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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-4 section-6

Each section contains 100 MCQs on Number System .
31
The numbers 2272 and 875 are divided by a three-digit numbers N, giving the same remainder. The sum of the digits of N is :
Discuss
Answer & Solution
Answer: Option A
Solution:
Clearly, (2272 - 875) = 1397, is exactly divisible by N.
Now, 1397 = 11 × 127
∴ The required 3-digit number is 127, the sum of whose digits is 10
32
The remainder when (1523 + 2323) is divided by 19, is :
Discuss
Answer & Solution
Answer: Option A
Solution:
(xn + an) is divisible by (x + a) when n is odd
∴ (1523 + 2323) is divisible by (15 + 23)
⇒ (1523 + 2323) is divisible by 38 and hence by 19
⇒ On dividing (1523 + 2323) by 19, we get 0 as remainder.
33
Which one of the following numbers is divisible by 15 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Consider the number is 17325
Its unit digit is 5, so it is divisible by 5
Sum of its digits = (5 + 2 + 3 + 7 + 1) = 18, which is divisible by 3
So, the given number is divisible by 3
And since 5 and 3 are co-primes,
So the given number is divisible by (5 × 3), i.e., 15
34
How many numbers will be there between 300 and 500, where 4 comes only one time ?
Discuss
Answer & Solution
Answer: Option B
Solution:
From 300 to 399, we note that when '4' comes only one time = 19 such instances.
From 400 to 499, we note that when '4' comes only one time = 80 such instances.
So, total = (19 + 80) = 99 such instances.
35
A number when divided by three consecutive numbers 9, 11, 13 leaves the remainders 8, 9 and 8 respectively. If the order of divisors is reversed, the remainders will be :
Discuss
Answer & Solution
Answer: Option B
Solution:
Number System mcq solution image
z = 13 × 1 + 8 = 21
y = 11 × z + 9 = 11 × 21 + 9 = 240
x = 9 × y + 8 = 9 × 240 + 8 = 2168
Now, when order of divisor is reversed, we have :
Number System mcq solution image
∴ Respective remainders are 10, 1 and 6
36
The divisor is 25 times the quotient and 5 times the remainder. If the quotient is 16, then the dividend is :
Discuss
Answer & Solution
Answer: Option D
Solution:
Quotient = 16, Divisor = (25 × 16) = 400
5 × Remainder = Divisor
⇒ Remainder = $$\frac{400}{5}$$ = 80
Divided = (400 × 16) + 80 = 6480
37
The remainder when 784 is divided by 342 is :
Discuss
Answer & Solution
Answer: Option B
Solution:
784 = (73)28 = (343)28
Now, (xn - an) is divisible by (x - a) for all values of n
∴ [(343)28 - 1] is divisible by (343 - 1)
⇒ [(343)28 - 1] is divisible by 342
⇒ (784 - 1) is divisible by 342
⇒ On dividing 784 by 342, we get 1 as remainder.
38
The difference between the square of two consecutive odd integers is always divisible by :
Discuss
Answer & Solution
Answer: Option D
Solution:
Let the two consecutive odd integers be (2m + 1) and (2m + 3)
Then, (2m + 3)2 - (2m + 1)2
= [(2m + 3) + (2m + 1)] [(2m + 3) - (2m + 1)]
= (4m + 4) × 2
= 8m + 8
= 8(m + 1), which is always divisible by 8
39
The smallest number that must be added to 803642 in order to obtain a multiple of 11 is :
Discuss
Answer & Solution
Answer: Option C
Solution:
On dividing 803642 by 11, we get 4 as remainder.
Required number to be added = (11 - 4) = 7
40
A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232 etc. Any number of this form is exactly divisible by :
Discuss
Answer & Solution
Answer: Option D
Solution:
Clearly, 2525 is not divisible by any of the numbers 7, 11 and 13
The smallest 3-digit prime number is 101
Number System mcq solution image
Hence (D) is true.