Day 1 : Arithmetic and Reasoning Practice Questions

Day 1 – Number System & Number Series Challenge

Welcome to Day 1 of the 100 Days Arithmetic & Reasoning Skills Challenge.

Today, we are starting with two important topics that form the foundation for many competitive examinations:

• 🧮 Arithmetic: Number System

• 🧠 Reasoning: Number Series

These topics are useful for examinations such as Banking, SSC, Railways, Government Jobs, Police Recruitment, Insurance and other competitive examinations.

The goal of Day 1 is not just to solve questions, but to understand the basic concepts and improve your calculation speed.

Day 1 Challenge Overview

Part 1: Number System – Learn the Basics

The Number System is one of the fundamental topics in arithmetic. It deals with different types of numbers and their properties.

Before solving competitive-exam questions, you should understand the basic types of numbers.

Types of Numbers

1. Natural Numbers

Natural numbers are the numbers used for counting.

Examples:
1, 2, 3, 4, 5, 6, 7, …

The smallest natural number is 1.

2. Whole Numbers

Whole numbers include zero along with natural numbers.

Examples:
0, 1, 2, 3, 4, 5, …

The smallest whole number is 0.

3. Integers

Integers include positive numbers, negative numbers and zero.

Examples:
…, -3, -2, -1, 0, 1, 2, 3, …

4. Even Numbers

Numbers that are exactly divisible by 2 are called even numbers.

Examples:
2, 4, 6, 8, 10, 12, …

5. Odd Numbers

Numbers that are not exactly divisible by 2 are called odd numbers.

Examples:
1, 3, 5, 7, 9, 11, …

6. Prime Numbers

A prime number has exactly two factors: 1 and itself.

Examples:
2, 3, 5, 7, 11, 13, 17, 19, …

Remember:

2 is the smallest prime number and the only even prime number.

7. Composite Numbers

A composite number has more than two factors.

Examples:
4, 6, 8, 9, 10, 12, …

Place Value and Face Value

Understanding place value and face value is important for solving Number System questions.

Consider the number:

57,843

The digit 7 is in the thousands place.

Therefore:

Place Value of 7 = 7 × 1,000 = 7,000

But the face value of 7 is simply:

Face Value = 7

Easy Trick

Face Value = The digit itself

Place Value = Digit × Position Value

Divisibility by 8

A number is divisible by 8 if its last three digits are divisible by 8.

Example

Consider:

1,256

The last three digits are 256.

Since:

256 ÷ 8 = 32

Therefore, 1,256 is divisible by 8.

This shortcut is very useful in competitive examinations.

Number System – Solved Examples

Example 1

Find the place value of 5 in 45,672.

The digit 5 is in the thousands place.

Therefore:

5 × 1,000 = 5,000

Answer: 5,000

Example 2

Is 4,328 divisible by 8?

Consider the last three digits:

328

Now:

328 ÷ 8 = 41

Therefore, 4,328 is divisible by 8.

Answer: Yes

Example 3

Which is the smallest natural number?

Natural numbers start from 1.

Therefore:

Answer: 1

Part 2: Number Series – Learn the Basics

A number series is a sequence of numbers arranged according to a particular pattern or rule.

Your task is to identify the pattern and find the missing or next number.

Example

2, 4, 6, 8, ___

The difference between consecutive numbers is:

+2, +2, +2

Therefore:

8 + 2 = 10

Answer: 10

Common Number Series Patterns

When solving a number series, check these patterns first:

Pattern 1: Addition

Example:

5, 10, 15, 20, ___

Pattern:

+5, +5, +5

Answer:

25

Pattern 2: Subtraction

Example:

100, 90, 80, 70, ___

Pattern:

-10, -10, -10

Answer:

60

Pattern 3: Multiplication

Example:

2, 4, 8, 16, ___

Pattern:

×2, ×2, ×2

Answer:

32

Pattern 4: Division

Example:

64, 32, 16, 8, ___

Pattern:

÷2, ÷2, ÷2

Answer:

4

Pattern 5: Increasing Difference

Example:

2, 5, 9, 14, 20, ___

Differences:

+3, +4, +5, +6

Next difference = +7

Therefore:

20 + 7 = 27

Number Series Solved Examples

Example 1

Find the next number:

3, 6, 12, 24, ___

Pattern:

3 × 2 = 6
6 × 2 = 12
12 × 2 = 24

Therefore:

24 × 2 = 48

Answer: 48

Example 2

Find the next number:

100, 90, 81, 73, ___

Look at the differences:

100 − 10 = 90

90 − 9 = 81

81 − 8 = 73

The subtraction is decreasing by 1 each time:

−10, −9, −8

Therefore, next:

73 − 7 = 66

Answer: 66

Example 3

Find the next number:

5, 10, 20, 40, ___

Each number is multiplied by 2.

40 × 2 = 80

Answer: 80

Day 1 – Practice Challenge

🧮 Arithmetic – Number System

Question 1

What is the place value of 7 in 57,843?

A) 7
B) 70
C) 700
D) 7,000

Question 2

Find the smallest 4-digit number divisible by 8.

A) 1,000
B) 1,004
C) 1,008
D) 1,012

Question 3

What is the difference between the face value and place value of 6 in 46,281?

A) 5,994
B) 5,994
C) 6,000
D) 5,900

Question 4

Find the next number:

125, 250, 375, ___

A) 400
B) 450
C) 500
D) 525

Question 5

What is the smallest natural number?

A) 0
B) 1
C) 2
D) -1

Question 6

Which of the following is a prime number?

A) 21
B) 27
C) 29
D) 33

Question 7

Which of the following is an even number?

A) 37
B) 41
C) 53
D) 64

Question 8

Which of the following is divisible by 8?

A) 1,234
B) 1,248
C) 1,253
D) 1,267

Question 9

What is the face value of 8 in 38,452?

A) 8
B) 80
C) 800
D) 8,000

Question 10

Which is the smallest whole number?

A) 0
B) 1
C) -1
D) 2

🧠 Reasoning – Number Series

Question 11

Find the next number:

2, 4, 8, 16, ___

A) 24
B) 28
C) 32
D) 36

Question 12

Find the missing number:

5, 10, 20, 40, ___

A) 50
B) 60
C) 70
D) 80

Question 13

Find the odd number:

12, 18, 24, 31, 36

A) 12
B) 18
C) 24
D) 31

Question 14

Find the next number:

3, 6, 12, 24, ___

A) 36
B) 42
C) 48
D) 54

Question 15

Complete the series:

100, 90, 81, 73, ___

A) 64
B) 65
C) 66
D) 67

Question 16

Find the next number:

10, 20, 30, 40, ___

A) 45
B) 50
C) 55
D) 60

Question 17

Find the missing number:

4, 8, 16, 32, ___

A) 48
B) 56
C) 64
D) 72

Question 18

Find the next number:

50, 45, 40, 35, ___

A) 25
B) 30
C) 32
D) 33

Question 19

Find the next number:

1, 4, 9, 16, ___

A) 20
B) 24
C) 25
D) 27

Question 20

Find the next number:

2, 5, 10, 17, 26, ___

A) 35
B) 36
C) 37
D) 38

Day 1 Answer Key

Note: In Question 3, the digit 6 in 46,281 is in the thousands place. Its place value is 6,000 and face value is 6. Therefore, the difference is 5,994. The options should ideally contain only one 5,994 option.

Detailed Explanations

Question 1 – Answer: 7,000

Number = 57,843

The digit 7 is in the thousands place.

Therefore:

7 × 1,000 = 7,000

Question 2 – Answer: 1,008

The smallest 4-digit number is 1,000.

1,000 is not divisible by 8.

The next multiples are:

1,000 ÷ 8 → not exact
1,008 ÷ 8 = 126

Therefore:

Answer = 1,008

Question 3 – Answer: 5,994

Number = 46,281

The place value of 6 is:

6,000

Face value:

6

Difference:

6,000 − 6 = 5,994

Therefore:

Answer = 5,994

Question 4 – Answer: 500

Series:

125, 250, 375, ___

Difference:

250 − 125 = 125

375 − 250 = 125

Therefore:

375 + 125 = 500

Question 5 – Answer: 1

Natural numbers start from:

1, 2, 3, 4, 5…

Therefore, the smallest natural number is 1.

Question 6 – Answer: 29

29 has only two factors:

1 and 29

Therefore, 29 is a prime number.

Question 7 – Answer: 64

An even number is exactly divisible by 2.

64 ÷ 2 = 32

Therefore, 64 is even.

Question 8 – Answer: 1,248

Check the last three digits:

248 ÷ 8 = 31

Therefore, 1,248 is divisible by 8.

Question 9 – Answer: 8

Face value means the digit itself.

Therefore, the face value of 8 is:

8

Question 10 – Answer: 0

Whole numbers start from zero:

0, 1, 2, 3, 4…

Therefore:

Smallest whole number = 0

Question 11 – Answer: 32

2 × 2 = 4
4 × 2 = 8
8 × 2 = 16
16 × 2 = 32

Question 12 – Answer: 80

5 × 2 = 10
10 × 2 = 20
20 × 2 = 40
40 × 2 = 80

Question 13 – Answer: 31

12, 18, 24 and 36 are even numbers.

31 is an odd number.

Therefore:

Answer = 31

Question 14 – Answer: 48

3 × 2 = 6
6 × 2 = 12
12 × 2 = 24
24 × 2 = 48

Question 15 – Answer: 66

Series:

100, 90, 81, 73, ___

Differences:

100 − 10 = 90
90 − 9 = 81
81 − 8 = 73

Next subtraction = 7

73 − 7 = 66

Question 16 – Answer: 50

10, 20, 30, 40, ___

The difference is +10.

40 + 10 = 50

Question 17 – Answer: 64

4 × 2 = 8
8 × 2 = 16
16 × 2 = 32
32 × 2 = 64

Question 18 – Answer: 30

50 − 5 = 45
45 − 5 = 40
40 − 5 = 35
35 − 5 = 30

Question 19 – Answer: 25

These are square numbers:

1² = 1
2² = 4
3² = 9
4² = 16
5² = 25

Therefore, the answer is 25.

Question 20 – Answer: 37

Series:

2, 5, 10, 17, 26, ___

Look at the differences:

5 − 2 = 3
10 − 5 = 5
17 − 10 = 7
26 − 17 = 9

The differences are:

+3, +5, +7, +9

The next difference is +11.

Therefore:

26 + 11 = 37

⚡ Day 1 Speed Challenge

Now try these questions without looking at the explanations.

Challenge 1

What is the smallest 3-digit number divisible by 5?

Challenge 2

Find the next number:

7, 14, 28, 56, ___

Challenge 3

What is the place value of 4 in 64,321?

Challenge 4

Find the next number:

2, 6, 12, 20, 30, ___

Challenge 5

Which is the smallest prime number?

Speed Challenge Answers

Quick Explanation

Challenge 1: The smallest 3-digit number is 100, and 100 is divisible by 5.

Challenge 2: Each number is multiplied by 2. 56 × 2 = 112.

Challenge 3: 4 is in the thousands place. Therefore, its place value is 4,000.

Challenge 4: Differences are +4, +6, +8, +10. Next difference is +12. Therefore, 30 + 12 = 42.

Challenge 5: 2 has exactly two factors: 1 and 2. Therefore, 2 is the smallest prime number.

🎯 Day 1 Learning Checklist

Before moving to Day 2, make sure you can:

• Understand natural, whole and integer numbers

• Identify even and odd numbers

• Identify prime and composite numbers

• Find face value

• Find place value

• Apply the divisibility rule of 8

• Identify simple number-series patterns

• Recognize addition and subtraction series

• Recognize multiplication series

• Identify square-number patterns

• Solve basic number-series questions quickly

🏆 Day 1 Target

Questions: 20
Suggested Time: 15 minutes
Target Accuracy: 80% or above

If you score:

Remember

Speed + Accuracy + Consistent Practice = Competitive Exam Success

Complete Day 1, note down the questions you got wrong, revise those concepts, and then move to Day 2 

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