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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-2 section-6

Each section contains 100 MCQs on Number System .
11
(46)2 - (?)2 = 4398 - 3066
Discuss
Answer & Solution
Answer: Option B
Solution:
Let (46)2 - x2 = 4398 - 3066
Then, (46)2 - x2 = 1332
⇒ x2 = (46)2 - 1332
∴ x2 = (50 - 4)2 - 1332
x2 = (50)2 + 42 - 2 × 50 × 4 - 1332
x2 = 2500 + 16 - 400 - 1332
x2 = 2516 - 1732
x2 = 784
x = 28
12
Given n = 1 + x and x is the product of four consecutive integers. Then which of the following us true ?
I. n is an odd integer.
II. n is prime.
III. n is a perfect square
Discuss
Answer & Solution
Answer: Option D
Solution:
Out of four consecutive integers two are even and therefore, their product is even and on adding 1 to it, we get an odd integer. So, n is odd. Some possible values of n are as under :
n = 1 + (1 × 2 × 3 × 4) = (1 + 24) = 25 = 52
n = 1 + (2 × 3 × 4 × 5) = (1 + 120) = 121 = 112
n = 1 + (3 × 4 × 5 × 6) = (1 + 360) = 361 = 192
n = 1 + (4 × 5 × 6 × 7) = (1 + 840) = 841 = 292
Ans so on.....
Hence, n is odd and a perfect square.
13
A boy multiplies 987 by a certain number and obtains 559981 as his answer. If in the answer both 9's are wrong but the other digits are correct, then the correct answer will be :
Discuss
Answer & Solution
Answer: Option C
Solution:
Number System mcq solution image
Clearly, 7261 must be replaced by 2961,
which is possible if 6648 is replaced by 6218,
which in turn is possible if 5599 is replaced by 5556.
Thus, the correct number is 555681
14
The product of any three consecutive natural numbers is always divisible by :
Discuss
Answer & Solution
Answer: Option B
Solution:
Let the required product be n (n + 1) (n + 2)
Then,
n = 1 ⇒ n (n + 1) (n + 2) = (1 × 2 × 3) = 6
n = 2 ⇒ n (n + 1) (n + 2) = (2 × 3 × 4) = 24
n = 3 ⇒ n (n + 1) (n + 2) = (3 × 4 × 5) = 60
So, each such product is divisible by 6
15
If (6767 + 67) is divided by 68, the remainder is :
Discuss
Answer & Solution
Answer: Option C
Solution:
(xn + an) is divisible by (x + a) when n is odd
∴ (6767 + 167) is divisible by (67 + 1)
⇒ (6767 + 1) is divisible by 68
⇒ On dividing (6767 + 67) by 68, we get (67 - 1) = 66 as remainder.
16
If 11,109,999 is divided by 1111, then what is the remainder ?
Discuss
Answer & Solution
Answer: Option C
Solution:
On dividing 11109999 by 1111, we get 9999
So, the required remainder is 1110
Number System mcq solution image
17
How many 3-digit numbers are there in between 100 and 300, having first and the last digit as 2 ?
Discuss
Answer & Solution
Answer: Option B
Solution:
Such numbers are 202, 212, 222, 232, 242, 252, 262, 272, 282, 292.
There are 10 such numbers.
18
The unit's digit in the product 274 × 318 × 577 × 313 is :
Discuss
Answer & Solution
Answer: Option A
Solution:
Unit digit in the given product = Unit digit of (4 × 8 × 7 × 3), which is 2
19
Which one of the following is the common factor of (4743 + 4343) and (4747 + 4347) = ?
Discuss
Answer & Solution
Answer: Option B
Solution:
When n is odd, (xn + an) is always divisible by (x + a).
∴ Each one of (4743 + 4343) and (4747 + 4347) is divisible by (47 + 43)
20
If a number 774958A96B is divisible by 8 and 9, the respective values of A and B will be :
Discuss
Answer & Solution
Answer: Option C
Solution:
Since 774958A96B is divisible by 8, so the number 96B must be divisible by 8.
So, B = 0, as 960 is divisible by 8.
Now, 774958A960 is divisible by 9.
So, (55 + A) must be divisible by 9.
This happens when A = 8
Hence, A = 8 and B = 0