 - Question 9

Highest number of families not using either a mixer or an air conditioner = 100 - 66 = 34%

Test Level 1: Set Theory - 1 - Question 10
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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.  
Detailed Solution for Test Level 1: Set Theory - 1 - Question 10

From the Venn diagram,
(24 + 25 + 10) i.e. 59% passed in one or both.
∴ 41% failed in both.

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