CBSE Class 8 Maths Chapter 5: Number Play — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 5: Number Play from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Every odd integer can be written as the sum of two consecutive integers.
Reason (R): For odd 2n + 1, the consecutive integers n and n + 1 have that sum.
Reason (R): For odd 2n + 1, the consecutive integers n and n + 1 have that sum.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Their sum is 2n + 1.
2
Assertion (A): Some numbers have more than one representation as sums of consecutive positive integers.
Reason (R): A decimal number ending in 0 is divisible by 10.
Reason (R): A decimal number ending in 0 is divisible by 10.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the divisibility fact does not explain consecutive-sum representations.
3
Assertion (A): The sum of two consecutive integers is always odd.
Reason (R): Two consecutive integers are either both even or both odd.
Reason (R): Two consecutive integers are either both even or both odd.
Answer: (c)
A is true, but R is false. One is even and the other odd, so their sum is odd.
4
Assertion (A): Every power of 2 can be written as a sum of two or more consecutive positive integers.
Reason (R): Powers of 2 have no odd factor greater than 1.
Reason (R): Powers of 2 have no odd factor greater than 1.
Answer: (d)
A is false, but R is true. That factor property prevents such positive consecutive-sum representations.
5
Assertion (A): Divisibility by 2 is determined by the units digit.
Reason (R): A decimal number is even when its last digit is even.
Reason (R): A decimal number is even when its last digit is even.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. All higher place values are multiples of 10 and hence even.
6
Assertion (A): A number is divisible by 5 when its last digit is 0 or 5.
Reason (R): A number is divisible by 10 when its last digit is 0.
Reason (R): A number is divisible by 10 when its last digit is 0.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the test for 10 does not explain the full test for 5.
7
Assertion (A): Divisibility by 3 depends on the sum of all decimal digits.
Reason (R): Only the last digit matters for divisibility by 3.
Reason (R): Only the last digit matters for divisibility by 3.
Answer: (c)
A is true, but R is false. All decimal place values are congruent to 1 modulo 3.
8
Assertion (A): If a digit sum is divisible by 9, the number is never divisible by 9.
Reason (R): A number and its digit sum have the same remainder modulo 9.
Reason (R): A number and its digit sum have the same remainder modulo 9.
Answer: (d)
A is false, but R is true. The condition actually guarantees divisibility by 9.
9
Assertion (A): A decimal number is divisible by 11 when its alternating digit sum is a multiple of 11.
Reason (R): Powers of 10 alternate between remainders 1 and -1 modulo 11.
Reason (R): Powers of 10 alternate between remainders 1 and -1 modulo 11.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Place-value expansion produces the alternating-sum rule.
10
Assertion (A): The number 1232 is divisible by 11 because 1 - 2 + 3 - 2 = 0.
Reason (R): The number 121 is also divisible by 11.
Reason (R): The number 121 is also divisible by 11.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the second example does not explain the first calculation.
11
Assertion (A): A number divisible by 6 must be divisible by both 2 and 3.
Reason (R): Divisibility by 3 alone is sufficient for divisibility by 6.
Reason (R): Divisibility by 3 alone is sufficient for divisibility by 6.
Answer: (c)
A is true, but R is false. An even condition is also required.
12
Assertion (A): Every number divisible by 4 must end in 4.
Reason (R): Divisibility by 4 depends on whether the last two digits form a multiple of 4.
Reason (R): Divisibility by 4 depends on whether the last two digits form a multiple of 4.
Answer: (d)
A is false, but R is true. Numbers ending in 00, 12 or 28 may also be divisible by 4.
13
Assertion (A): A two-digit number with tens digit a and units digit b is 10a + b.
Reason (R): Decimal place value assigns ten times the tens digit plus the units digit.
Reason (R): Decimal place value assigns ten times the tens digit plus the units digit.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The algebraic form follows directly from notation.
14
Assertion (A): Reversing the digits of 10a + b gives 10b + a.
Reason (R): The difference of the two numbers is divisible by 9.
Reason (R): The difference of the two numbers is divisible by 9.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the divisibility consequence does not explain the reversed form.
15
Assertion (A): The sum of a two-digit number and its reversal is always divisible by 11.
Reason (R): It is always divisible by 9.
Reason (R): It is always divisible by 9.
Answer: (c)
A is true, but R is false. The sum is 11(a + b).
16
Assertion (A): The difference of a two-digit number and its reversal is never divisible by 9.
Reason (R): The difference is 9(a - b).
Reason (R): The difference is 9(a - b).
Answer: (d)
A is false, but R is true. It is always a multiple of 9.
17
Assertion (A): Algebra can prove digit tricks for every allowed digit choice.
Reason (R): Letters represent the digits while place value creates general expressions.
Reason (R): Letters represent the digits while place value creates general expressions.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Simplifying those expressions establishes the pattern generally.
18
Assertion (A): A counterexample is enough to disprove a claim about all natural numbers.
Reason (R): The number 26 disproves the claim that every number ending in 6 is a square.
Reason (R): The number 26 disproves the claim that every number ending in 6 is a square.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the example illustrates rather than defines the logical role.
19
Assertion (A): Testing examples can suggest but not prove a universal divisibility rule.
Reason (R): A finite list of successful examples proves the rule for all natural numbers.
Reason (R): A finite list of successful examples proves the rule for all natural numbers.
Answer: (c)
A is true, but R is false. A general proof is needed for an unlimited set of cases.
20
Assertion (A): A digit can take any integer value when it represents one decimal digit.
Reason (R): A decimal digit variable must be an integer from 0 to 9, with a leading digit nonzero.
Reason (R): A decimal digit variable must be an integer from 0 to 9, with a leading digit nonzero.
Answer: (d)
A is false, but R is true. Digit constraints are essential in number puzzles.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 5 Number Play?
This chapter covers all key topics from Number Play as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Number Play online for free?
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