Set Theory Model Questions Set 2 Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 2 EXERCISES
The following question based on Set Theory topic of quantitative aptitude
(a) 2 and 2
(b) 4 and 2
(c) 2 and 4
(d) 4 and 4
The correct answers to the above question in:
Answer: (b)
A = {7, 8, 9, 10, 11, 12}; B = {7, 10, 14, 15}
(A – B) = {8, 9, 11, 12} (B – A) = {14, 15}
n (A – B) = 4; n (B – A) = 2
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Read more model question set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
In an examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% candidates failed in both English and Mathematics, what percentage of candidates passed in both the subjects?
a) 23%
b) 21%
c) 18%
d) 25%
Answer »Answer: (a)
Total number of candidates = 100%
Percentage of candidates passed in both the subjects
= {100 – (25 + 17 + 35)}% = 23%
Question : 2
Let A and B be finite non-empty sets with the number of elements in A = m and number of elements in B = n. Let m > n. If for some integer k ≥ 1, the number of nonempty subsets of A = $2^k$ + the number of non-empty subsets of B, then which one of the following is correct?
a) m = n + p for some odd prime number p
b) m = n + 1
c) m = n + 2
d) m = n + t for some composite number t
Answer »Answer: (b)
A and B are non-empty set
A = m elements
B = n elements
m > n, A > B
m = n + 1
Question : 3
If A = (x : x is a multiple of 7),
B = (x : x is a multiple of 5) and
C = (X : x is a multiple of 35),
then which one of the following is a null set ?
a) (A ∩ B) ∩ C
b) (A– B) – C
c) (A – B) ∪ C
d) (A ∩ B) – C
Answer »Answer: (d)
A = {7, 14, 21.............}
B = {5, 10, 15..............}
C = {35, 70, 105..............}
(A ∩ B) = {35, 70, 105.......} i.e. LCM of 7 and 5 i.e. multiple of 35
A ∩ B – C = Φ
Question : 4
In an examination, 35% students failed in Hindi, 45% students failed in English and 20% students failed in both the subjects. What is the percentage of students passing in both the subjects?
a) 30
b) 20
c) 0
d) 40
Answer »Answer: (d)
Let the total number of students be 100%
Number of students failed in Hindi = 35%
Number of students failed in English = 45%
Number of students failed in both the subjects = 20%
Total number of students failed = (35 + 45 – 20)% = 60%
Number of students passing in both the subjects = (100 – 60)% = 40%
Question : 5
Which one of the following is a null set?
a) C = {Φ}
b) B = {x : x + 3 = 3}
c) A = {x is a real number : x > 1 and x < 1}
d) D = {x is a real number : x ≥ 1 and x ≤ 1}
Answer »Answer: (c)
From option (a),
A = {x is a real number : x > 1 and x < 1}.
So, there is no element which is greater or less than 1.
So, A is a null set.
From option (b),
B = {x : x + 3 = 3} = {0}
= Singleton set
From option (c):
C = {Φ} = Singleton set
From option (d),
D = {x is a real number : x ≥ 1 and x ≤ 1}
= {1} = Singleton set
Question : 6
If a set A contains 60 elements and another set B contains 70 elements and there are 50 elements in common, then how many elements does A ∪ B contain?
a) 80
b) 100
c) 130
d) 70
Answer »Answer: (a)
Here, n(A) = 60, n(B) = 70, n(A ∩ B) = 50 and n(A ∪ B) = ?
We know that:
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 60 + 70 – 50 = 130 – 50 = 80
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