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NUMBER SYSTEM

A golden opportunity for Bank exams aspirants. Thousands of posts in SBI and other Banks. Out of five papers in the SBI clerk exam, Quantitative Aptitude plays major role. Arithmetic and Data Interpretation questions will be there in this paper. Arithmetic is the maths, which we use in our day-to-day life. As arithmetic chapters are there upto 10th class only all the aspirants inclusive of non-maths might have studied this. By understanding all the chapters thoroughly and with a lot of practice it is not difficult to solve all the questions of the paper. Also important is simplifications. Out of 40 questions in Q.A., 20 are simplification questions. Students need to mug up tables upto 20, squares of numbers upto 25 and cubes of numbers upto 15 to make simplifications easy. They also learn Speed Maths for solving simplification questions in seconds without pen. All the chapters in arithmetic have to be practiced thoroughly. Let us see all the chapters of arithmetic in detail.

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

Some points about prime numbers

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)(a− ab + b2)

7. a3 - b3 = (a − b) (a2 + ab + b2)

8. (a + b + c)2 = a+ b+ c2 + 2ab + 2bc + 2ac

9. a3+b3+c3− 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)(a− 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:    

         

                     hence answer (E)

 

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:  

  hence answer (E)

 

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  

        x2 − 163= 3825 --- x = 89

         hence answer (C).

 

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

        x2 + 922 = 3825    x = 48

          hence answer (C).

 

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

  A - Addition

  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: 4780/296 × 529 = 8542.63

   Approximately 8540, hence answer(E)

 

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 : 16-03-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.

 

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