NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - True or False Questions
Question 85

Question. 85

All numbers which are divisible by 4 may not be divisible by 8.

Answer:

true

Detailed Answer with Explanation:

Idea: A number is divisible by 4 if it can be written as \(4 \times k\) (no remainder).

But to be divisible by 8, it must be \(8 \times m\) (no remainder).

Counterexample: Take \(12\).

Check with 4: \(12 \div 4 = 3\) (remainder \(0\)). So 12 is divisible by 4.

Check with 8: \(12 \div 8 = 1\) (remainder \(4\)). So 12 is not divisible by 8.

Conclusion: There are numbers (like \(12\)) that are divisible by 4 but not by 8. Therefore, the statement is true.

NCERT Exemplar Solutions Class 6 – Mathematics – Unit 1: Number System – True or False Questions | Detailed Answers