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# Number System| Formula of Number System| Get Number System Questions Pdf with Solutions|

NUMBER SYSTEM - Part - I

Number system is a basic chapter of mathematics. So, you should have a clear concept about this chapter. Before knowing any formula of number system, we know about the type of numbers.

Roughly, 1 and 2 questions from number system are regularly asked in different competitive exams. So here, we also provide number system questions pdf with solutions.

# Number System| Formula of Number System| Get Number System Questions PDF with Solutions|

Number system is also important to solve other questions, as it is a basic concept.
In this chapter, different methods are used. So, maximum practice is the way to success.

## Check  the Number Tree:

### Different type of Numbers:

Natural Numbers : What is Natural Number?
Natural numbers are those, which can be counted. It is denoted by N, where
N = {1,2,3,...∞}

Even Numbers : What is Even Number?
Natural numbers which are divisible by 2, are called even numbers. It is denoted by E.
Where, E = {2,4,6,...∞}

Odd Numbers : What is Odd Numbers?
Odd number are those which are not divisible by 2.
In other words, the natural numbers which are not even numbers, are odd numbers.
O = {1,3,5...∞}

Whole Numbers : What is Whole Numbers?
When zero is included to the set of all natural numbers, then this set is called whole number.
It is denoted by W.
Where, W= {0,1,2,3,...∞}

Integers : What is Whole Numbers?
When natural numbers with negative sign are included, then it becomes set of integers.
It is denoted by 1 or Z.
I = {-∞,...-4, -3, -2, -1, 0, 1, 2, 3, 4...∞}

Prime Numbers : What is Whole Numbers?
The natural numbers which have no factors others than 1 and itself are called prime numbers.
Such as 2, 3, 5, 7, 11... etc.

Co-Prime Numbers : What is Whole Numbers?
Two numbers which have no common factor except 1, are called Co-Prime numbers.
Such as, 9 and 16, 4 and 17 and 80 and 81 etc.

Divisible Numbers/Composite Numbers : What is Whole Numbers?
The whole numbers which are divisible by numbers other than itself and 1 are called divisible numbers or we can say the numbers which are not prime numbers are composite or divisible numbers.
As, 4,6,9,15...

Rational Numbers : What is Rational Numbers?
The numbers which can be expressed in the form of p/q where p and q are integers and Co-Prime.
E.g. 4/5, 5/1, -1/2

Irrational Numbers : What is Irrational Numbers?
The numbers which can not be expressed in the form of p/q, are called irrational numbers. Such as
√2 = 1.414213562...

Real Number : What is Real Number?
Set of all rational numbers as well as irrational numbers is called Real Numbers. The square of all of them is positive.

Cyclic Numbers : What is Cyclic Number?
Cyclic numbers are those numbers of n digits which when multiplied by any other number up to n gives same digits in a different order.
They are in the same line.

As 142857
2 × 142857 = 285714
3 × 142857 = 428571

Perfect Numbers : What is Perfect Number?
If the sum of all divisors of a number N (except N) is equal to the number N itself then the number is called perfect number.
Such as,

6 = 1+2+3 = 6

28 = 1+2+4+7+14 = 28

Complex Numbers : What is Complex Number?
Z = a + ib, is called complex number, where a and b are real numbers, b = 0 and I = √(-1).
So, a+ib or 4+5i are complex numbers.

### Some Important Points on Numbers:

• 2 is only even prime number
• 1 is neither divisible nor prime number.
• Two consecutive odd prime numbers are prime pair.
• The place or position of a digit in a number is called it's place value. Such as, place value of 2 in 8273 is 200.
• The real value of any digit in a certain number is called its face value. As, face value of 2 in 9276 is 2.

### Important Number System Questions PDF with Solutions:

Q1.  How many whole numbers are there between 244 and 332 which are exactly divisible by 7?

... Ans:  d. 13

Q2. What is the value of 21 + 24 + 27 + ...... + 51?

Q3. In a two-digit number, the digit at the unit’s place is 1 less than twice the digit at the ten’s place. If the digits at unit’s and ten’s place are interchanged, the difference between the new and the original number is less than the original number by 20. The original number is?

Q4.  The denominator of a fraction is 3 more than its numerator. If the numerator is increased by 7 and the denominator is decreased by 2, we obtain 2. The sum of the numerator and denominator of the fraction is?

Q5. A girl was asked to multiply a number by 7/8, instead, she divided the number by 7/8 and got the result 15 more than the correct result. The sum of the digits of the number was?

Q6.  A farmer divides his herd of n cows among his four sons, so that the first son gets one-half that herd, the second son gets one-fourth, the third son gets one-fifth and the fourth son gets 7 cows. The value of n is?

Q7. 1/10 of a rod is coloured red, 1/20 orange, 1/30 yellow, 1/40 green, 1/50 blue, 1/60 black, and the rest are violet. If the length of the violent portion of the rod is 12.08 m, then the length of the rod is?

Q8. The numbers from 1 to 29 are written side by side as follows — 12345678910_ _272829, if this number is divided by 9, then what is the remainder?

Q9.  A number when divided by three consecutive numbers leave 9,11,13 leaves the remainders 8,9 and 8 respectively. if the order of divisors is reversed, the remainders will be?

Q10.  A number when divided by 195 leaves a remainder 47. if the same number is divided by 15, the remainder will be?

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I am wishing you all the best for your exam. Hope you will ace it. Good luck.

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