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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-5

Each section contains 100 MCQs on Number System .
81
Which of the following is a prime number ?
Discuss
Answer & Solution
Answer: Option C
Solution:
We know that 115 is divisible by 5, so it is not prime.
119 is divisible by 7, so it is not prime.
127 < (12)2 and prime numbers less than 12 are 2, 3, 5, 7, 11.
Clearly, 127 is not exactly divisible by any of them.
Hence, 127 is a prime number.
82
The number of prime numbers between 301 and 320 are :
Discuss
Answer & Solution
Answer: Option B
Solution:
Each of the numbers 302, 303, 304, 305, 306, 308, 309, 310, 312, 314, 315, 316, 318 and 319 is clearly a composite number.
Out of 307, 311, 313 and 317 clearly every one is prime.
Hence, there are 4 prime numbers between 301 and 320.
83
6 × 66 × 666 = ?
Discuss
Answer & Solution
Answer: Option C
Solution:
= 6 × 66 × 666
= 6 × (6 × 11) × (6 × 111)
= (6 × 6 × 6) × (11 × 111)
= (216 × 1221)
= (1221 × 216)
= 1221 × (200 + 10 + 6)
= (1221 × 200) + (1221 × 10) + (1221 × 6)
= 244200 + 12210 + 7326
= 263736
84
What is 394 times 113 ?
Discuss
Answer & Solution
Answer: Option B
Solution:
= 394 × 113
= 394 × (100 + 10 + 3)
= (394 × 100) + (394 × 10) + (394 × 3)
= 39400 + 3940 + 1182
= 44522
85
12345679 × 72 is equal to :
Discuss
Answer & Solution
Answer: Option B
Solution:
= 12345679 × 72
= 12345679 × (70 + 2)
= (12345679 × 70) + (12345679 × 2)
= 864197530 + 24691358)
= 888888888
86
(71 × 29 + 27 × 15 + 8 × 4) equals :
Discuss
Answer & Solution
Answer: Option A
Solution:
= (71 × 29 + 27 × 15 + 8 × 4)
= (80 - 9) × 29 + 405 + 32
= (80 × 29) - (9 × 29) + 437
= 2320 - 261 + 437
= 2757 - 261
= 2496
87
$$\frac{{{{\left( {489 + 375} \right)}^2} - {{\left( {489 - 375} \right)}^2}}}{{\left( {489 \times 375} \right)}} = ?$$
Discuss
Answer & Solution
Answer: Option D
Solution:
Given expression :
$$ = \frac{{{{\left( {a + b} \right)}^2} - {{\left( {a - b} \right)}^2}}}{{ab}}$$     (where a = 489, b = 375)
$$\eqalign{ & = \frac{{4ab}}{{ab}} \cr & = 4 \cr} $$
88
If all the numbers from 501 to 700 are written, what is the total number of times the digit 6 appears ?
Discuss
Answer & Solution
Answer: Option C
Solution:
Numbers from 501 to 599 which have 6 as digit are 506, 516, 526, 536, 546, 556, 560, 561, 562, 563, 564, 565, 566, 567. 568, 569, 576, 586 and 596, i.e., 6 occurs 20 times.
Number of times 6 occurs from 600 to 699 = 100 + 20 = 120
∴ Total number of times 6 occurs = 20 + 120 = 140
89
The number (248 - 1) is exactly divisible by two numbers between 60 and 70. The numbers are :
Discuss
Answer & Solution
Answer: Option A
Solution:
(248 - 1)
= [(26)8 - 1]
= (64)8 - 1
When n is even , (xn - an) is completely divisible by both (x - a) and (x + a)
∴ (648 - 18) is divisible by both (64 - 1) and (64 + 1)
⇒ (248 - 1) is divisible by both 63 and 65
90
When the square of any odd number, greater than 1, is divided by 8, it always leaves remainder :
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the number be N = 2x + 1
N2 = (2x + 1)2
    = 4x2 + 1 + 4x
    = 4x (x + 1) + 1
Clearly, 4x (x + 1) is always divisible by 8 since one of x and (x + 1) is even which when multiplied by 4 is always divisible by 8.
Hence, required remainder = 1