SSC GD Number System

Table of Contents

• Introduction to Number System for SSC GD
• Types of Numbers
  • Natural Numbers
  • Whole Numbers
  • Integers
  • Rational and Irrational Numbers
• Special Types of Numbers
  • Prime, Composite, Even, and Odd Numbers
• Core Concepts for SSC GD Number System Questions
  • Divisibility Rules
  • Place Value and Face Value
  • The Number Line

Introduction to Number System for SSC GD

The SSC GD number system is the most important topic in Math. It is the foundation for all other chapters. If you understand numbers well, you can solve many ssc gd number system questions easily.

We will learn about different types of numbers. We will also learn how they behave. This knowledge is key to scoring high in your exam. Make sure you practice these concepts daily. You can find many ssc gd number system questions pdf online for practice.

Types of Numbers

Natural Numbers

Natural numbers are the counting numbers. They are the numbers you use when you count things.

• They start from 1.
• They go on forever: 1, 2, 3, 4, 5, …
• We use the letter $N$ to show them.
• The smallest natural number is 1.

4 Solved Examples

Example 1: What is the sum of the first 5 natural numbers?

Solution:

1. The first 5 natural numbers are 1, 2, 3, 4, and 5.
2. We add them up: $1+2+3+4+5$.
3. The sum is 15.

Example 2: If $x$ is a natural number, and $x+3=7$, what is $x$?

Solution:

1. We want to find $x$. We move 3 to the other side of the equals sign.
2. $x=7-3$.
3. $x=4$. Since 4 is a counting number, it is a natural number.

Example 3: Is 0 a natural number?

Solution:

1. Natural numbers are counting numbers. They start at 1.
2. Zero (0) is not used for counting things (you don’t say “I have 0 apples”).
3. So, 0 is not a natural number.

Example 4: Find the product of the smallest and largest single-digit natural numbers.

Solution:

1. The smallest single-digit natural number is 1.
2. The largest single-digit natural number is 9.
3. We multiply them: $1\times 9=9$.

Whole Numbers

Whole numbers are natural numbers plus zero.

• They start from 0.
• They go on forever: 0, 1, 2, 3, 4, …
• We use the letter $W$ to show them.
• The smallest whole number is 0.

4 Solved Examples

Example 1: What is the difference between the smallest whole number and the smallest natural number?

Solution:

1. Smallest whole number is 0.
2. Smallest natural number is 1.
3. We find the difference: $1-0=1$.

Example 2: If $y$ is a whole number, and $y\times 5=0$, what is $y$?

Solution:

1. We need a number that, when multiplied by 5, gives 0.
2. The only number that does this is 0.
3. $y=0$. Since 0 is a whole number, this is correct.

Example 3: Are all natural numbers also whole numbers?

Solution:

1. Natural numbers are $1,2,3,...$.
2. Whole numbers are $0,1,2,3,...$.
3. Since every natural number is included in the set of whole numbers, the answer is Yes.

Example 4: Find the next whole number after 99.

Solution:

1. Whole numbers increase by 1 each time.
2. We add 1 to 99.
3. $99+1=100$.

Integers

Integers include all whole numbers and their negative partners.

• They include positive numbers (1, 2, 3…).
• They include negative numbers (-1, -2, -3…).
• They include zero (0).
• Integers do not include fractions or decimals (like 1.5 or $1/2$).

4 Solved Examples

Example 1: Calculate: $-5+12$.

Solution:

1. We start at -5 on the number line.
2. We move 12 steps to the right (because it is +12).
3. The result is $12-5=7$.

Example 2: Which is greater: $-10$ or $-2$?

Solution:

1. On the number line, numbers get bigger as you move right.
2. $-2$ is closer to 0 than $-10$.
3. Therefore, $-2$ is greater than $-10$.

Example 3: Find the value of $|-15|+|5|$. (The vertical bars mean Absolute Value, which is the distance from zero).

Solution:

1. The absolute value of $-15$ is 15 (distance is always positive).
2. The absolute value of 5 is 5.
3. We add them: $15+5=20$.

Example 4: If the temperature drops from $5^{\circ }C$ to $-8^{\circ }C$, what is the total drop in degrees?

Solution:

1. We calculate the distance between 5 and -8.
2. Distance from 5 to 0 is 5 degrees.
3. Distance from 0 to -8 is 8 degrees.
4. Total drop is $5+8=13$ degrees.

Rational and Irrational Numbers

This is a key area for SSC GD number system questions.

Rational Numbers

• A rational number can be written as a fraction $\frac{p}{q}$.
• Here, $p$ and $q$ must be integers.
• The bottom number $q$ cannot be 0.
• Examples: $1/2$, $4$ (which is $4/1$), $0.5$ (which is $1/2$).
• Decimals that stop (like 0.25) or repeat (like $0.333...$) are rational.

Irrational Numbers

• An irrational number cannot be written as a simple fraction.
• Their decimal form goes on forever and never repeats.
• Examples: $\sqrt{2}$, $\sqrt{3}$, and $\pi$ (Pi).

4 Solved Examples

Example 1: Is $0.75$ a rational or irrational number?

Solution:

1. $0.75$ is a decimal that stops (terminates).
2. We can write $0.75$ as the fraction $\frac{75}{100}$.
3. Since it can be written as $\frac{p}{q}$, it is a rational number.

Example 2: Find a rational number between 3 and 4.

Solution:

1. We can write 3 as $3/1$ and 4 as $4/1$.
2. To find a number between them easily, we can use a common denominator, like 10.
3. $3=30/10$ and $4=40/10$.
4. A number between them is $35/10$, or $3.5$.

Example 3: Identify the irrational number: $\sqrt{9},\sqrt{10},0.5$.

Solution:

1. $\sqrt{9}$ is 3 (Rational).
2. $0.5$ is $1/2$ (Rational).
3. $\sqrt{10}$ cannot be simplified to a whole number or a terminating decimal.
4. $\sqrt{10}$ is the irrational number.

Example 4: If $x=1/3$, is $x$ rational?

Solution:

1. The number $x$ is already in the form $\frac{p}{q}$, where $p=1$ and $q=3$.
2. $p$ and $q$ are integers, and $q$ is not zero.
3. Therefore, $x=1/3$ is a rational number.

Special Types of Numbers

Prime, Composite, Even, and Odd Numbers

Understanding these types is vital for solving ssc gd number system questions pdf problems quickly.

Even and Odd Numbers

• Even Numbers: Can be divided exactly by 2. They end in 0, 2, 4, 6, or 8. (Example: 10, 48, 102).
• Odd Numbers: Cannot be divided exactly by 2. They end in 1, 3, 5, 7, or 9. (Example: 7, 19, 55).

Prime and Composite Numbers

• Prime Numbers: Have exactly two factors (divisors): 1 and the number itself. (Example: 2, 3, 5, 7, 11).
  • Important: 2 is the only even prime number.
  • Important: 1 is neither prime nor composite.
• Composite Numbers: Have more than two factors. (Example: 4, 6, 8, 9, 10).

4 Solved Examples

Example 1: Find the sum of the first three prime numbers.

Solution:

1. The first three prime numbers are 2, 3, and 5.
2. We add them: $2+3+5$.
3. The sum is 10.

Example 2: If you multiply an odd number by an even number, is the result odd or even?

Solution:

1. Let’s pick an odd number (3) and an even number (4).
2. Multiply them: $3\times 4=12$.
3. 12 is an even number. (This rule always holds true).

Example 3: How many prime numbers are there between 10 and 20?

Solution:

1. List the numbers: 11, 12, 13, 14, 15, 16, 17, 18, 19.
2. Check for factors: 11 (Prime), 13 (Prime), 17 (Prime), 19 (Prime).
3. There are 4 prime numbers between 10 and 20.

Example 4: If $P$ is a prime number greater than 2, is $P+1$ even or odd?

Solution:

1. Any prime number greater than 2 must be odd (since 2 is the only even prime).
2. If $P$ is odd, then $P+1$ means Odd + 1.
3. Odd + 1 always results in an Even number. (Example: $5+1=6$).

Core Concepts for SSC GD Number System Questions

Divisibility Rules

These rules help you check if a number can be divided by another number without doing the long division. This saves huge time in your ssc gd number system mock test.

4 Solved Examples

Example 1: Is the number 789 divisible by 3?

Solution:

1. We use the rule for 3: Sum the digits.
2. $7+8+9=24$.
3. Since 24 is divisible by 3 ($24÷3=8$), the number 789 is divisible by 3.

Example 2: Find the smallest digit $X$ so that $45X2$ is divisible by 4.

Solution:

1. We use the rule for 4: The last two digits ($X2$) must be divisible by 4.
2. We try small numbers for $X$: If $X=0$, $02$ is not divisible by 4.
3. If $X=1$, $12$ is divisible by 4 ($12÷4=3$).
4. The smallest digit $X$ is 1.

Example 3: If $987X5$ is divisible by 9, find the value of $X$. (A common type of SSC GD number system problem).

Solution:

1. Rule for 9: The sum of digits must be divisible by 9.
2. Sum the known digits: $9+8+7+5=29$.
3. We need $29+X$ to be the next multiple of 9 (which is 36).
4. $29+X=36$. So, $X=36-29=7$.

Example 4: Check if 1331 is divisible by 11.

Solution:

1. Identify odd and even places (starting from the right):
   • Odd places: 1st digit (1) and 3rd digit (3). Sum = $1+3=4$.
   • Even places: 2nd digit (3) and 4th digit (1). Sum = $3+1=4$.
2. Find the difference: $4-4=0$.
3. Since the difference is 0, 1331 is divisible by 11.

Place Value and Face Value

This concept helps you understand the value of digits in a large number.

• Face Value: The actual value of the digit itself. The face value of 5 is always 5.
• Place Value: The value of the digit based on its position (ones, tens, hundreds, etc.).

4 Solved Examples

Example 1: In the number 5,678, what is the place value of 6?

Solution:

1. The digit 6 is in the hundreds place.
2. Place Value = Digit $\times$ Position Value.
3. Place Value of 6 is $6\times 100=600$.

Example 2: What is the face value of 9 in the number 9,123?

Solution:

1. Face value is the digit itself, no matter where it is placed.
2. The face value of 9 is 9.

Example 3: Find the difference between the place value and the face value of the digit 4 in the number 34,500.

Solution:

1. The digit 4 is in the thousands place.
2. Place Value of 4 is $4\times 1,000=4,000$.
3. Face Value of 4 is 4.
4. Difference is $4,000-4=3,996$.

Example 4: Write the number 7,000 + 50 + 2 in standard form.

Solution:

1. We look at the place values given: 7 thousands, 0 hundreds, 5 tens, 2 ones.
2. Combine the values: $7,000+50+2$.
3. The standard form is 7,052.

The Number Line

The number line is a straight line where every point represents a number.

• Zero (0) is the center point.
• Positive numbers are to the right of 0.
• Negative numbers are to the left of 0.
• Numbers increase as you move right.

4 Solved Examples

Example 1: Show the addition $3+(-5)$ on the number line.

Solution:

1. Start at 3.
2. Adding $-5$ means moving 5 steps to the left.
3. $3\to 2\to 1\to 0\to -1\to -2$.
4. The result is $-2$.

Example 2: Which integer is 4 units to the left of 1 on the number line?

Solution:

1. Start at 1.
2. Move 4 units left: $1-4$.
3. $1-4=-3$.

Example 3: How far apart are $-7$ and $2$ on the number line?

Solution:

1. Distance from $-7$ to 0 is 7 units.
2. Distance from 0 to 2 is 2 units.
3. Total distance is $7+2=9$ units.

Example 4: Mark the position of the rational number $1/2$ on the number line.

Solution:

1. $1/2$ is equal to $0.5$.
2. $0.5$ is greater than 0 but less than 1.
3. The position is exactly halfway between 0 and 1.

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Remember to practice these ssc gd number system questions regularly. Solving the ssc gd number system mock test papers will help you master these concepts.