Practice Model question set 2 - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) If A = {1, 2, 3, 4}, then what is the number of subsets of A with atleast three elements?
(a)
(b)
(c)
(d)
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}
Q-2) Let x ε {2, 3, 4} and y ε {4, 6, 9, 10}. If A be the set of all order pairs (x, y) such that x is a factor of y. Then, how many elements does the set A contain?
(a)
(b)
(c)
(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
Q-3) Let S be a set of first ten natural numbers. What is the possible number of pairs (a, b) where a, b E S and a ≠ b such that the product ab (> 12) leaves remainder 4 when divided by 12 ?
(a)
(b)
(c)
(d)
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.
Q-4) If A and B are any two non-empty subsets of a set E, then what is A ∪ (A ∩ B) equal to?
(a)
(b)
(c)
(d)
A and B are non-empty subsets of E.
∴ A ∪ (A ∩ B) = A ∪ (Shaded portion) = A
Q-5) 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)
(b)
(c)
(d)
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
Q-6) 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)
(b)
(c)
(d)
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.
Q-7) 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)
(b)
(c)
(d)
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
Q-8) 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)
(b)
(c)
(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%
Q-9) In a class of 60 boys, there are 45 boys who play chess and 30 boys who plays carrom. If every boy of the class plays at least one of the two games, then how many boys play carrom only?
(a)
(b)
(c)
(d)
Total number of boys in the class
n(A ∪ B) = 60
Number of boy play chess n(A) = 45
Number of boy play carrom n(B) = 30
∴ Number of boy play both chess and Carrom
n(A ∩ B) = n(A) + n(B) – n(A ∪ B) = 45 + 30 – 60 = 15
Number of boys plays only carrom n(B) – n(A ∩ B)
= 30 – 15 = 15
42.
Q-10) 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)
(b)
(c)
(d)
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%