How many practice questions are available for Number Patterns & Puzzles?

SparkEd Math offers 60+ practice questions for Number Patterns & Puzzles across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Number Patterns & Puzzles content free on SparkEd Math?

Yes! All Number Patterns & Puzzles content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Number Patterns & Puzzles differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Number Patterns & Puzzles problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Number Patterns & Puzzles content aligned with the CBSE syllabus?

Yes, all Number Patterns & Puzzles questions and lessons on SparkEd Math are fully aligned with the Central Board of Secondary Education (CBSE) syllabus for Class 8. The content follows the official curriculum structure and exam pattern.

Number Patterns & Puzzles — Class 8 CBSE (2025-26)

About Number Patterns & Puzzles — Class 8 CBSE

Explore divisibility rules, number patterns, and mathematical puzzles. This topic is part of the CBSE Class 8 mathematics syllabus (chapter: Chapter 5). On this page you can practice 62 questions across three difficulty levels — 20 easy, 20 medium, and 22 hard — each with a visual step-by-step solution, plus a timed 37-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

Number Patterns & Puzzles — solved examples for Class 8 CBSE

Example 1easy

A two-digit number has 'a' in the tens place and 'b' in the units place. Which of the following expressions correctly represents the value of this number?

A)a + b
B)ab
C)10a + b
D)10b + a

Step-by-step solution

In a two-digit number, the digit in the tens place represents its value multiplied by 10.
The digit in the units place represents its value multiplied by 1.
So, if 'a' is in the tens place and 'b' is in the units place, the number is (a × 10) + (b × 1).
$Number = 10a + b$

Answer: 10a + b

Example 2medium

A two-digit number has its tens digit as 'x' and units digit as 'y'. If the number formed by reversing its digits is added to the original number, the sum is always divisible by:

A)9
B)10
C)11
D)13

Step-by-step solution

The original two-digit number can be written as 10x + y.
The number formed by reversing its digits is 10y + x.
Adding these two numbers: (10x + y) + (10y + x) = 11x + 11y.
Factoring out 11, we get 11(x + y). This expression is always divisible by 11.

Answer: 11

Example 3hard

Consider a 3-digit number 'abc' where a, b, c are its digits. If this number is subtracted from the number formed by reversing its digits, 'cba', the absolute difference is always divisible by a particular set of numbers. Which of the following numbers will *always* divide |abc - cba| (assuming a ≠ c)?

A)5
B)7
C)9
D)13

Step-by-step solution

Let the 3-digit number be abc, which can be written as 100a + 10b + c.
The number formed by reversing its digits is cba, which can be written as 100c + 10b + a.
The difference is (100a + 10b + c) - (100c + 10b + a) = 100a + 10b + c - 100c - 10b - a = 99a - 99c = 99(a - c).
Since 99(a - c) = 9 × 11 × (a - c), the difference is always divisible by 9 and 11. Among the given options, 9 is the correct answer.
$|abc - cba| = |99(a - c)| = 99|a - c|$

Answer: 9

Practice questions on Number Patterns & Puzzles

Q1.easy
A three-digit number has 'x' in the hundreds place, 'y' in the tens place, and 'z' in the units place. If the digits are reversed, what will be the new number in its generalized form?
1. A)100x + 10y + z
2. B)100z + 10y + x
3. C)x + y + z
4. D)100z + 10x + y
Show answer
Answer: 100z + 10y + x
Hint: When digits are reversed, the units digit becomes the hundreds digit, the tens digit remains the tens digit, and the hundreds digit becomes the units digit.
Q2.easy
The sum of a two-digit number and the number obtained by reversing its digits is 132. If the units digit is 4, what is the tens digit of the original number?
1. A)7
2. B)8
3. C)9
4. D)6
Show answer
Answer: 8
Hint: Represent the two-digit number and its reverse using variables for the digits. Form an equation based on the given sum.
Q3.easy
In the addition problem below, A and B each represent a single digit. Find the value of B.
A 8
+ 2 B
-----
7 1
1. A)2
2. B)3
3. C)4
4. D)5
Show answer
Answer: 3
Hint: Start with the units column (8 + B). The sum ends in 1. What value of B would make this possible, considering a potential carry-over?
Q4.medium
A three-digit number is represented as 100A + 10B + C. If the number formed by reversing its digits, 100C + 10B + A, is subtracted from the original number, the absolute difference is always divisible by 99. What does the quotient of this division represent?
1. A)The sum of the first and last digit (A+C)
2. B)The difference between the first and last digit (|A-C|)
3. C)The middle digit (B)
4. D)The sum of all digits (A+B+C)
Show answer
Answer: The difference between the first and last digit (|A-C|)
Hint: Write both numbers in their general form and perform the subtraction. Observe the resulting expression.
Q5.medium
In the addition problem below, P, Q, R, and S represent distinct digits.
```
P Q
+ Q P
-----
R S 2
```
If Q = 7, what is the value of P?
1. A)3
2. B)5
3. C)7
4. D)9
Show answer
Answer: 5
Hint: Start by analyzing the units column, considering any possible carry-over. Then move to the tens column.
Q6.medium
In the multiplication problem below, A, B, and C are distinct non-zero digits.
```
A B
× C
-----
1 7 5
```
What is the value of A + B + C?
1. A)12
2. B)13
3. C)14
4. D)15
Show answer
Answer: 14
Hint: The product 175 is a result of multiplying a two-digit number (AB) by a single digit (C). Consider the prime factors of 175 to find possible values for C.
Q7.hard
In the following addition, where P, Q, R are distinct digits:
4 P
+ Q 6
-----
R 2
If P + 6 results in a sum with 2 in the units place and a carry-over, and 4 + Q + (carry-over) = R, find the value of P + Q + R.
1. A)15
2. B)17
3. C)18
4. D)19
Show answer
Answer: 17
Hint: Start by analyzing the units column (P + 6 = ...2). This will give you possible values for P and the carry-over. Then move to the tens column.
Q8.hard
A 5-digit number 72X3Y is divisible by 9. If the digit Y is twice the digit X, what is the smallest possible sum of X + Y?
1. A)3
2. B)6
3. C)9
4. D)12
Show answer
Answer: 3
Hint: Use the divisibility rule for 9: the sum of its digits must be divisible by 9. Also, consider the condition Y = 2X and that X, Y are single digits.
Q9.hard
A number 'N' leaves a remainder of 1 when divided by 3, and a remainder of 2 when divided by 5. Which of the following statements must be true about N?
1. A)N is always an even number.
2. B)N is always a multiple of 7.
3. C)N always ends with the digit 2 or 7.
4. D)N is always divisible by 15.
Show answer
Answer: N always ends with the digit 2 or 7.
Hint: List numbers that satisfy each condition separately. Then find the common numbers in the lists and observe their properties.

These are 9 of the 62 questions available for Number Patterns & Puzzles. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.