Are these practice questions for Number Play based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 8 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Number Play free?

Yes. Every chapter includes free practice questions for Class 8 students to get you started.

What types of questions are included?

The practice set for Number Play mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Number Play for full coverage.

How many practice questions are there for Number Play?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Number Play Class 8 Mathematics Practice Questions with Answers

easy

Identify if the number 45678 is divisible by 3 using the divisibility rule. Explain the steps.

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easy

Examine if the number 135792 is divisible by 11.

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easy

Describe the algebraic form for any number that leaves a remainder of 4 when divided by 7. Provide three examples.

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easy

State the rule for checking divisibility by 10.

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easy

Calculate the digital root of the number 87654.

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easy

The sum of three consecutive odd numbers is 87. Calculate the numbers.

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easy

Evaluate the statement: "The product of any three consecutive integers is always divisible by 6." Justify your conclusion.

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easy

State the divisibility rule for 9.

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easy

What is the general rule about the parity (odd or even) of the sum or difference of any two integers? List the three possible cases.

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easy

Recall the general form of a number that leaves a remainder of 3 when divided by 5.

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easy

Calculate the smallest possible value of the digit 'x' if the number

7x3

is divisible by 3.

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easy

Define the term 'digital root' of a number.

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medium

Examine the statement: "If a number is divisible by 15, then it is also divisible by all the factors of 15." Justify your claim using reasoning.

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medium

List the conditions for the sum of two even numbers to be a multiple of 4.

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medium

A student claims, "If the sum of the digits of a number is divisible by 6, the number itself must be divisible by 6." Evaluate this claim, and provide a counterexample if it is false, explaining why it fails.

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medium

If the number

42a3b

is divisible by 12, solve for one possible pair of values for

a

and

b

.

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medium

Describe the divisibility rules for 2, 5, and 10. Explain the common principle behind these three rules using the general form of a number.

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medium

Apply the concept of remainders to write an algebraic expression for all numbers that leave a remainder of 4 when divided by 7.

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medium

Prove that the difference between any 3-digit number and the number formed by reversing its digits is always divisible by 99.

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medium

Justify why the sum of any four consecutive integers is never divisible by 4.

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medium

Analyze the statement: "The sum of any four consecutive integers is never divisible by 4." Demonstrate its truth using an algebraic proof.

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medium

Solve the following cryptarithm, where A, B, and C are distinct digits:

AB \times 6 = CCC

.

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medium

A student claims, "If a number is divisible by both 4 and 8, it must be divisible by 32." Critique this claim with a counterexample and a justification.

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medium

Explain why checking for divisibility by 4 and 6 is not sufficient to check for divisibility by 24. Provide a counterexample.

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medium

Explain why any number whose digits are all 9s (for example, 99 or 9999) must be divisible by 9.

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medium

Evaluate whether the expression

n^3 - n

is always divisible by 3 for any positive integer

n

. Justify your conclusion with a proof.

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medium

Examine if the number 5335 is divisible by 55. Demonstrate the steps used.

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medium

Justify why checking for divisibility by its co-prime factors (e.g., 4 and 9 for 36) is a valid test for a composite number, whereas checking with non-co-prime factors (e.g., 6 and 6 for 36) is not.

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medium

A number leaves a remainder of 5 when divided by 8. Another number leaves a remainder of 3 when divided by 8. Analyze the remainder when their sum is divided by 8.

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medium

Explain why a number that is divisible by 9 is also always divisible by 3.

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medium

Summarize the process to check if the number 5291 is divisible by 11.

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medium

A number is divisible by both 5 and 6. Analyze which of the following numbers it must also be divisible by: 15, 20, 30, 40.

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hard

Solve for the smallest number that leaves a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, and a remainder of 3 when divided by 4.

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hard

Formulate a single algebraic expression that represents all positive integers that leave a remainder of 1 when divided by 2, a remainder of 1 when divided by 3, and a remainder of 1 when divided by 4. Find the smallest such positive integer.

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hard

Explain in detail why the divisibility rule for 9 works. Use the general form of a 4-digit number, dcba, to illustrate your explanation.

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hard

Create a 4-digit number that is a multiple of 11, has a digital root of 5, and uses only two distinct digits. Justify your answer.

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hard

Solve the cryptarithm

AB \times 7 = CAB

. Demonstrate the step-by-step logical deduction to find the values of A, B, and C, where A, B, and C are distinct digits.

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hard

Design a cryptarithm of the form AB + BA = CDC. Find the values of the letters A, B, C, and D, where each letter represents a unique digit. Justify your reasoning.

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hard

Formulate a general rule to describe when the sum of two odd numbers is divisible by 4. Justify your rule.

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hard

The 6-digit number

15x1y2

is divisible by 44. Calculate all possible pairs of values for

x

and

y

.

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hard

Summarize the property: "If a number k divides two numbers M and N separately, then k must also divide their sum M+N and their difference M-N." Justify this property using algebra.

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Number PlayClass 8 Mathematics Practice Questions