# SSC Exam Quantitative Study Material: A conceptual guide for Preparing Number System

Jun 21, 2016 17:23 IST

SSC is well known for the recruitment of Group ‘B’ and ‘C’ posts under the Ministries/Departments in The Government of India. SSC organizes various examinations like Combined Graduate Level examination, Combine Higher Secondary Level, Stenographer and for SI/DP/CAPF, etc., throughout the year having almost the same Exam Pattern. The Exam paper is comprised of basically 4 subjects.

a. General Intelligence & Reasoning

b. English language & Comprehension

c. Quantitative Aptitude

d. General knowledge

For more detail, click the link given below.

So, Jagranjosh.com has introduced a brief plan for revising topics at the time of examination. In this article, Number System which sometimes appear more difficult to understand in terms of  Human Relationship.

Introduction

Number is a symbol which represents quantity. There are three types of numbers:

1. Real Numbers: Real numbers are those numbers which can be easily indentify and quantify.

For example:  -10, -7.33, -1, 0, 1, 2, 5.77 etc.

2. Imaginary Numbers: Imaginary numbers are those numbers which we can just imagine but cannot physically perceive.

3. Complex Number: Combination of Real and Imaginary number is called complex numbers.

For example: (2+5i) , (1+3i) etc .

Here we will only discuss  about the real numbers .

Types of Real Numbers: there are two types of real numbers

Again Rational numbers are classified as:

(a) Integers: All rational numbers which do not have decimal or fractional parts are called integers.

For example:  -3, -1, 0 , 1 , 2 etc .

Integers are of two type whole numbers and natural numbers. All the non negative integers are whole numbers , for example 0 , 1 , 2 , 3 etc and all the whole numbers except 0 are natural numbers , for example 1, 2 , 3 etc

On the basis of origin:

1. Prime Numbers: All the natural numbers greater than 1 which are only divisible by 1 and the number itself are called prime numbers.

For example: 2, 3, 5, 7, 11, 13, 17 etc.

2. Composite Numbers: All the natural numbers greater than 1 which are divisible by at least one more number other than 1 and the number itself are called composite numbers.

For example: 4, 6, 8, 9, 10, 12 etc.

Note: 1 is neither a prime number nor a composite.

On basis of divisor:

1. Even Numbers: All the natural numbers which are multiple of 2 are called even numbers.

For example: 2, 4, 6, 8, 10 etc.

Odd Numbers: All the natural numbers which are not a multiple of 2 are called odd numbers. They are denoted as 2k ± 1, where k is a natural number.

For example: 3, 5, 7, 9, 11 etc.

To find whether a number is prime or not.

Step 1: Find the approximate square root of a number .

Step 2: Check if any prime number from 2 to that square root divides that number or not.

Step 3: If none of those prime number divides the number than the number must be prime number.

Example: Take 631 , the approx square root of 631 is 25 , now from  2 to 25 there are 2 , 3 ,5 , 7 , 11 , 13 , 17 , 19 and 23  prime number . Since none of these divides 631, so 631 must be a prime number.

Conversion of recurring decimal into fraction.

For Number

Divisibility Rule

Example

Note

2

If the last digit of a number is 0,2,4,6,8 , then  the number  is divisible by 2

742 is divisible by 2 but 743 is not.

3

If the sum of all the digits of a number is divisible by 3 , then the number is divisible by 3

1458 (sum of digits = 18) is divisible by 3, but 766 (sum of digits =19) is not divisible by 3.

766 (sum of digits =19) the remainder  when 19 is divided by 3 i.e. 1 will also be the remainder when 766 is divided by3

4

If the last two digits of a number are divisible by 4, then the number is also divisible by 4

6732 is divisible by 4 as 32 is divisible by 4, but 2142 is not divisible by 4.

Similarly the remainder when 42 is divided by 4 i.e 2 will also be the remainder when 2142 is divided by 4.

5

If the last digits of a number are 0 and 5, then the number is divisible by 5.

1465, 1320 are divisible by 5 as their last digit is 5 and 0 respectively.

6

If the number is divisible by 2 and 3 both, then it is also divisible by 6.

1452 is divisible by both 2 and 3 so it is divisible by 6 also, but 3362 is not divisible by 6 as it is not divisible by 3.

If the number is divisible by 4 and 6 both, then it is not necessary that it is divisible by 24 (6×4).

8

If the last three digit of a number are divisible by 8 or are 000, then the number is divisible by 8 .

43102 and 13000 are divisible by 8 since 102 is divisible by 8 and 13000 have 000 as last three digits, but 2148 is not as 148 is not divisible by 8

The remainder when 148 is divided by 8 i.e. 4 will also be the remainder of 2148 when divided by 8.

9

If the sum of all digits of a number is divisible by 9 , then the number is also divisible by 9.

25344 (sum of digits = 18) is divisible by 9 , 764 (sum of digits =17) is not.

The remainder when 17 is divided by 9 i.e 8 will also be the remainder when 764 is divided by 9.

11

If the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or is divisible by 11 , then the number is also divisible by 11.

9415956 is divisible by 11 as the difference of 9+1+9+6 =25 and 4+5+5 = 14 is 11, but 31872 is not as the sum of even places = 13 and sum of odd is 8 their difference is neither 0 nor 11.

1. When X is subtracted from the numbers 9, 15 and 27, the remainders are in continued proportion. What is the value of X?

(1) 8

(2) 6

(3) 4

(4) 5

(5) None of these

Ans: (5)

2. Sum of three consecutive numbers is 2262. What is 41% of the highest number?

(1) 301.5.1

(2) 303.14

(3) 308.73

(4) 306.35

(5) 309.55

Ans: (5)

3. Rachita enters a shop to buy ice-creams, cookies and pastries. She has to buy at least 9 units of each. She buys more cookies than ice-creams and more pastries than cookies. She picks up a total of 32 items. How many cookies does she buy?

(1) Either 12 or 13

(2) Either 11 or 12

(3) Either 10 or 11

(4) Either 9 or 11

(5) Either 9 or 10

Hence number of cookies is either 10 or 11.

Number of pastries is either 13 or 12.

Ans: (3)

4. The fare of a bus is Rs. x for the first five kilometres and Rs. 13/- per kilometre thereafter. If a passenger pays Rs. 2402/- for a journey of 187 kilometres, what is the value of X?

(1) Rs. 29

(2) Rs. 39

(3) Rs. 36

(4) Rs. 31

(5) None of these

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