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) 7
(b) 10
(c) 12
(d) 6
The correct answers to the above question in:
Answer: (d)
Given that
x ε {2, 3, 4}
and
y ε {4, 6, 9, 10}
A = x × y
But, A is set of pairs in which $1^{st}$ number is factor of second number.
A = {2, 3, 4} × {4, 6, 9, 10}
= {(2, 4); (2, 6); (2, 10); (3, 6); (3, 9); (4, 4)}
Total number of elements = 6
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Read more model question set 2 Based Quantitative Aptitude Questions and Answers
Question : 1
The Venn diagram given above represents four sets of students who have opted for Mathematics, Physics, Chemistry and Electronics. What does the shaded region represent?
a) Students who opted for Mathematics, Physics and Electronics only
b) Students who opted for Mathematics, Physics and Chemistry
c) Students who opted for Physics, Chemistry and Electronics
d) Students who opted for Mathematics, Chemistry and Electronics only
Answer »Answer: (a)
It is clear from the given Venn diagram that shaded portion represent the students who opted for Mathematics, Physics and Electronics only.
Question : 2
The set of natural numbers is closed under
I. addition
II. subtraction
III. multiplication
IV. division
Which of the above is/are correct?
a) I, II and III
b) Both I and III
c) Only I
d) Both III and IV
Answer »Answer: (b)
Set of natural numbers,
N = {1, 2, 3, 4, 5, 6, ...
(i) Addition: 2 + 3 = 5 is also an element of N.
(ii) Subtraction: 2 – 3 = –1 ∉ N
(iii) Multiplication: 2 × 3 = 6 ε N
(iv) Division: $3/2$. = 1.5 ∉ N (since, N contains only positive integers)
Therefore, the set of natural numbers is closed under addition and multiplication.
Question : 3
Consider the following in respect of the sets A and B.
I. (A ∩ B) ⊆ A
II. (A ∩ B) ⊆ B
III. A ⊆ (A ∪ B)
Which of the above are correct?
a) I and III
b) II and III
c) I and II
d) I, II and III
Answer »Answer: (d)
From figure,
(A ∩ B) ⊆ A (true)
(A ∩ B) ⊆ B (true)
and A ⊆ (A ∪ B) also (true)
Thus, all three statements are correct.
Shaded region = (A ∪ B).
Question : 4
In an examination, 50% of the candidates failed in English, 40% failed in Hindi and 15% failed in both the subjects. The percentage of candidates who passed in both English and Hindi is
a) 60%
b) 25%
c) 20%
d) 75%
Answer »Answer: (b)
Percent of candidates, who failed in either Hindi or English
= (50 + 40 – 15)% = 75%
∴ Percent of candidates who passed in both subject
= 100 – 75 = 25%
Question : 5
If A = {1, 2, 3, 4}, then what is the number of subsets of A with atleast three elements?
a) 5
b) 4
c) 3
d) 10
Answer »Answer: (a)
Given, A = {1, 2, 3, 4}
So, the required subsets are {1, 2, 3}, {1, 2, 4}, {1, 3, 4}, {2, 3, 4}
and {1, 2, 3, 4}
Question : 6
In a class of 110 students, x students take both Mathematics and Statistics, 2x + 20 students take Mathematics and 2x + 30 students take Statistics. There are no students who take neither Mathematics nor Statistics. What is x equal to?
a) 25
b) 20
c) 15
d) 30
Answer »Answer: (b)
n(M) = 2x + 20
n(S) = 2x + 30
n(M ∩ S) = x
n(M ∪ S) = 110
We know that,
n(M ∪ S) = n(M) + n(S) – n(M ∩ S)
⇒ 110 = 2x + 20 + 2x + 30 – x
⇒ 110 = 3x + 50
⇒ 3x = 60
∴ x = 20
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