Quick Short Notes from Exam Point of View :

• Number 1 is neither divisible nor prime.
• Two consecutive odd prime numbers are called prime pairs.
• All natural numbers are whole, rational, integer, and real.
• All whole numbers are rational, integer, and real.
• All rational numbers include the integers since every integer can be written as a fraction with a denominator of 1.
• All whole numbers, rational, and irrational numbers are real.
• Natural (including Prime, Composite, even, or odd) numbers and whole numbers are never negative.
• Any Prime Number can never be a Composite Number.
• Fractions are rational.
• All prime numbers except 2 are odd, and 2 is the only even prime number.
• Zero (0) is neither negative nor positive.
• If 'a' is any number, then if 'a' divides zero, the result will be zero. If 0 divides 'a', then the result will be infinite or not defined (0/a = 0, but a/0 = ∞, where 'a' is a real number).
• The sum and the product of two rational numbers are always rational.
• The product or the sum of a rational number and an irrational number is always an irrational number.
• Pi (π) is an irrational number.
• There can be an infinite number of rational or irrational numbers between two rational numbers or two irrational numbers.
• The decimal indication of an irrational number is infinite, as in √3 or √2.
• The square of an even number is even, and the square of an odd number is odd.

Are you preparing for Bank Clerk, Bank PO, Railways, SSC, or UPSC exams? If yes, you're in for a treat! We've (govtjobworld) compiled an exciting array of number system questions that frequently appear in these coveted exams. From brain-teasers to head-scratchers, these questions will test your mathematical prowess and help you ace the upcoming sarkari exams

QA: -9 is what type of number?

1.  Real number
2.  Integer
3.  Whole number
4.  Both (1) and (2)
5.  None of these

QB: Which of the following is a prime pair?

1.  (3, 5)
2.  (6, 8)
3.  (9, 11)
4.  (10, 12)

QC: Simplify the expression: 5/2 + 3/4

1.  7/6
2.  13/4
3.  9/8
4.  21/4

QD:  Determine the value of 'x' in the equation: 3x - 5 = 16

1.  5
2.  7
3.  9
4.  10

Q E: The square of any even number is an odd number.

1. True
2. False

QF: Find the sum of the first five prime numbers.

1.  15
2.  18
3.  28
4.  35

QG: Which number is neither Prime nor Composite?

1.  15
2.  41
3.  18
4.  1
5.  None of these

QH: On dividing a number by 5, we get 3 as a remainder. what will be the remainder when the square of this number is divided by 5?

1. 3
2. 4
3. 7
4. 2

QI : How many rational numbers are there between 2 and 3?

1.  1
2.  2
3.  5
4.  Infinite

QJ:  Find the greatest number of 5 digits which is exactly divisible by 137.

1. 99873
2. 99876
3. 99271
4. 99673

QK: When n is divided by 6, the remainder is 4. When 2n is divided by 6, the remainder is : 

1. 3
2. 6
3. 2
4. 0

QL: The difference of a number consisting of two digits from the number formed by inter changing the digits is always divisible by: 

1. 11
2. 10
3. 9
4. 6

QM: The least number, which must be added to 6709 to make it exactly divisible by 9, is 

1. 7
2. 5
3. 4
4. 2

Answers :

A.  4  (Both (1) and (2))

B.  1 (3,5)

C.  2 (13/4)

D.  2 (7)

E.  2(False)

F.  3(28)

G. 4(1)

H. 2 (remainder = remainder of square of 3 divided by 5 = 4)

Explanation : If we get 3 as remainder after dividing by 5 then lets say number is 5+3 = 8

 and square of 8 =64 and if we divide by 5 .. we will get 4 as remainder.

I. 4 (Infinite)

J. 1 (99873)

Explanation : The greatest number of 5 digits is 99999, on dividing it by 137 we get 126 as a remainder.

therefore the required number = 99999 - 126 = 99873

K. 3 (2)

L. 3(9)

M. 2(5)