ARITHMETIC REASONING FOR RRB JE GUIDE BY CIVILENGGFORALL FREE DOWNLOAD PDF

Number System and HCF, LCF
Simplification
Ratio & Proportion, Partnership
Average, Problem on Ages
Percentage
Profit and Loss
Time and Distance
Mixture and Alligations
Time and Work
Interest
Mensuration
Data Interpretation

NUMBER SYSTEM

The ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits, which can represent any number.

Natural Numbers: These are the numbers (1, 2, 3, etc.) that are used for counting.
Even numbers: Natural numbers which are divisible by 2 are even numbers.
Odd numbers: Natural numbers which are not divisible by 2 are odd numbers.
Prime Numbers: Natural numbers which have exactly two factors, i.e., 1 and the number itself are called prime numbers. The lowest prime number is 2. 2 is also the only even prime number.
Whole Numbers: The natural numbers along with zero (0), form the system of whole numbers.
Integers: The number system consisting of natural numbers, their negative and zero is called integers. Real Numbers: All numbers that can be represented on the number line are called real numbers.
Real numbers = Rational numbers + Irrational numbers.
Rational numbers: Any number that can be put in the form of p q , where p and q are integers and q is not equal to 0, is called a rational number. It is denoted by Q. Zero (0) is also a rational number.
Fraction: A fraction is a quantity which expresses a part of the whole. Fraction = Numerator/Denominator

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DECIMAL EXPANSION

The decimal expansion of a rational number is either terminating or non-terminating recurring. Moreover, a number whose decimal expansion is terminating or nonterminating recurring is rational.
The decimal expansion of an irrational number is non-terminating non-recurring. Moreover, a number whose decimal expansion is non-terminating non-recurring is irrational.

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FACTORS

A number may be made by multiplying two or more other numbers together. The numbers that are multiplied together are called factors of the final number. Factors of 12 = 1, 2, 3, 4, 6, and 12. All the numbers have a factor of one.

Common factor: A common factor of two or more given numbers is a number which divides each given number completely. Common factor of 12 and 18 are 1, 2, 3, 6.

Co-prime numbers: Two or more numbers that do not have a common factor are known as co-prime or relatively prime. For example: 4 and 15 are Co-prime numbers.

Highest common factor: The highest common factor (H.C.F.) of two or more numbers is the greatest number which divides each of them exactly. It is also known as greatest common divisor (G.C.D.). H.C.F. can be calculated by: (i) Prime factorisation method (ii) Division method

Multiples: Multiples of a number are all those numbers which can be divided completely by the given number. For example, Multiples of 5 are 5, 10, 15, 20 etc.

Common multiples: Common multiples of two or more numbers are the numbers which can be exactly divided by each of the given number. For example, Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24 etc. and Multiples of 4 are 4, 8, 12, 16, 20, 24, 28 etc. Hence, Common multiples of 3 and 4 are 12, 24 etc.

Least common multiple: The least common multiple (L.C.M.) of two or more numbers is the smallest number which is exactly divisible by each of them. L.C.M. can be calculated by: (i) Prime factorisation method (ii) Division method

POINTS TO REMEMBER

The greatest number that will exactly divide x, y, z = HCF of x, y and z.
The greatest number that will divide x, y and z leaving remainders a, b and c respectively = HCF of (x – a), (y – b) and (z – c).
The least number which is exactly divisible by x, y and z = LCM of x, y and z.
The least number which when divided by x, y and z leaves the remainder a, b and c respectively= LCM of(x, y and z)– R where R = (x – a) = (y – b) = (z – c)
The least number which when divided by x, y and z leaves the same remainder r in each case = LCM of (x, y and z) + r
The greatest number that will divide x, y and z leaving the same remainder in each case = HCF of (x – y), (y – z) and (z – x).

ABOVE THEORY IS THE BRIEF SAMPLE OF VARIOUS TOPICS EXPLANATION TAKEN FROM THIS BOOK

ARITHMETIC REASONING FOR RRB JE GUIDE BY CIVILENGGFORALL PDF

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