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) x = 9
(b) 0 ≤ x < 8
(c) 9 < x ≤ 30
(d) x = 8
The correct answers to the above question in:
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.
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Read more model question set 1 Based Quantitative Aptitude Questions and Answers
Question : 1
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 : 2
What is {[(A ∪ B)' ∩ A]} - (A - B) equal to?
a) B
b) A
c) Φ
d) B'
Answer »Answer: (c)
{(A ∪ B)' ∩ A} - (A - B)
= {(U – (A ∪ B)) ∩ A} – (A – B)
= {(U ∩ A) – {(A ∪ B) ∩ A}} – (A – B)
= {A – A} – (A – B)
= Φ – (A – B) = Φ
Question : 3
Consider the following for the next 04 (four) items that follow :In an examination of Class XII, 55% students passed in Biology, 62% passed in Physics, 60% passed in Chemistry, 25% passed in Physics and Biology, 30% passed in Physics and Chemistry, 28% passed in Biology and Chemistry. Only 2% failed in all the subjects.What percentage of students passed in all the three subjects?
a) 4
b) 5
c) 6
d) 3
Answer »Answer: (a)
Total passed student = 98%
7 + x + 2 + x + 2+ x + 30 – x + 25 – x + 28 – x + x = 98
94 + x = 98 ; x = 4%
Question : 4
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 : 5
Consider the following for the next 04 (four) items that follow : In an examination of Class XII, 55% students passed in Biology, 62% passed in Physics, 60% passed in Chemistry, 25% passed in Physics and Biology, 30% passed in Physics and Chemistry, 28% passed in Biology and Chemistry. Only 2% failed in all the subjects.If the number of students is 360, then how many passed in at least two subjects?
a) 265
b) 263
c) 270
d) 260
Answer »Answer: (c)
Passed in at least two subject
= ${25 - x + 30 - x + 28 - x + x}/{100}$ × 360
= ${83 - 2x}/{100}$ × 360 = 270
Question : 6
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.
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