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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-8 section-5

Each section contains 100 MCQs on Number System .
71
If 0 < x < 1, which of the following is greatest ?
Discuss
Answer & Solution
Answer: Option D
Solution:
0 < x < 1
⇒ x2 < x < 1 ..... (i)
⇒ $$\frac{1}{{{x^2}}}$$ > $$\frac{1}{x}$$ > 1 > x > x2 [using ...(i)]
Hence, $$\frac{1}{{{x^2}}}$$ is the greatest.
72
Which one of the following is a prime number ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\sqrt {437} > 20$$
All prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, 221 is divisible by 13 and 437 is divisible by 19.
373 is not divisible by any of the above prime numbers.
∴ 373 is prime.
73
If the sum of two numbers is 14 and their difference is 10. Find the product of these two numbers.
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the numbers be a and b
∴ a + b = 14.....(i)
a - b = 10..... (ii)
From equation (i) and (ii)
2a = 24
a = 12
and b = 2
Product = 12 × 2 = 24
⇒ ab = 24
74
7 is added to a certain number; the sum is multiplied by 5 ; the product is divided by 9 and 3 is subtracted from the quotient. Thus, if the remainder left is 12, what was the original number ?
Discuss
Answer & Solution
Answer: Option A
Solution:
Let the original number be x.
Then,
$$\frac{(x + 7) × 5}{9}$$   - 3 = 12
⇒ $$\frac{5x + 35}{9}$$  = 15
⇒ 5x + 35 = 135
⇒ 5x = 100
⇒ x = 20
75
If n is an integer, how many values of n will give an integral value of $$\left( {\frac{{16{n^2} + 7n + 6}}{n}} \right)$$   ?
Discuss
Answer & Solution
Answer: Option C
Solution:
$$\eqalign{ & = \left( {\frac{{16{n^2} + 7n + 6}}{n}} \right) \cr & = \left( {\frac{{16{n^2}}}{n} + \frac{{7n}}{n} + \frac{6}{n}} \right) \cr & = \left( {16n + 7 + \frac{6}{n}} \right) \cr} $$
For $$\left( {16n + 7 + \frac{6}{n}} \right)$$   to be an integer, we may have n = 1 or n = 2 or n = 3 or n = 6
Hence, 4 value of n will give the desired result.
76
What is 786 times 964 ?
Discuss
Answer & Solution
Answer: Option A
Solution:
786 × 964
= (800 − 14) × 964
= (800 × 964) − (14 × 964)
= (771200 − 13496)
= 757704
77
Let x be the product of two numbers 3, 659, 893, 456, 789, 325, 678 and 342, 973, 489, 379, 256. The number of digits in x is :
Discuss
Answer & Solution
Answer: Option B
Solution:
Sum of digits in the two numbers = 19 + 15 = 34
So, the product will have 33 or 34 digits
Since 36 × 34 = 1224 (i.e., product has 2 + 2 = 4 digits)
So, the number of digits in x is 34
78
8899 - 6644 - 3322 = ? - 1122
Discuss
Answer & Solution
Answer: Option A
Solution:
8899 - 6644 - 3322 = x - 1122
⇒ 2255 - 3322 + 1122 = x
⇒ x = 3377 - 3322
⇒ x = 55
79
76n - 66n, where n is an integer > 0, is divisible by :
Discuss
Answer & Solution
Answer: Option D
Solution:
When n is even, (xn - an) is divisible by both (x - a) as well as (x + a).
Now,
(76n - 66n)
= [(73)2n - (63)2n]
= [(343)2n - (216)2n]
∴ (76n - 66n) is divisible by both (7 - 6) and (7 + 6)
(76n - 66n) is divisible by 13
And, [(343)2n - (216)2n] is divisible by both (343 - 216) and (343 + 216)
⇒ (76n - 66n) is divisible by both 127 and 559
80
What minimum value should be assigned to *, so that 2361*48 is exactly divisible by 9 ?
Discuss
Answer & Solution
Answer: Option B
Solution:
2361*48 will be divisible by 9 if the sum of the digits of the given number is divisible by 9
2 + 3 + 6 + 1 + * + 4 + 8 i.e., (24 + *) is divisible by 9
Clearly, * = 3 because 27 is divisible by 9