Set Theory Model Questions Set 1 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) 265
(b) 263
(c) 270
(d) 260
The correct answers to the above question in:
Answer: (c)
Passed in at least two subject
= ${25 - x + 30 - x + 28 - x + x}/{100}$ × 360
= ${83 - 2x}/{100}$ × 360 = 270
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Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
Out of 105 students taking an examination English and Mathematics, 80 students pass in English, 75 students pass in Mathematics 10 students fail in both the subjects. How many students fail in only one subject?
a) 35
b) 30
c) 26
d) 45
Answer »Answer: (d)
Number of students failing in Mathematics
= 105 – 75 = 30
Number of students failing in English
= 105 – 80 = 25
∴ Number of students failing in 1 subject
= (25 + 30) – 10 = 45
Question : 2
In a gathering of 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French Further, 30 of them can speak both Hindi and English. 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages)
a) x = 9
b) 0 ≤ x < 8
c) 9 < x ≤ 30
d) x = 8
Answer »Answer: (a)
Let n(A) be no. of people who speak Hindi
⇒ n(A) = 70
Let n(B) be no. of people who speak English
⇒ n(B) = 60
Let n(C) be no. of people who speak French
⇒ n(C) = 30
Given n (A ∪ B ∪ C) = 100
n(A ∩ B) = 30, n(A ∪ C) = 20
n (B ∩ C) = x, n(A ∩ B ∩ C) = 1
We know that
n(A ∪ B ∪ C) = n(A) + n(B) + n (C) - n(A ∩ B)
- n (B ∩ C) - n(C ∩ A) - n(A ∩ B ∩ C)
100 = 70 + 60 + 30 – 30 – x – 20 – 1
100 = 109 – x
⇒ x = 109 – 100
⇒ x = 9
∴ Option (a) is correct.
Question : 3
The set {2, 4, 16, 256, ...} can be represented as which one of the following?
a) {x ε N| x = $2^{4n}$ , n = 0, 1, 2, ..}
b) {x ε N | x = $2^2^n$, n = 0,1, 2, ...}
c) {x ε N | x = $2^2^n$ , n ε N }
d) {x ε N| x = $2^{2n}$, n = 0, 1, 2....}
Answer »Answer: (b)
Let A = {2, 4, 16, 256, ...}
This set can be re-written as :
{x ε N | x = $2^2^n$, n = 0, 1, 2, 3,........}
Question : 4
In a school there are 30 teachers who teach Mathematics or Physics. Of these teachers, 20 teach Mathematics and 15 teach Physics, 5 teach both Mathematics and Physics. The number of teachers teaching only Mathematics is
a) 15
b) 10
c) 5
d) 20
Answer »Answer: (a)
Total number of teachers = 30.
Number of teachers who teaches only Math
= 20 – 5 = 15.
Question : 5
Which one of the following is not correct in respect of the sets A and B?
a) If A ⊆ B, then B ∩ A = A
b) If A ⊆ B, then A ∩ (A – B) = Φ
c) If A ⊆ B, then B ∪ A = B
d) If A ∩ B = Φ, then either A = Φ or B = Φ
Answer »Answer: (d)
If A ∩ B = Φ, then it is not necessary that either A = f or B = f
GET Set Theory PRACTICE TEST EXERCISES
Set Theory Model Questions Set 1
Set Theory Model Questions Set 2
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