Number System for SSC CGL, Download PDF of Questions & Formulas

Number System For SSC CGL Exam: As we know the number system is one of the most important topics in the SSC CGL Exam but many candidates don’t know the right approach to finding questions and related questions of the Number System for SSC CGL exam. Since it is a vast topic you must know how much you have to study for the SSC CGL exam. For that, you have to study smartly. The Number System for SSC CGL Exam consists of 2-3 questions at an easy to moderate level. In this blog, we have provided the basic concepts and questions related to the number system for SSC CGL exam along with the solution with explanations. You have to just download the PDF for free of number system basics and formulas and questions for SSC CGL exam.

Concept of Number System

Number System is a mathematical concept, it is the representation of numbers or writing the numbers by using some set of digits or other symbols.

A number is a numerical value or mathematical value that is used for counting or measuring objects.

Type of Numbers:

• Rational Numbers (Q):- A number that can be expressed as p/q is called a rational number. where p and q are integers and q ≠ 0 (Note: The denominator cannot be 0, but the numerator can be)
  • For example 1/2, 3/4, 7/2,3/5,7
• Irrational Numbers:- The numbers that cannot be expressed in the form of p/q are called irrational numbers. where p and q are integers and q ≠ 0
  • For example √2, π, √3, √99, √11
• Natural Numbers (N):- Natural numbers are a part of the number system which includes all the positive integers from 1 till infinity.
  • They are denoted by N.
  • For example N= {1, 2, 3, 4…..}
• Whole Numbers (W):- The whole numbers are the part of the number system in which it includes all the positive integers from 0 to infinity.
  • They are denoted by W.
  • For example W= {0, 1, 2, 3, 4…..}
• Integers (Z):- Integers include all whole numbers and their negative counterpart. They are denoted by I.
  • For example I= {…-4,-3,-2,-1, 0, 1, 2, 3, 4…..}
• Real Numbers (R): Any number such as positive integers, negative integers, fractional numbers or decimal numbers without imaginary numbers are called real numbers. Real numbers are denoted by R.
  • For example √ 2, √ 3,8/5,6/2,-0.65, π, 8

Properties of Number System

• Divisibility Rules: Understand the divisibility rules for numbers like 2, 3, 5, 9, 11, etc.
  • Example: 1. A number is divisible by 3 if the sum of its digits is divisible by 3.
  • 2. If the last two digits of a number are divisible by 4, then the number is divisible by 4.
• LCM and HCF (Highest Common Factor) and (Least Common Multiple) respectively:
  • LCM: The least common multiple (LCM) is defined as the smallest multiple that two or more numbers have in common.
  • HCF: HCF is used to find the highest common factors of any two or more given integers
• Sequence: A sequence is an arrangement of numbers in definite order according to some rule
• Remainder Theorem: The remainder is the value left after the division if the dividend is not completely divided by the divisor.

Number System Previous Year’s Questions for SSC CGL, Download Free PDF

Now it’s time to practice the questions on different types of questions on the Number System. Practicing questions is very important to boost preparation and score the highest in the exam. Here we have provided the number system questions for SSC CGL that have been asked in the previous years.

1. Find the sum of squares of the greatest value and smallest value of K in the number so that the number 45082K is divisible by 3.

(a) 68
(b) 64
(c) 100
(d) 50

2. Find the difference between squares of the greatest value and the smallest value of P if the number 5306P2 is divisible by 3.

(a) 60
(b) 68
(c) 36
(d) 6

3. What is the value of K such that the number 72K460K is divisible by 6?

(a) 4
(b) 9
(c) 7
(d) 8

4. Find the smallest value of a so that 42a48b (a > b) is divisible by 11.

(a) 4
(b) 5
(c) 0
(d) 9

5. Find the greatest value of b so that 30a68b (a > b) is divisible by 11.

(a) 4
(b) 9
(c) 3
(d) 6

6. Find the sum of all the possible values of (a + b) so that the number 4a067b is divisible by 11.

(a) 5
(b) 16
(c) 21
(d) 11

7. If the nine-digit number 7p5964q28 is completely divisible by 88, what is the value of (p² – q) for the largest value of q, where p and q are natural numbers?

(a) 72
(b) 9
(c) 0
(d) 81

8. If the 6-digit number 5x423y is divisible by 88, then what is the value of (5x – 8y)?

(a) 28
(b) 14
(c) 16
(d) 24

9. If the seven-digit number 94x29y6 is divisible by 72, then what is the value of (2x + 3y) for x ≠ y?

(a) 35
(b) 21
(c) 37
(d) 23

10. If the 8-digit number 888x53y4 is divisible by 72, then what is the value of (7x + 2y) for the maximum value of y?

(a) 19
(b) 15
(c) 23
(d) 27

Number System Test for SSC CGL

Now it’s time to practice under time constraints and required to check how much you understand the number system. This can be done by attempting the number system test. Click on the link provided below to attempt the Number System Test for SSC CGL.

SSC CGL Sample Questions on Number System

Question 1: If (50/3)% of a number is added to itself then the number obtained is 4956 then find the original number.

A) 8428

B) 4248

C) 4824

D) 4284

Question 2: The 3^rd and 7^th terms of an arithmetic progression is 143 and 399 respectively. Find its 15^th term.

A) 749

B) 865

C) 911

D) 857

Question 3: When a number is divided by 13 then it leaves a remainder 8 and when the quotient thus obtained, is divided by 5, it leaves a remainder 3. What will be the remainder if the number is divided by 65?

A) 28

B) 37

C) 47

D) 42

Question 4: By interchanging the digits of a two-digit number we get a number which is four times the original number minus 24. If the unit’s digit of the original number exceeds its ten’s digit by 7, then find the number.

A) 29

B) 18

C) 36

D) 58

Question 5: When a number is divided by 49 the remainder is 24. Find the remainder when the same number is divided by 7.

A) 6

B) 4

C) 3

D) 5

Question 6: (4²⁵ + 4²⁶ + 4²⁷ + 4²⁸) is divisible by which of the following?

A) 21

B) 19

C) 11

D) 17

Question 7: Find the remainder when (10⁵⁶ + 5) is divided by 9

A) 3

B) 6

C) 2

D) 4

Question 8: If six-digit number 5x2y6z is divisible by 7, 11 and 13, then the value of 2x + 3y – 4z is:

A) 19

B) 11

C) 21

D) 23

Question 9: How many natural numbers less than 500 is divisible by 4 or 6 but not 24?

A) 187

B) 240

C) 120

D) 167

Question 10: Find the value of (2² + 22²) – (1² + 11²).

A) 512

B) 424

C) 366

D) 242

ANSWER KEYS and SOLUTIONS:

Number System Solutions with Explanation

Solution 1: 2)

Let the original number be 6x

Since, (50/3)% = 1/6

New number = 6x + 6x × (1/6) = 7x

According to question,

7x = 4956

x = 708

Original number = 6x = 6 × 708 = 4248

Hence, option b.

Solution 2: 3)

Let the first term and common difference of the series be ‘a’ and ‘d’ respectively

According to the question,

{a + (7 – 1)d} – {a + (3 – 1)d} = 399 – 143

Or, 4d = 256

Or, d = 64

Therefore, a = 143 – 128 = 15

Therefore, 15^th term of the series = a + (15 – 1)d = 911

Hence, option c.

Solution 3: 3)

Let the number be ‘x’ and the quotient be ‘y’

So, x = 13y + 8………………..(1)

And, y = 5z + 3

Putting value of ‘y’ in (1) we get

x = 13 × (5y + 3) + 8

x = 65y + 39 + 8

x = 65y + 47

So, when x is divided by 65 we will get remainder 47

Hence, option c.

Solution 4: 1)

Let the original number be ‘10x + y’

According to question;

y – x = 7……………………………………….(1)

10y + x = 4 × (10x + y) – 24

10y + x = 40x + 4y – 24

39x – 6y = 24…………………………………(2)

From equation (1) and (2), we get

39x – 6(x + 7) = 24

39x – 6x – 42 = 24

33x = 66

x = 2

y = 9

So, the desired number is 29.

Hence, option a.

Solution 5: 3)

According to the question,

Number = 49x + 24

Required remainder = (49x + 24)/7 = 7x + (7 × 3) + 3

Hence, option c.

Solution 6: 4)

(4²⁵ + 4²⁶ + 4²⁷ + 4²⁸) = 4²⁵(1 + 4 + 4² + 4³) = 4²⁵ × 85 = 4²⁴ × 340

Therefore, it is divisible by 17 only

Hence, option d.

Solution 7: 2)

(10⁵⁶ + 5) can be written as (9 + 1)⁵⁶ + 5

Therefore, remainder = 1⁵⁶ + 5 = 6

Hence, option b.

Solution 8: 1)

LCM of 7, 11 and 13 = 1001

So, a six digit number will be divisible by 1001 if it is in the form of abcabc

So, comparing first three and last three digits of 5x2y6z, we get x = 6, y = 5 an z = 2

So, 2x + 3y – 4z = 2 × 6 + 3 × 5 – 4 × 2 = 19

Hence, option a.

Solution 9: 4)

Numbers less than 500 which are divisible by 4 = Quotient of (499/4) = 124

Number less than 500 which are divisible by 6 = Quotient of (499/6) = 83

Numbers less than 500 which are divisible by 24 = Quotient of (499/24) = 20

Therefore, required number of natural numbers = 124 + 83 – (2 × 20) = 167

Hence, option d.

Solution 10: 3)

Given, (2² + 22²) – (1² + 11²) = 4(1 + 11²) – (1 + 11²) = (1 + 11²)(4 – 1) = 122 × 3 = 366

Hence, option c.

Tips to Master the Number System

Below we have provided some tips that will help you master the number system for SSC CGL exam.

• Know the Basics: Understanding the basics must be the first step for any preparation of any topic. The basics and formulas for the number system are provided in the form of a PDF in this blog. So, download that PDF for free and start knowing the basics of the number system.
• Divisibility Rules: Knowing the divisibility rules will help you in problem-solving to solve problems easily and quickly. You must be aware of the divisibility rules for at least 2, 3, 4, 5, 9, 11, etc.
• Learn Shortcuts and Tricks: Some questions can be solved by using shortcuts and tricks which will be very helpful in saving your time and providing you the accurate answers too.
• Learn Square and Cube Table: Make sure that you have learned at least 30 squares and 20 cubes to find the answers quickly while solving the questions.
• Practice is Mandatory: At last, practice is very important, you can download the PDF provided in this blog for free as the best tool for practicing the number system questions.

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