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) 8
(b) 6
(c) 4
(d) 10
The correct answers to the above question in:
Answer: (a)
Since numbers which and leave 4 as Remainder when devided by 12 are
16, 28, 40, 52, 64, 76, 88, 100 and 124
16 = 2 × 8, 8 × 2
28 = 4 × 7, 7 × 4
40 = 4 × 10, 10 × 4, 5 × 5, 8 × 5
All remaining numbers doesn't meet the requirement
Answer is 8.
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Read more model question set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
If two sets A and B have 2n and 4n elements, respectively. When n is a natural number. What can be the minimum number of elements in A ∪ B?
a) 4n
b) 3n
c) 2n
d) 6n
Answer »Answer: (a)
Here, n(A ∩ B) = 2n
∴ n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 2n + 4n – 2n = 4n
Hence, minimum number of elements of A ∪ B is 4n.
Question : 2
If A and B are any two non-empty subsets of a set E, then what is A ∪ (A ∩ B) equal to?
a) A
b) A ∪ B
c) A ∩ B
d) B
Answer »Answer: (a)
A and B are non-empty subsets of E.
∴ A ∪ (A ∩ B) = A ∪ (Shaded portion) = A
Question : 3
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
Question : 4
Which one of the following is an infinite set?
a) {x : x is a positive integer less than or equal to 1000}
b) {x : x is a natural number less than 1000}
c) {x : x is a whole number less than or equal to 1000}
d) {x : x is an integer and less than 1000}
Answer »Answer: (d)
In a given option only,
{x : x is an integer and less than 1000}
i.e., x ε (– ∞, 1000) is an infinite set.
Question : 5
Which one of the following is a correct statement?
a) Φ = P(Φ)
b) Φ ∉ P (Φ)
c) Φ ε Φ
d) Φ ε P(Φ)
Answer »Answer: (d)
In the given options, the correct statement is Φ ε P(Φ).
Question : 6
A is a set of positive integers such that when divided by 2, 3, 4, 5 and 6 leaves the remainder 1, 2, 3, 4 and 5 respectively. How many integers between 0 and 100 belong to the set A ?
a) Two
b) One
c) No integer
d) Three
Answer »Answer: (b)
LCM of 2, 3, 4, 5, 6 = 60
Number when divided by 2, 3, 4, 5, 6 gives
remainder 1, 2, 3, 4, 5 respectively here 2 – 1 = 1
3 – 2 = 1, 4 – 3, = 1, 5 – 4 = 1, 6 – 5 = 1
So required no. = 60 – 1 = 59
other no. 59 × 2 = 118
i.e. there is one no. below 100.
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