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Number System - Aptitude MCQ Questions and Solutions with Explanations

Number System MCQ Questions and answers with easy and logical explanations.Arithmetic Ability provides you all type of quantitative and competitive aptitude mcq questions on Number System with easy and logical explanations. Number System MCQ is important for exams like Banking exams,IBPS,SCC,CAT,XAT,MAT etc. Page-9 section-3

Each section contains 100 MCQs on Number System .
81
A rational number between $${\text{ }}\frac{3}{4}$$ and $${\text{ }}\frac{3}{8}$$ is :
Discuss
Answer & Solution
Answer: Option C
Solution:
given $${\text{ }}\frac{3}{4}$$ = 0.75     $${\text{ }}\frac{3}{8}$$ = 0.375
(a) $${\text{ }}\frac{7}{9}$$ → 0.77
(b) $${\text{ }}\frac{7}{3}$$ → 2.3
(c) $${\text{ }}\frac{5}{9}$$ → 0.55
(d) $${1\text{ }}\frac{9}{16}$$ = $${\text{ }}\frac{25}{16}$$ → 1.5
$${\text{ }}\frac{5}{9}$$ = 0.55
82
If the operation '*' is defined by a * b = a + b - ab, then 5 * 7 equals :
Discuss
Answer & Solution
Answer: Option C
Solution:
5 * 7
= 5 + 7 - 5 × 7
= 12 - 35
= - 23
83
The smallest five digit number which is divisible by 12, 18 and 21 is :
Discuss
Answer & Solution
Answer: Option A
Solution:
We know,
Smallest five digit number is = 10000
L.C.M. of 12, 18, 21 = 252
10000 is divided by 252
then the remainder is 172
Difference = 252 - 172 = 80
Then number is = 10000 + 80 = 10080
84
$$1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{{14}} + \frac{1}{{28}}$$      is equal to :
Discuss
Answer & Solution
Answer: Option A
Solution:
$$\eqalign{ & = 1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{7} + \frac{1}{{14}} + \frac{1}{{28}} \cr & = \frac{{28 + 14 + 7 + 4 + 2 + 1}}{{28}} \cr & = \frac{{56}}{{28}} \cr & = 2 \cr} $$
85
In a two digit number, the digit at the unit's place is 1 less than twice the digit at the ten's place. If the digits at unit's and ten's place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is :
Discuss
Answer & Solution
Answer: Option D
Solution:
Let the ten's digits be x
Unit digit be 2x - 1
Original number :
= 10x + 2x - 1
= 12x - 1
New number :
= 10(2x - 1) + x
= 20x - 10 + x
= 21x - 10
According to the question,
(21x - 10) - (12x - 1) = (12x - 1) - 20
9x - 9 = 12x - 21
3x = 12
x = 4
Original number :
= 12x - 1
= 12 × 4 - 1
= 47
86
Find the sum of all positive multiples of 3 less than 50 :
Discuss
Answer & Solution
Answer: Option C
Solution:
First multiple = 3
Last multiple (less than 50) = 48
Number of multiples of 3
= $$\frac{48 - 3}{3}$$ + 1
= 16
Sum :
= $$\frac{16}{2}$$ [2 × 3 + (16 - 1)3]
= 8 × 51
= 408
87
The value of $$\left( {0.\overline {63} + 0.\overline {37} } \right)$$    is :
Discuss
Answer & Solution
Answer: Option B
Solution:
$$\eqalign{ & \Rightarrow \left( {0.\overline {63} + 0.\overline {37} } \right) \cr & = \frac{{63}}{{99}} + \frac{{37}}{{99}} \cr & = \frac{{63 + 37}}{{99}} \cr & = \frac{{100}}{{99}} \cr} $$
88
If 1 is added to the both the numerator and the denominator of a fraction, it becomes $$\frac{1}{4}$$ . If 2 is added to both the numerator and the denominator of that fraction it becomes $$\frac{1}{3}$$ . The sum of the numerator and the denominator and the denominator of the fraction is -
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the numerator and denominator x and y
According to question,
$$\eqalign{ & \frac{{x + 1}}{{y + 1}} = \frac{1}{4} \cr & 4x + 4 = y + 1 \cr & 4x - y = - 3.....(i) \cr & \frac{{x + 2}}{{y + 2}} = \frac{1}{3} \cr & 3x + 6 = y + 2 \cr & 3x - y = - 4.....(ii) \cr & {\text{Solve (i) and (ii) }} \cr & x = 1\,\,\,\& \,\,\,y = 7 \cr} $$
Sum of numerator and denominator of fraction :
= x + y
= 1 + 7
= 8
89
A man ate 100 grapes in 5 days. Each day he ate 6 more grapes then those he ate on the earlier day. How many grapes did he eat on the first day ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Man eats G grapes on 1st day
According to question
G + (G + 6) + (G + 12) + (G + 18) + (G + 24) = 100
5G + 60 = 100
5G = 40
G = 8
90
The least number of five digits which is divisible by 123 ?
Discuss
Answer & Solution
Answer: Option B
Solution:
Least number of 5 digit is 10000
10000 is divided by 123
then the remainder is 37
Least number that divisible by 123
=10000 − 37 + 123
=10086