# NUMBER SYSTEM

Digit: 0 to 9 are the digits.
Number: By using digits we write numbers.
Face Value: The real value of the digit.
Place Value: The value of the digit according to the place.
e.g.: In 2794, the face value of 7 is '7'and the place value is '700'.

Classification of Numbers
Odd Numbers
Numbers which are not divisible by 2
e.g.: 1, 3, 5, 7, .......

Even Numbers
Numbers which are divisible by 2
e.g.: 2, 4, 6, 8, .......

Natural Numbers
All counting numbers             e.g.: N = {1, 2, 3, ........}
Sum of first 'n' natural numbers is Sum of squares of first 'n' natural numbers is Sum of cubes of first 'n' natural numbers is Whole Numbers
0 and all natural numbers
e.g.: W = { 0, 1, 2, 3, ...}

Integers
Natural numbers, zero and negative of natural numbers
e.g.: I = { ........, -3, -2, -1, 0, +1, +2, +3, .......}

Rational Numbers
These are of the form of p/q, where q π 0
e.g.: etc

Irrational Numbers
Can't be written in p/q form, where q ≠ 0
e.g.: π  etc

Composite Numbers
Numbers having more than two factors

Prime Numbers
Numbers divisible by one and the number itself or numbers having only two factors.
e.g.: 2, 3, 5, 7, 11, 13, ...... etc
*  All prime numbers end with 1, 3, 7 or 9 except 2 and 5.
*  2 is the only even prime number.
*  '1' is neither a prime nor composite number. It is a unitary.
*  There are 25 prime numbers upto 100.

Twin prime numbers
The difference between two prime numbers is '2'.
e.g.: 3 - 5, 5 - 7, 11 - 13 etc

Co prime numbers
Numbers not having any common factors.
e.g.: 3, 5 and 8 are co primes to each other.

Some important Identities
1. (a + b)2 = a2 + b2 + 2ab
2. (a - b)2 = a2 + b2 - 2ab
3. (a + b)(a - b) = a2 - b2
4. (a + b)2 = a2 + b2 + 3a2b + 3ab2
5. (a - b)3 = a3 - b3 - 3a2b + 3ab2
6. a3 + b3 = (a + b)(a2 - ab + b2)
7. a3 - b3 = (a - b) (a2 + ab+ b2)
8. (a + b + c)2 = a+ b+ c2 + 2ab + 2bc + 2ac
9. a+ b+ c- 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ac)

e.g.: 1) 2.01        2) 2        3) 1           4) 1.93           5) None of these
Sol: It is based on the formula a3 + b3 = (a+b)(a2−ab+b2)
∴ 1.07 + 0.93 = 2, hence answer (2).
To solve the equations based on numbers, the number is written in algebraic form.
For example let the number be x.

The numerator of a fraction is written in the following form
Three-fourth of a number = Two-third of a number = Double of a number = 2x, Thrice of a number = 3x
20% of a number = 30% of 3/4 of one-third of a number = e.g. 1.  4/5  of  4/7  of  5/6  of  1218 = ?   (SBI 2008)
(A) 415        (B) 384          (C) 492        (D) 346         (E) None of these
sol: 2. One-seventh of a number is 51. What will be 64% of that number?    (SBI 2008)
(A) 248.12       (B) 228.48        (C) 238.24       (D) 198.36       (E) None of these
Sol: 3. If (16)3 is subtracted from the square of a number, the answer so obtained is 3825. What is the number ?   (SBI 2008)
(A) 69           (B) 59            (C) 89            (D) 79           (E) None of these
Sol: Let the number be x
x− 163= 3825 ∴ x = 89

4. If (92)2 is added to the square of a number, the answer so obtained is 10768. What is the number?     (SBI 2008)
(A) 46            (B) 2304                (C) 48                    (D) 2116              (E) None of these
Sol: Let the number be x
x+ 922= 3825   ∴ x = 48

5. If an amount of Rs. 97,836 is distributed equally amongst 31 children. How much amount would each child get?  (SBI 2008)
(A) Rs.3,756        (B) Rs.3,556       (C) Rs. 3,356       (D) Rs. 3,156       (E) None of these
Sol: hence answer (D).
Three consecutive odd numbers are x, (x+2) and (x+4), or (x-2), x and (x+2), where x is an odd number.
Similarly, three consecutive even numbers are x, (x+2) and (x+4) or (x-2), x and (x+2) where x is an even number
If a number 'a' is multiplied by itself for n times, the product is called n th power of
'a'. This is written as an.
In an, a is called base and n is called index or exponent or power.

Laws of Indices All simplification questions have to be solved based on BODMAS rule only.
B - Bracket
O - Of
D - Division
M - Multiplication
S - Subtraction
e.g. 1: What is 394 times 113? (SBI 2008)
(A) 44402         (B) 44632          (C) 44802        (D) 44522       (E) None of these
Sol:   394 × 113 = 44522,     hence answer (D)

2. What approximate value should come in place of the question mark (?) in the following question?  4780 ÷ 296 × (23)2 = ?
(A) 9870             (B) 6760            (C)7590           (D) 3430        (E) 8540
Sol: × 529 = 8542.63

3. When 40% of first number is added to the second number the second number becomes 1.2 times of itself. What is the ratio between the first and second numbers?
(A) 2:3              (B) 4:3               (C) 1:2             (D) 5:7           (E) None of these
Sol: Let the first and second number be x and y Posted Date : 07-02-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.